Science, Faculty of
Physics and Astronomy, Department of
DSpace
UBCV
Fordyce, Jordan A. M.
Master of Science - MSc
University of British Columbia
The feasibility of using rotating molecules as “nanoprobes” for testing the superfluidity of helium nanodroplets is explored in this thesis. Helium nanodroplets have an internal temperature of 0.37 K and are below the superfluid transition temperature in bulk helium of 2.17 K. The onset of superfluidity in this microscopic environment will be explored by rotationally exciting molecules using a tool called an optical centrifuge. This tool affords a high degree of precision in the final rotational frequency that the molecule will reach and makes it useful in probing the coupling between the rotor and helium. A unique helium nanodroplet vacuum chamber system was characterized for the range of operation possible, especially with focus on the signal to background detection conditions. Two techniques were explored to characterize the dynamical rotational behaviour of the molecules in these conditions: direct measurement of the molecular orientation and direct measurement of the angular momentum state. The molecular orientation of a molecule is characterized by it’s confinement to the rotational plane using ⟨cos² θ2D⟩ as the metric. A ⟨cos² θ2D⟩ measurement of ≈ 0.7 was successfully recovered from background for carbon disulfide doped helium droplets using an alignment probe pulse, however, with the centrifuge it was ultimately unclear if the molecule was rotating or simply aligning to the plane of rotation. The angular momenta of a molecule was characterized via its ion signal from a Resonance Enhanced Multiphoton Ionization (REMPI) scheme. The feasibility of measuring a transition in oxygen at the low signal to background densities was studied and would be promising to use with oxygen doped helium droplets. In order to continue the research, improvements need to be made to the set up and the two techniques should be used in tandem so that rotation can be better detected and characterized.
TOWARDS ROTATIONAL CONTROL OFMOLECULES IN HELIUM NANODROPLETSbyJordan A. M. FordyceB.Sc., University of Alberta, 2015A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Physics)The University of British Columbia(Vancouver)June 2020c© Jordan A. M. Fordyce, 2020The following individuals certify that they have read, and recommend to the Facultyof Graduate and Postdoctoral Studies for acceptance, the thesis entitled:TOWARDSROTATIONALCONTROLOFMOLECULES INHELIUMNANODROPLETSsubmitted by Jordan A. M. Fordyce in partial fulfillment of the requirements forthe degree of Master of Science in Physics.Examining Committee:Dr. Valery Milner, PhysicsSupervisorDr. Takamasa Momose, ChemistrySupervisory Committee MemberiiAbstractThe feasibility of using rotating molecules as “nanoprobes” for testing the superflu-idity of helium nanodroplets is explored in this thesis. Helium nanodroplets have aninternal temperature of 0.37 K and are below the superfluid transition temperature inbulk helium of 2.17 K. The onset of superfluidity in this microscopic environmentwill be explored by rotationally exciting molecules using a tool called an optical cen-trifuge. This tool affords a high degree of precision in the final rotational frequencythat the molecule will reach and makes it useful in probing the coupling betweenthe rotor and helium. A unique helium nanodroplet vacuum chamber system wascharacterized for the range of operation possible, especially with focus on the signalto background detection conditions. Two techniques were explored to characterizethe dynamical rotational behaviour of the molecules in these conditions: directmeasurement of the molecular orientation and direct measurement of the angularmomentum state. The molecular orientation of a molecule is characterized by it’sconfinement to the rotational plane using 〈cos2 θ2D〉 as the metric. A 〈cos2 θ2D〉measurement of ≈ 0.7 was successfully recovered from background for carbondisulfide doped helium droplets using an alignment probe pulse, however, with thecentrifuge it was ultimately unclear if the molecule was rotating or simply aligningto the plane of rotation. The angular momenta of a molecule was characterized viaits ion signal from a Resonance Enhanced Multiphoton Ionization (REMPI) scheme.The feasibility of measuring a transition in oxygen at the low signal to backgrounddensities was studied and would be promising to use with oxygen doped heliumdroplets. In order to continue the research, improvements need to be made to the setup and the two techniques should be used in tandem so that rotation can be betterdetected and characterized.iiiLay SummaryHelium is a substance that is known to have superfluid properties at very lowtemperatures which means that it behaves like a fluid that creates no resistance orfriction to objects moving through it. Helium nanodroplets are small clusters ofhelium atoms (1000 - 10000) that are created in a vacuum chamber. The ultimategoal is to investigate the superfluid properties of these nanodroplets using controlledrotation of a molecule. Using a special tool in our lab called an optical centrifuge,individual molecules that are placed inside of the helium nanodroplets can be setto rotate at frequencies up to 10 THz and be precisely controlled at the frequenciesleading up to this limit. This work details the characterization of the apparatusused to create the helium nanodroplets and the preliminary work on two differenttechniques that can be used to study the rotation in this environment.ivPrefaceThis thesis is based on the characterization of the helium nanodroplet apparatusand data taken for the optical centrifuge experiments that I conducted. The contentof this thesis is not taken directly from previously published or collaborative articles.Chapter 3 is a description of modifications and characterization performed pri-marily by me on the vacuum chamber system used to create helium nanodropletsthat was designed and built by previous students. Chapter 4 includes calibrationand detection imaging techniques that I learned from other groups subsequentlyimplemented on our unique set up. Chapter 5 includes Monte Carlo simulations thatI created to understand the signal to background conditions and the measurements Imade that support the main lessons learned throughout the thesis.Ian MacPhail-Bartley contributed a lot of the data acquisition software used tocollect the data and he helped make the modifications necessary on the heliumdroplet machine to keep it working properly. A visiting student, Audrey Scog-namiglio, was directly involved in the REMPI detection technique discussed inChapter 4 and 5. She analyzed the spectra to assign the rotational states and wasdirectly involved in collecting the data. Dr. Frank Stienkemeier was a collaboratingpartner involved in characterizing the helium nanodroplet apparatus discussed inChapter 3. Dr. Alexander Milner was always available to help with the equipment,analysis, and for general discussions regarding any part of the project.Dr. Valery Milner supervised the overall project, was always available to offerhelp, and assisted with editing the thesis.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Rotational Excitation Techniques . . . . . . . . . . . . . . . . . . . . 42.1 Eigenfunctions and Eigenvalues of a Rigid Rotor . . . . . . . . . 42.2 Optical Centrifuge . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 Impulsive Alignment . . . . . . . . . . . . . . . . . . . . . . . . 132.4 Optical Set Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Helium Nanodroplets . . . . . . . . . . . . . . . . . . . . . . . . . . 193.1 Droplet Formation . . . . . . . . . . . . . . . . . . . . . . . . . 193.2 Experimental Set up . . . . . . . . . . . . . . . . . . . . . . . . . 21vi3.2.1 Source Chamber . . . . . . . . . . . . . . . . . . . . . . 253.2.2 Hard Drive Shutter . . . . . . . . . . . . . . . . . . . . . 293.2.3 Doping Chamber . . . . . . . . . . . . . . . . . . . . . . 323.2.4 Science Chamber . . . . . . . . . . . . . . . . . . . . . . 353.3 Characterizing a Droplet Beam . . . . . . . . . . . . . . . . . . . 353.4 Molecular Jet Dilution . . . . . . . . . . . . . . . . . . . . . . . 424 Detection Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 444.1 Velocity Map Imaging . . . . . . . . . . . . . . . . . . . . . . . 444.1.1 Velocity Map Imaging Calibration . . . . . . . . . . . . . 474.1.2 Interpretting Ion Images . . . . . . . . . . . . . . . . . . 514.2 Resonance Enhanced Multiphoton Ionization . . . . . . . . . . . 544.2.1 Dye Laser System . . . . . . . . . . . . . . . . . . . . . 545 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 595.1 Direct Measurement of Molecular Orientation . . . . . . . . . . . 595.1.1 Kick Alignment as a Benchmark Experiment . . . . . . . 595.1.2 Planar Alignment with the Optical Centrifuge . . . . . . . 645.2 Direct Measurement of Angular Momenta . . . . . . . . . . . . . 765.2.1 Resonance Enhanced Multiphoton Ionization Spectroscopyof Centrifuged Oxygen . . . . . . . . . . . . . . . . . . . 765.2.2 Measurements Limiting the Signal to Background Ratio . 786 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86viiList of TablesTable 2.1 Molecular information regarding their rotational properties andthe effect of the optical centrifuge (CF) on them. . . . . . . . . 13Table 2.2 Calibration Table Corresponding to Rotational Frequency, Du-ration, and Spectral Settings. Note that the duration needsto be calculated using a factor of pi in the value of β so t =10/(0.31/pi) = 101.3. . . . . . . . . . . . . . . . . . . . . . . 17Table 3.1 List of Turbopumps and Pressure Gauges Used. . . . . . . . . 23Table 3.2 Normal operating pressures when producing droplets with T0=14.5 Kand P0=24 bar. . . . . . . . . . . . . . . . . . . . . . . . . . . 25Table 3.3 Useful electrical diagnostics for shutter. . . . . . . . . . . . . . 32Table 3.4 Ratio of Peaks; comparing our measurements to another experi-ment at 14 K found in [45]. . . . . . . . . . . . . . . . . . . . 40Table 4.1 Detector Specifications. . . . . . . . . . . . . . . . . . . . . . 51Table 5.1 Table describing background subtraction sensitivity and collec-tion time for 95% confidence intervals (p < 0.05 is significant)with respect to a null distribution of 〈cos2 θ2D〉= 0.5. . . . . . 68viiiList of FiguresFigure 2.1 The CF field is a linearly polarized field whose polarizationvector is rotating with a constant angular acceleration and hasan intensity profile that decays. This results in a corkscrewappearance. . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Figure 2.2 An illustration depicting how the circularly polarized fieldscombine to give the linear polarization (top figure) and how thefrequency difference between the two circularly polarized fieldsleads to rotation (bottom). . . . . . . . . . . . . . . . . . . . 9Figure 2.3 Illustration of two-photon Raman transitions that demonstratehow the CF can change the rotational excitation of the moleculewith non-resonant processes via a virtual, intermediate state. . 12Figure 2.4 CF optical shaper illustrating gratings (GR), lenses (L), andmirrors (M,R) that are set up to produce the two CF arms Inset:Truncation and cutting prisms used to modify the CF pulse.Adapted from [31] and [23]. . . . . . . . . . . . . . . . . . . 15Figure 2.5 Centrifuge field profile in various configurations used duringexperiments. . . . . . . . . . . . . . . . . . . . . . . . . . . 16Figure 2.6 CF and probe beam alignment. The CF is ≈10 µm while theprobe is ≈5 µm. . . . . . . . . . . . . . . . . . . . . . . . . . 18Figure 3.1 Mean size of helium nanodroplets based on different operatingconditions controlled by P0, the backing pressure, and T0, thenozzle temperature. Adapted from [44]. . . . . . . . . . . . . 20ixFigure 3.2 Pick up statistics for 1, 2, and 3 molecules. One point of interestis when the doping pressure, PD = 9.8∗10−7torr, because thisis the chamber pressure required to begin picking up 2 CS2molecules. This point is shown with the purple dotted line andthere is a 21% probability of picking up 2 molecules. . . . . . 22Figure 3.3 Nested vacuum chamber configuration of the droplet machine.Apparatus was designed and assembled for high density molec-ular jet experiments. Left to right: Source Chamber, DopingChamber, Science Chamber. . . . . . . . . . . . . . . . . . . 23Figure 3.4 Cold head manipulator. The ConFlat flange that contains theO-ring is marked in oragne, the adjustment bolts are markedin red, the square that moves the cold head is marked in green,and the rails installed that pull the ConFlat flange off of thechamber to open the source chamber is marked in grey. . . . . 25Figure 3.5 Nozzle mounted on the rail, with resistor and temperature sensorattached. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Figure 3.6 Left: Shutter mounted in the source chamber in front of theskimmer. Right: Shutter mounted to be tested with a HeNelaser beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Figure 3.7 Normal Operations of Shutter seen by observing the M/Q = 4partial pressure on the RGA. . . . . . . . . . . . . . . . . . . 32Figure 3.8 Skimmer, doping line, and holder assembled on outside ofsource chamber. . . . . . . . . . . . . . . . . . . . . . . . . . 33Figure 3.9 The effective doping “cell”. The gas line is inserted in theend of the skimmer holder and the doping gas can fill the pathmarked by the blue area. The droplets can collide with it on thepath marked in red and pick up molecules. . . . . . . . . . . . 34Figure 3.10 Left: Chamber Pressure Cool down Curves Right: RGA Pres-sure Cool down Curves. . . . . . . . . . . . . . . . . . . . . 36Figure 3.11 Comparison of our RGA Partial Pressures (normalized) with thedroplet signature seen in other chambers, shown in the lowestpanel. Adapted from [8]. . . . . . . . . . . . . . . . . . . . . 38xFigure 3.12 The effect of changing the backing pressure on the cool downcurve. The effect is a change in the coldest temperature thatcan be reached in the system. Pushing this system to operate atcolder nozzle temperatures results in producing larger heliumdroplets and a larger pressure load in the source chamber. Weare at the limit of throttling the turbo pump and it can be seenthat the beam starts to be destroyed with the jumps down inpressure for P0 = 20 and 24 bar. . . . . . . . . . . . . . . . . 39Figure 3.13 Partial Clog of Skimmer: the shutter switched from beam on tobeam off at 72.5 min and remains off. We do not observe theanticipated square wave. . . . . . . . . . . . . . . . . . . . . 40Figure 3.14 Droplet signal TOF for various probe energies. . . . . . . . . 41Figure 3.15 CS2 Dimer Doping 13.6 K at PD = 1∗10−6 torr. . . . . . . . 41Figure 4.1 velocity map imaging (VMI) Configuration. . . . . . . . . . . 46Figure 4.2 N+ ion distribution for a probe polarized perpendicular to theTOF path. The circle had a radius of 250 pixels. The ions werecreated by ionizing a jet of N2 expanded at 20 bar with the fsprobe set to an intensity of 2.1∗1015Wcm−2 and the VMI setat VR = 4500 V, VE = 3230 V, VMCP = 800 V and the PhosphorScreen = 4300 V. . . . . . . . . . . . . . . . . . . . . . . . . 48Figure 4.3 Determining the scaling in eV/pixel2 for CS2 dimers. . . . . . 50Figure 4.4 The shift of the jet with respect to the background. . . . . . . 52Figure 4.5 Illustration depicting the angle important in quantifying howmuch the molecule is squeezed into the plane of the centrifuge.For high J states, the molecule is squeezed into a line so thatthat θ2D→ 0,pi . . . . . . . . . . . . . . . . . . . . . . . . . . 53Figure 4.6 CF and (2+1)resonance enhanced multiphoton ionization (REMPI)excitation scheme of Oxygen. . . . . . . . . . . . . . . . . . 55Figure 4.7 The timing diagram that shows how the YAG laser is triggeredwith respect to the Legend laser. . . . . . . . . . . . . . . . . 56Figure 4.8 Output beam profile of the Sirah at the UHV chamber withouta telescope left and in far field with the telescope right. . . . . 57xiFigure 5.1 An illustrative sketch of the dynamics of CS2 doped heliumnanodroplets found in [10] in comparison to their gas phasekick dynamics found in [27]. This highlights how the helium in-teractions change the response of the rotor to the kick alignmentpulse. The gas phase CS2 molecules go through alignment/anti-alignment peaks and show characteristic half and full revivalsat 76.5ps and 152.9ps, respectively, whereas the response ofthe CS2 doped helium droplets look like an exponentially de-caying sinusoid with a period that is less than the half revivaltime. The difference in the dynamics will be extremely usefulin distinguishing the background (gas phase, revivals) to thesignal (droplet, oscillations) response. . . . . . . . . . . . . . 61Figure 5.2 Left: Non adiabatic alignment of CS2 showing the initial align-ment along with the half and full revivals. This was collectedfrom a seeded CS2:He jet expanded from 30 bar, gating theMCP to 25 ns around S+, and the VMI set at VR = 4500 V, VE= 3230 V, VMCP = 815 V and the Phosphor Screen = 4300 V.The ions were excited by a pump pulse with a fluence of12 Jcm−2 (ω0 = 6 µm) and ionized with a probe of intensity7.2∗1014Wcm−2 (ω0 = 6 µm, τ = 90 fs Gaussian pulse). Right:Non-adiabatic alignment of N+ showing the behaviour up totwo full revivals from the initial alignment. This was collectedfrom a pure N2 jet expanded from 20 bar, gating the MCP to20 ns around N+, and the VMI set at VR = 4500 V, VE = 3230 V,VMCP = 815 V and the Phosphor Screen = 4300 V. The ionswere excited by a pump pulse with a fluence of 7 Jcm−2 (ω0 =6 µm) and ionized with a probe of intensity 1.2∗1015Wcm−2(ω0 = 6 µm, τ = 90 fs Gaussian pulse). . . . . . . . . . . . . . 63xiiFigure 5.3 Non-adiabatic alignment of CS2 using a 15 ps and 90 fs pulse.The collection parameters for the fs pulse are the same as inFigure 5.2. For the ps pulse, the VMI collection parameters arethe same but the jet was expanded at 20 bar and the fluencewas increased to 36 Jcm−2 (ω0 = 8 µm) to try and increasethe maximum alignment. The probe intensity was set to 2.9∗1015Wcm−2. . . . . . . . . . . . . . . . . . . . . . . . . . . 64Figure 5.4 Simulating an Ion Image. The import parameters is the angularwidth and rotational energy of the rotating ions created. Thiswill directly change 〈cos2 θ2D〉 measured. Another importantparameter is the separation of the signal and the background dueto the difference of velocities. Seeded jets travel at 1500 ms−1and droplet beams travel at 200 ms−1 to 400 ms−1. . . . . . . 67Figure 5.5 Left: The image subtraction results for 1 hour of measurements(30 minutes per pump/probe delay) and for 3 hours of measure-ments (1.5 hours per pump/probe delay). Right: The accuracy(or percent difference) between the measured value and thetrue value. 10% difference would need error bars of 0.06 and0.09 for 0.570 and 0.864 to cover the difference of means. Aswell, the measurements capture the true value better for the3 hr measurements (red and pink points) except for the 3 hrmeasurement with low signal to background (S:B). See belowfor discussion. . . . . . . . . . . . . . . . . . . . . . . . . . 70xiiiFigure 5.6 Image subtraction technique used to extract the signal. Left toright: Beam On = Doped droplets and background, Beam off =background, BS = Beam On - Beam Off. The red rings indicatethe region considered for measuring 〈cos2 θ2D〉 and correspondto the energy range 0.5 eV to 2.5 eV, which was chosen becausehelium droplets shifted the kinetic energies to lower values, orthe center of the image. In BS, 〈cos2 θ2D〉 = 0.651± 0.005and in Beam On/Beam Off 〈cos2 θ2D〉= 0.73. In contrast, thepurple rings show the typical region measured for a seededmolecular jet experiment and correspond to an energy rangeof 6.3 eV to 8.3 eV. There were much fewer counts in the BSimage, and 〈cos2 θ2D〉= 0.66±0.03. . . . . . . . . . . . . . 71Figure 5.7 Example of the anisotropic effect that the broken CF has incomparison to the working CF in a molecular jet experimentof O2 expanded at 20 bar. In molecular jet experiments, weknow that the CF is working to spin molecules because thereis a lasting effect past ≈100 ps, but at the beginning between0 ps to 20 ps it is difficult to distinguish. Collected with thefull, untruncated CF set to 1.3 ∗ 1013Wcm−2 (average energy2.1 mJ) and the probe set to 2.3∗1015Wcm−2 and VMI settingsfor O+ at VR =4500 V. . . . . . . . . . . . . . . . . . . . . . 72xivFigure 5.8 Droplet Measurements with Centrifuge. The difference in thedroplet vs no droplet curves agrees with the conclusion fromFigure 5.6 - we are successfully extracting a signal. However,if the signal disappears we wouldn’t be sensitive to this inthese measurements. These experiments were done for dropletconditions of TN =15 K and P0 =24 bar. The doping was setso that the CS2+ signal counted 2 ions/frame with a probepolarized perpendicular to the TOF axis with an intensity of2.9∗1015 Wcm−2(the ion gauge was broken). The CF was setto the 6 nm/arm settings from Table 2.2 with an average energyof 0.5 mJ. The probe was polarized parallel to the TOF axis andhad an intensity of 2.9∗1015 Wcm−2. The VMI settings wereVR = 4500 V, VE = 3230 V, VMCP = 850 V and the PhosphorScreen = 4300 V. . . . . . . . . . . . . . . . . . . . . . . . . 74Figure 5.9 A dissection of the results plotted in Figure 5.8 for the 30 psCF. Left: Variance of the data in one day over subsequent datacollection runs. Right: Variance of the data day to day. . . . . 75Figure 5.10 Reproducing a slice of the 2D Spectrogram in [24]. The ionsignal was measured as a function of the nanosecond probewavelength for the CF truncated to 6 nm/arm and without theCF. These scans were measured with an average energy ofthe nanosecond probe set to 500 µJ at 287 nm and the averageenergy of the CF was 0.76 mJ. The MCP was gated for O+signal was collected with 100 averages of images taken with30 ms of exposure time. VR = 4500 V, VE = 3230 V, VMCP =800 V and the Phosphor Screen = 4300 V. . . . . . . . . . . . 78Figure 5.11 Cold Oxygen, 10 K in blue, vs Warm Oxygen, 298 K in red.Ionization signal from the nanosecond probe only set to an en-ergy of 500 µJ at 287 nm. The cold distribution is from 20 barexpansion of pure O2 and the warm distribution is from adding3.32∗10−7torr O2 to the science chamber via the doping cham-ber. VR = 4500 V, VE = 3230 V, VMCP = 1000 V and the Phos-phor Screen = 4300 V. . . . . . . . . . . . . . . . . . . . . . 80xvFigure 5.12 A peak counting experiment observing the ion signal the CF+probetruncated to 7 nm/arm (≈ 38}) as a function of decreasing O2density and the probe was set to λ =285.26 nm. A total of 1500frames (at 50 Hz, ¡1 min of collection time) were collected foreach data point and the MCP was gated to observe the O2+. VR= 4500 V, VE = 3230 V, VMCP = 800 V and the Phosphor Screen= 4300 V. The diluted gas was expanded through the nozzle atroom temperature with P0=20 bar. . . . . . . . . . . . . . . . 81Figure 5.13 Using the nanosecond probe only, the transitions were investi-gated by lowering the signal density and added background gas.Our detection set up was sensitive enough to capture a smallsignal 0.0007 times lower than a pure molecular jet. . . . . . . 83xviGlossaryCE Coulomb energyCF optical centrifugeFWHM full with half maxRE rotational energyREMPI resonance enhanced multiphoton ionizationS:B signal to backgroundSMI spatial map imagingTE total energyVMI velocity map imagingxviiAcknowledgmentsI would like to express my gratitude to my supervisor Dr. Valery Milner for su-pervising and supporting my research. I learned a great deal from my time inhis lab and the project would not have progressed to the stage it did without hisguidance. I would like to thank Dr. Alexander Milner for sharing his lab spacewith me, instilling his good lab habits in me, and for always being open to physicsdiscussions. I would also like to thank Dr. Frank Stienkemeier for welcoming me tohis lab in Freiburg and helping me gain confidence as a scientist - your support andwisdom was invaluable.I am extremely grateful to have been able to work with everyone that was a partof the lab, but especially Ian MacPhail-Bartley, Walter Wasserman, and AudreyScognamiglio. Your daily contributions made all of my work possible and youhelped keep morale in the lab high. I look forward to seeing the scientists youbecome at the end of your projects! Audrey, in addition to the science you alsohelped me through so many tough moments. Thank you for being so consistentlydependable and going for all of the coffee and cigarette breaks I needed.I would also like to thank all my Van City ”frandz” who are probably only going toread the Acknowledgements part of my thesis to make sure they are referenced -you know who you are. I appreciate the support you’ve given me and you’ve mademy time in Vancouver truly enjoyable.Finally, I would like to thank my family for their constant support and encour-agement. You made me the type of person who could conquer all of those late nightxviiilab shifts and keep moving forward no matter what challenge was thrown my way. Iwould especially like to thank my mom, Sherry, who I lost along the way but wasthe first to introduce me to math and nurture my creativity.xixChapter 1IntroductionHelium nanodroplets have been an exciting area of research since their introductionin 1992 [43]. They have been used for cryogenic matrix isolation in spectroscopyand as a reactor to synthesize new molecular complexes [25][45]. Studying theproperties of individual nanodroplets is interesting and challenging as well. Thediscovery of superfluids and Bose-Einstein condensates demonstrate that a singlequantum state can extend it’s properties across macroscopic lengths, for examplebulk 4He has zero viscosity below the liquid phase transition temperature of 2.17 K[1]. While superfluidity in bulk medium is well understood, the onset of super-fluidity in finite, microscopic systems such as clusters and helium nanodroplets isan active area of research. One of the first interesting findings was in the infrared(IR) absorption spectrum of SF6 where the rotational lines were sharp and couldbe fit assuming a free molecular spectrum [15]. However, the line spacing revealedthat the moment of inertia was larger by a factor of 2.8 from a free molecule andwas hypothesized to be due to interactions between the molecule and the liquidhelium environment. A follow up study was done to further test the superfluidnature of the helium nanodroplets and was called a microscopic Andronikashviliexperiment, by embedding OCS inside of 4He and 3He nanodroplets [17]. 4Henanodroplets have an internal temperature of 0.37 K and are in the superfluid regimebut 3He nanodroplets have an internal temperature of 0.15 K and are well abovetheir superfluid transitional temperature of 3 mK. This allowed the IR spectrum ofOCS to be observed in a normal fluid and in a superfluid while both were still cold,1microscopic environments. The study showed that OCS could freely rotate in 4Hebut not in 3He because the lines were sharp for 4He and pronounced but a large,broad peak was seen for 3He. However, the spacing was, again, different from a freemolecule by about a factor of 3. This increased moment of inertia suggested thatthere could be local non-superfluid layers still existing [28] and that it depended onthe anisotropy of the molecule.Recently, understanding this polyatomic impurity problem with the quasiparti-cle approach typical in condensed matter physics has been employed and has beenhaving success [30][10][40]. A quasiparticle describes microscopic interactions in acomplicated environment as if they were the interaction between different particles.This approach introduces an “angulon” which describes the molecular rotor dressedby phonon interactions from the helium nanodroplets. This is done to simplifythe computational demand that would be required to consider all the degrees offreedom in the problem. The scaling of the moment of inertia seen in the previouslymentioned experiments, or “renormalization” of the rotational constant, can beexplained from the strength of the interaction between the molecule and the heliumbath [29]. In the strong coupling limit, generally describing heavy rotors where theinteractions with the helium atoms happen to be strong, a nonsuperfluid helium shellrotates along with a slowly moving molecule. This regime predicts a decrease inthe rotational constant on the order of a factor of 3 for molecules like OCS, SF6, orCS2 as expected from experiment. In the weak coupling limit, generally describingthe light rotors, renormalization occurs due to a slightly different process and therotational levels are shifted due to virtual phonon absorption. This regime predictsless of a decrease in the rotational constant, and rotors like C2H2 are barely shiftedfrom their free molecule rotational constant.Studying the dependence of superfluid behaviour on the rotational excitation couldbe a way to gain more insight into the quantum effects in this environment. In orderto achieve that degree of control, an optical centrifuge (CF) was proposed to rotatethe molecules. An CF is a combination of shaped laser pulses that results in a uni-directional, rotating polarization vector that can accelerate molecules to rotationalfrequencies of up to 10 THz [22]. It has been used to study molecular dynamics2and properties at extreme levels of rotational excitation and has a degree of controlover the excitation unknown to other techniques [31][33]. This degree of controlallows us to use molecular rotors as “nano-probes” to investigate the conditionsfor superfluidity in nanodroplets. The CF would also allow the behaviour to bestudied at rotational speeds that could probe a microscopic analogue to Landau’scritical velocity [5]. This critical velocity describes the speed at which helium canmove and still behave as a superfluid. The dispersion curve of helium reveals thatsuperfluidity will only exist if an object is moving below 58 ms−1. This velocityregime translates into rotational speeds on the order of 1 THz, depending on themolecule, and with the precise control over the final rotational frequency achievedusing the CF it could be studied.This work presents two different techniques that can be used to study the superfluidproperties of helium nanodroplets. A helium nanodroplet vacuum system wasbuilt and characterized for the first time in our lab. After excitation with the CF,the molecules’ orientation could be imaged to observe energy dissipation. It isimportant to implement background subtraction techniques as the density of anyhelium nanodroplet beam is low, especially in comparison to the high backgroundin our system not normally seen. As well, the spectra of the molecules could bemeasured to quantify the strength of the helium interactions using resonant ioniza-tion techniques. The thesis explains the fundamentals of the rotational excitationscheme, the fundamentals of helium nanodroplet production and important methodsfor characterization, the detection techniques implemented, and presents some pre-liminary results with a focus on behaviour in the low signal to background countrate regime. The techniques have been studied extensively with two different linearrotors: CS2 and O2, which are also good candidates for observing differences in theweak and strong coupling regimes in the angulon quasiparticle theory. Extendingthe superfluidity investigation to the high rotational states only possible using the CFwould enable the investigation of a quantum rotational analog to Landau’s criticalvelocity. After this technique is developed, clusters of different atoms could betested for superfluid properties.3Chapter 2Rotational Excitation Techniques2.1 Eigenfunctions and Eigenvalues of a Rigid RotorThe Born Oppenheimer approximation is the assumption that the total wavefunctioncan be separated into electronic and nuclear components:Ψtotal = ψelectronicψnuclear= ψelψvibψrot (2.1)This is a good approximation that is extensively used in molecular physics. Theassumption stems from the difference between nuclear and electronic masses, whichis about a factor of 1000. There is a mutual attractive force of Ze2r2 between an atomicnucleus and an electron which causes the particle to accelerate. Since acceleration isinversely proportional to mass, the electrons experience a much larger accelerationthan the nuclei (by a factor of more than 2000). Therefore, the electrons are movingand responding to forces much faster than the nuclei. Because of this, the electronicpart can be solved ignoring the nuclear kinetic energy and then used for subsequentcomputations involving the nuclear terms.Following the derivation in [2], we can find the eigenvalues and eigenfunctions fora diatomic molecule to understand some fundamental behaviour. The Hamiltonianis broken up into the nuclear term, the electronic term, and the term representing4Coulomb repulsion of the two nuclei:H(r,R) = Hnuc(R)+e24piε0ZAZBR+Helec(r,R) (2.2)Hnuc(R) =− }22MA∇2A−}22MB∇2B (2.3)Helec(r,R) =−}22m ∑i∇2i +e24piε0(−∑iZArAi−∑iZBrBi+12∑i ∑j 6=i1ri j)(2.4)The Hamiltonian for the electrons includes their attraction for the nuclei and mutualrepulsion, respectively. Note, lower case symbols are used to describe electrons andupper case symbols are used for nuclei.In molecular spectroscopy, the Born Oppenheimer approximation is extended to theelectronic, vibrational, and rotational energies because the ratios are related to eachother on scales on the order of a thousand. So the energy is written as:Etotal = Eelectronic+Evibrational +Erotational +Enuclear (2.5)For a sense of scale, note that pure vibrational transitions are studied using infraredradiation (GHz), whereas pure rotational transitions are studied using microwaveradiation (MHz).The rigid rotor is a very simple system that can be used to describe rotating diatomicmolecules. This model is too restrictive to be extremely accurate, but one can stillgain a lot of insight into the dynamics of the system. Consider a collection of nucleiof mass mα located at positions rα relative to the origin and rotating with angularvelocity ω . The angular momentum can be written as:L =∑αrα ×pα= Iω (2.6)where I is the moment of inertia. The molecular coordinate system can always bechosen such that the matrix I is diagonal - this is called the principal axis system.5These matrix elements are:Ix =∑αmα(y2α + z2α) =∑αmαr2x⊥Iy =∑αmα(x2α + z2α) =∑αmαr2y⊥ (2.7)Iz =∑αmα(x2α + y2α) =∑αmαr2z⊥Now the angular momentum expression is very simple:LxLyLz=Ix 0 00 Iy 00 0 Izωxωyωz (2.8)as is the expression for kinetic energy:Ek =12Iω2=L2x2Ix+L2y2Iy+L2z2Iz(2.9)For a rigid, linear rotor that has no net orbital and spin angular moment this is theclassical expression for the rotational kinetic energy. If we align the molecule so thebond is along the z-axis and put the moment of inertia at the origin, Iz = 0, Ix = Iy = I.For a diatomic, I = µr2 where µ is the reduced mass:µ =mAmBmA+mB(2.10)Letting J be the total angular momentum, without nuclear spin, then the Hamiltonianoperator is:Hˆ =Jˆ22I(2.11)Since we already know the eigenfunctions of the angular momentum operator fromother systems such as the Hydrogen atom, we know that ψrot is described by the6spherical harmonics Y ml .Y ml (θ ,φ) = NeimφPml (cosθ) (2.12)where N is a normalization constant and Pml is an associated Legrendre polynomial.Now we can solve for the energy eigenvalues:Jˆ22Iψ = EψJ(J+1)}22Iψ = BJ(J+1)ψ (2.13)where we have rewritten the energy eigenvalue, Erot(J), as BJ(J+1) with B as therotational constant (in J):B =}22I=h28pi2I(2.14)But, the conventional way to express B is in cm−1. Using E = hcλ = 100hcν¯ :B[cm−1] =10−2h28pi2cI(2.15)where c is the speed of light in ms−1 and λ is the wavelength in m. It is importantto take into account centrifugal distortion since the centrifuge can populate suchhigh J states that even a rigid rotors’ bonds soften and we add a correction term toeffectively decrease the value of B:E(J) = BJ(J+1)−DJ2(J+1)2 (2.16)where D is the centrifugal distortion constant.2.2 Optical CentrifugeThe CF is an intense, non-resonant field that is used to optically control the rotationof anisotropic molecules. This anisotropy refers to the polarizability of a molecule,or it’s ability to form a dipole in the presence of an electric field. This term is reallya symmetric tensor, but since we consider linear molecules that have cylindricalsymmetry, we can express it in terms of it’s polarizability with respect to molecular7symmetry axes: α‖−α⊥. For linear molecules, αxx = αyy = α⊥ and αzz = α‖.Molecules that have α‖ > α⊥ align to the polarization of the electric field[4].At a high level, the CF is the interference of two shaped pulses that result in aunidirectionally rotating polarization vector, in the shape of a corkscrew like inFigure 2.1.Figure 2.1: The CF field is a linearly polarized field whose polarization vectoris rotating with a constant angular acceleration and has an intensityprofile that decays. This results in a corkscrew appearance.To see what that looks like mathematically, we can review the polarization of fieldsas presented in [3]. First consider a plane wave, propagating in the negative zdirection. It can be broken up into it’s instantaneous x and y counterparts by:E˜(z, t) = E˜x(z, t)xˆ+ E˜y(z, t)yˆ)E˜x = Re[Exei(ωt+kz+ηx)] = Ex cos(ωt+ kz+ηx) (2.17)E˜y = Re[Eyei(ωt+kz+ηy)] = Ey cos(ωt+ kz+ηy) (2.18)where Ex and Ey are the maximum magnitudes. If ηy−ηx is an integer multiple ofpi , the field is linearly polarized. If the two components have the same amplitude,Ex = Ey = E0, and the time phase difference are odd multiples of pi/2 - ηy−ηx =±pi2 , and the resultant electric field would rotate in the xy plane. Right versus leftcircularly polarized light means that the electric field is rotating clockwise or counter8clockwise, respectively, as seen by the observer. This field would be described by:E˜ = E0(cos(ωt)xˆ± sin(ωt)yˆ (2.19)If we take a superposition of right and left (±yˆ terms) circularly polarized light withequal amplitude, we would recover linearly polarized light:E˜R+ E˜L = 2E0 cos(ωt)xˆ (2.20)This is illustrated in Figure 2.2 in the top panel.In the CF, the two constituent beams are rotating in opposite directions we will alsoFigure 2.2: An illustration depicting how the circularly polarized fields com-bine to give the linear polarization (top figure) and how the frequencydifference between the two circularly polarized fields leads to rotation(bottom).add an offset in the carrier phase, which we will call ±Ω [31]. These beams would9be written as:~ER =E02(cos[(ω+Ω)t]xˆ+ sin[(ω+Ω)t]yˆ)~EL =E02(cos[(ω−Ω)t]xˆ− sin[(ω−Ω)t]yˆ) (2.21)When these fields are superimposed, the result is a linearly polarized field thatrotates with constant frequency Ω:~ECF = ~ER+~EL = E0 cos(ωt)(cos(Ωt)xˆ+ sin(Ωt)yˆ)(2.22)The time averaged coupling energy a diatomic molecule experiences in a linearlypolarized field is given by [14]:V =−V0 cos2 θ =−14(α‖−α⊥)E2CF cos2 θ (2.23)where θ is the angle between the molecular axis and the laser polarization vector.Equation 2.23 shows that a molecule perfectly perpendicular to the electric fieldwill not feel the field because of the cos2 θ term. It also shows that the potentialenergy is minimized when θ = 0 and the molecule is aligned to the polarizationvector. In order to align the molecule to the polarization vector, the electric fieldproduces a torque which accelerates the molecule with amol , following [4] and [31].The torque is the first derivative of Equation 2.23 with respect to θ in the directiontowards θ = 0,pi:τ = Iamol = |dUdθ |=V0 sin2θ (2.24)where τ is the torque which goes to 0 when sin2θ = 0 and this occurs at θ = 0,pi(the bottom of the potential well in Equation 2.23). Finally, we have the averageangular acceleration imparted to the molecule:amol =τI≈ 2V0Ipi(2.25)Returning to Equation 2.22, the molecule will align and follow the rotating polar-ization vector if the acceleration of the CF, aCF is slow enough for the molecule tokeep up, i.e. aCF < amol . This means the field cannot start rotating suddenly, as in10Equation 2.22, but must start gradually before beginning the acceleration. In orderto achieve this, there must be time dependent terms in angular speed, since aCF = Ω˙.A constant acceleration can be achieved by having the frequency difference of thetwo fields increasing linearly with time. This is linearly chirping the pulses andadds a quadratic phase factor in the electric field expression. In our case we needthe pulses to be linearly chirped in opposite directions, so the fields have quadraticphase factors with opposite signs with respect to one another:~ER =E02(cos[ωt+βRt2]xˆ+ sin[ωt+βRt2]yˆ)~EL =E02(cos[ωt−βLt2]xˆ− sin[ωt−βLt2]yˆ)(2.26)Now when we add the fields, the instantaneous angular speed and acceleration aregiven by the average chirp rate, β = 12(βR+(−βL)):Ω(t) = 2β tamol = 2β (2.27)The combined effects of the frequency difference and the counter-rotating circularlypolarized pulses leading to a unidirectionally rotating field is illustrated in the bot-tom panel of Figure. 2.2. We call each of the constituent fields of the CF the “arms”of the CF. From classical mechanics, we know the kinetic energy of a rigid body isgiven by Equation 2.9 and so T = 12 IΩ(t)2. As long as the molecule is following therotating laser field, the rotational energy will increase as the frequency differencebetween the two interfering fields increases in this classical picture. The power ofthe centrifuge lies in the degree of control in the rotational excitation. To understandthat, we must return to the quantum mechanical description of molecular rotationfrom Section 2.1 and see how the CF can excite the discretized angular momentumstates.The spectrum of angular momentum states described by Equation 2.16 form aladder that the non-resonant CF “walks up” via two-photon Raman transitions andthis is illustrated in Figure 2.3. The photon from one of the arms of the CF excitesthe molecule into a virtual, intermediate state and almost immediately another pho-11Figure 2.3: Illustration of two-photon Raman transitions that demonstratehow the CF can change the rotational excitation of the molecule withnon-resonant processes via a virtual, intermediate state.ton, from the other arm of the CF, stimulates the molecule back into a lower state.However now the molecule is in a higher rotational state, ∆J =±2, than before theinitial photon.When the initial photon is absorbed and has, say, right hand circular polariza-tion, it increases J by 1 and M by 1 to conserve angular momentum since a photonhas spin 1. The next photon with left hand circular polarization causes emissionfrom this virtual state and increases J by 1 again and causes M to lose -1 and thefinal state is |J+2,M+2〉. Another way of understanding this increase of 2 isbecause the polarizability returns to its original position twice for each cycle of therotating field because there is a factor of 2 between the molecular rotation and theinduced dipole. The selection rules for the CF are then ∆J =±2 and ∆M =±2.Assuming the intensity of the centrifuge field is 1013Wcm−2, the well depth fromEquation 2.23 can be calculated for the molecule’s shown in Table. 2.112Molecule ∆α (A˚3) |U0| (K) B (cm−1)N2 0.68 51.6 1.99O2 1.07 81.3 1.44CS2 8.5 646 0.11Table 2.1: Molecular information regarding their rotational properties and theeffect of the CF on them.2.3 Impulsive AlignmentAn impulsive perturbation to a molecule is a kick pulse which means that it hasa duration much shorter than the ground state rotational period of the molecule,τ < τrot = pi}B [41]. We work with Gaussian femtosecond pulses to achieve thisfor light diatomic molecules, so the envelope of the field can be described byEK = E0e−t2/2σ2 . These molecules will feel a strong torque towards the polarizationdirection of the pulse, where the interaction potential is the same as in Equation 2.23but with ~ECF replaced with the kick pulse field. The torque is still described byEquation 2.24, and from that expression we can see that amol is proportional tosin2θ . Using the small angle approximation we can say that when θ << 1, amolwill be proportional to θ . This means that an ensemble of velocities is created withthe excitation and, though the molecules will simultaneously reach θ = 0,pi , theywill continue to rotate after the pulse leaves.The wavefunctions for a kicked linear rotor are also the spherical harmonics, Equa-tion 2.12. For a linearly polarized kick pulse, the selection rules are ∆M = 0 and∆J = 0,±2. Here, M is unchanged whereas for the CF ∆M = ±2 because of thecircularly polarized fields. Since rigid rotors are described by the discrete spectra ofEquation 2.16, the ensemble of velocities created from the impulsive perturbationforms a wave packet over the rotational states. The number of rotational J states13populated is proportional to the kick strength, P in units of } [4]:P =∆α4}∫E2(t)dt (2.28)which holds if the field is below the ionization limit of the molecule. If we solve theintegral for our Gaussian field, then the equation for P simplifies to P= δα4} E20√piσ .Another effect of the discrete rotational spectra is the periodic dynamics of thewave packet. There is a quantum revival effect that is proportional to the secondderivative of Equation 2.16. So the full revival time for a linear, rigid rotor is givenby:Trev =12cB(2.29)assuming there is negligible centrifugal distortion and with B in cm−1. At higherJ states, this term should be included. The revival time is one of the most usefulparameters for detecting and optimizing the effect because it occurs after the fieldsare no longer interacting with the system.2.4 Optical Set UpThe laser system used to perform the CF pump probe experiments was a commer-ical femtosecond laser from Coherent. The Titanium Sapphire oscillator (Micra)generated broad 80 nm full with half max (FWHM) pulses centered at 800 nm with arepetition rate of 80 MHz. These pulses only have an energy of 5 nJ and are used toseed a Titanium Sapphire amplifier (Legend Elite Duo) that has two stages: a re-generative amplifier and a single pass amplifier. After amplification, the bandwidthdecreases to≈30 nm and the repetition rate is 1 kHz. The output power is optimizedfor 10 W and the pulses had a duration of ≈120 ps. Details can be found in [23].The CF shaper is built according to the proposal from Corkum’s group back inthe late 90s [22] and is described in detail by our group in [31]. It is based ona common 4f geometry that allows the input beam to be split into components,spectrally, and allows pulses to be arbitrarily shaped in the Fourier transform plane.The 4f geometry is clear in Figure 2.4 from the arrows marked ’f’ as the focal length14of lenses L0 and L±. Stretching is typically done utilizing diffraction gratings (GR)and also implemented here. To do nothing to the pulse, these gratings should be setat the focal length of the lenses (points A,B). We play with these distances (l±) toimpart the appropriate chirp (β ) onto each arm of the centrifuge and when thesetwo pulses are combined using a quarter waveplate, the two arms of the CF arethen oppositely circularly polarized and counter rotating. Their interference cre-ates a unidirectionally rotating polarization vector with the profile seen in Figure 2.1.In order to shape the CF further, we place prisms in the focal plane near theFigure 2.4: CF optical shaper illustrating gratings (GR), lenses (L), and mirrors(M,R) that are set up to produce the two CF arms Inset: Truncation andcutting prisms used to modify the CF pulse. Adapted from [31] and [23].half mirror (M) to modify the CF pulse duration and ability to spin molecules. Pre-viously this was done with a shutter[23], but by placing a few prisms on motorizedstages, we have more control over the spectral width and the pulses are preciselyreproducible. As well, the prisms do not get damaged by the high intensity at thefocal spot. The configuration of prisms around the half mirror is depicted in theinset of Figure 2.4, though the distances from the half mirror are not to scale.15Figure 2.5: Centrifuge field profile in various configurations used during ex-periments.The prism that modifies the red (blue) arm of the CF is colored red (blue), andthe one that can move in two directions and modify the red and blue arm indepen-dently is colored with both. Truncating is done when the prism redirects the spectralcomponents from the outside of the pulse away from the beam. This is shown inFigure 2.5 on both the red and blue arms. Truncation of the CF shortens the pulse du-ration and limits the final rotational frequency the pulse will reach. It should be donesymmetrically (the same in both arms) to ensure efficient rotation of the molecule.“Cutting” is done when the prism redirects spectral components from the center ofthe pulse. This is also shown in in Figure 2.5, where there is space in the middle ofthe spectrum. When the CF is cut, the rotational frequency that a molecule sees whenthe field arrives is higher, and molecules can no long be trapped and follow the field.We call this the “broken CF” because we can match the pulse width and energy ofthe field but prevent the molecule from rotating. The purpose of cutting the CF is todiscriminate against alignment effects due to a strong field when looking for rotation.By measuring the FWHM position of the intensity profile of the CF in Figure 2.5,the prisms can be moved to give different final rotational frequencies. The positions16of the prisms and calculation of the frequency, energy, and duration (assumingβ = 0.31 THzps−1 [31]) is shown in Table 2.2. Aligning the CF with the probeSpectrumSettingJ (}) Energy(cm−1)Frequency(THz)Duration(ps)Red(Blue) ArmTerminal λ (nm)Full 118 19238 10 101.3 –(–)10nm/arm 55 4383.1 4.76 48.2 804.5(784.5)8nm/arm 43 2703.4 3.73 37.8 802.5(786.8)6nm/arm 33 1607.3 2.87 29.1 800.6(788.6)4nm/arm 23 792.3 2.08 21.1 798.8(790.0)Table 2.2: Calibration Table Corresponding to Rotational Frequency, Duration,and Spectral Settings. Note that the duration needs to be calculated usinga factor of pi in the value of β so t = 10/(0.31/pi) = 101.3.means aligning three different beams in space and time. The arms of the CF can bealigned independently using the Raman Spectroscopy set up in the lab. Aligningthe CF and probe in time can be done to within 1 ns using a fast photodiode in frontof the chamber and changing mirrors on the translation stage of the probe. Afterthis, the ion signal of S+ from CS2 can be maximized within a narrow mass gatewith sufficient intensities. To begin with, it is best to set the probe to arrive muchlater than the CF to ensure that some planar confinement can be observed and usedto maximize spatial alignment. This is difficult because the 3 beams ultimatelyneed to be aligned to a sphere that has a 10 µm diameter. If the beams are severelymisaligned, it is best to direct them to the far field and reflect them on a wall at theend of the lab. By aligning them to an aperture and to the same spot in the far field,they can be aligned to be quite collinear. Following this, it is best to use a refocusingmirror to simulate the focusing of the beams in the chamber, as shown in Figure 2.6.A pick off mirror is placed in the chamber path and then reflected at an angle offof the refocusing mirror to a CCD camera. The CCD camera is placed at the focalspot of the probe and the CF telescoping optics are adjusted so that it’s focal planeis the same as this point. This is shown on the left of Figure 2.6. The CF focal spot17is the top spot and the probe focal spot is the bottom. Once they overlap on theCCD camera, alignment can be optimized using the planar confinement signal. Thistype of set up is ideal for overlapping two color beams. If only one color is usedthe refocusing mirror can be replaced with an equivalent lens and the camera canbe placed behind this lens. Note that it is important to decrease the intensity usingthings like neutral density filters and not apertures because the apertures can causeaberrations in the focal spot. The reverse is true when trying to overlap the beamsin time because passing through different filtering optics will cause pulse delays.Figure 2.6: CF and probe beam alignment. The CF is ≈10 µm while the probeis ≈5 µm.18Chapter 3Helium Nanodroplets3.1 Droplet FormationMolecules are often cooled via a seeded free jet expansion in order to keep them in agaseous state and to make them easier to study. Free jet, or supersonic, expansion oc-curs when high pressure molecules expand through a small orifice into vacuum[53].This expansion causes the molecules to cool isentropically and even though there isno equilibrium of states we can still describe the process as an adiabatic expansion.This property means there is no flow of heat that occurs between different areas ofthe expansion and that the specific heats of the gas are constant[51]. The isentropicexpansion results in a decrease in the distribution of particle velocities and thus in adecrease of translational temperature, where≈ 1 K is possible without condensation.Two body collisions, still possible despite the decrease in particle density awayfrom the orifice, further cools the internal degrees of freedom of molecules where arotational temperature of a few K is attainable[53].Helium nanodroplets are created by free jet expansion of helium at 20 bar througha 5 µm nozzle cooled to between 10 K to 20 K. The helium gas is pre-cooled inthe nozzle before the final cooling process when it expands into vacuum. Initially,the droplet will not be in thermal equilibrium and if it is produced with excessenergy, that energy will be removed by evaporating helium atoms. The bindingenergy between helium atoms is weak; in bulk it is about 7 K, so the temperature19Figure 3.1: Mean size of helium nanodroplets based on different operatingconditions controlled by P0, the backing pressure, and T0, the nozzletemperature. Adapted from [44].is adjusted in small increments. Experimental measurements show that the steady-state temperature reached after this evaporative cooling is 0.37 K and is reachedin about 0.1 ms after exiting the nozzle. This is interesting because bulk liquid4He undergoes a phase change from liquid to superfluid at 2.18 K, meaning theviscosity approaches zero. Superfluidity is a special property of bosons, thoughthe fermionic isotope, 3He, can pair up to form bosons and become superfluidbelow 3 mK as well. Droplets of fermionic helium have been formed, but thesteady-state temperature reached is 0.15 K and higher than the superfluid phasetransition. 4He is used in order to exploit the superfluid nature of the droplets whenstudying rotation of molecules and is unique to this low temperature matrix. Us-ing 3He is normally done to clearly contrast the effect of superfluidity seen with 4He.The droplet formation regime characterized by a 10 K to 20 K nozzle temperatureis referred to as subcritical expansion since helium is gas phase before clustering.In this regime, the droplets contain about 1000− 10000 helium atoms and havea diameter on the nanometer scale (thus the name “nanodroplets”). The size dis-20tribution has been measured via scattering experiments to be log-normal with theoperating point denoted by the mean droplet size, 〈N〉[21]. In order to change 〈N〉,one only has to change the backing pressure to the nozzle or the nozzle temperature,according to these experimental measurements, shown in Figure 3.1[45], and normaljet scaling factors[18]. The velocities of the nanodroplets formed in the subcriticalregime are expected to lie in the range of 200 ms−1 to 400 ms−1[7][38], with themean of the velocity distribution roughly following a√T0 dependence. The velocitydistributions are typically quite narrow in this range and ∆v/v = 0.02 is typicallyachieved.Molecules are added to the droplets via collisions by adding a gas that fill a differentchamber. This is also called a pick up process which is statistical in nature andcannot allow for the droplet to pick up a specific number of dopant moleculesprecisely. The process is governed by Poisson statistics, with the probability of kmolecules being picked up determined by:Pk =(ρσ l)kk!e−ρσ l (3.1)where ρ is the number density of the pick up molecule in the chamber, σ is thecross sectional area of the droplets σ = 15.5〈N〉2/3A˚, and l is the length of the pickup chamber. Note that this equation uses the mean droplet size, although there isa distribution of sizes, and that when a molecule is picked up it will transfer itsenergy to the droplet and evaporate some helium atoms. As long as the droplets aresufficiently large that it can support the lost of≈ 100 atoms, this equation holds. Themolecules that are studied with the centrifuge reside inside the droplet because offavourable energetics, though some dopants can reside on the surface (like alkalis).3.2 Experimental Set upOur droplet machine was created by using a vacuum chamber originally designed tocreate a dense molecular beam. The chambers were inset to minimize the distancebetween the nozzle and the detection region. In order to turn it into a droplet ma-chine, the nozzle was mounted on a cold head and a gas line was placed in between21Figure 3.2: Pick up statistics for 1, 2, and 3 molecules. One point of interestis when the doping pressure, PD = 9.8 ∗ 10−7torr, because this is thechamber pressure required to begin picking up 2 CS2 molecules. Thispoint is shown with the purple dotted line and there is a 21% probabilityof picking up 2 molecules.the skimmer and the detection region to allow for doping. The set up we usedis depicted in Figure 3.3, but the Residual Gas Analyzer (RGA, SRS 100) that isattached to the end of the Science Chamber is not shown.The three chambers are equipped with the turbomolecular (turbo) pumps and pres-sure gauges listed in Table 3.1. The turbos have their fore-vacuum line pumped byan Edwards dry screw pump (iGX600L) which has a pumping speed of 800 m3 h−1.This pump is placed in a different room and is connected to the pumps via a PVCline with a 4” diameter and 0.1” wall thickness. A stainless steel reinforced PVChose connects the 4” line to the turbos with KF-40 and KF-25 adaptors (1.5” and 1”diameters). This set up can achieve a pressure of about 50 mtorr to 100 mtorr at theback of the turbo pump, depending on the gas load.22Figure 3.3: Nested vacuum chamber configuration of the droplet machine.Apparatus was designed and assembled for high density molecular jetexperiments. Left to right: Source Chamber, Doping Chamber, ScienceChamber.The gas distribution system that connects the tanks and the chamber requires threemain components for droplet operation: a line to pure helium (6.0 grade), a lineto pump (done with a hermetic scroll pump), and a high pressure regulator. Inaddition to those components, we have a line connected to oxygen and to a smallChamberTurboPumpPumpingSpeed (L/s)Pressure GaugePressureRange(Torr)SourceKYKY FF-200/1300E1300MKS 972B ColdCathode/MicroPi-rani TransducerAtmosphere- 10−8DopingPfeifferTMU 260260MKS 500 ColdCathode Gauge10−2 -10−10ScienceEdwardsD3962200075MKS 500 ColdCathode Gauge10−2 -10−10Table 3.1: List of Turbopumps and Pressure Gauges Used.23lecture bottle for seeded gas mixtures in order to perform molecular jet experiments.Many groups do not run any other gas through their nozzle that is used for dropletexperiments because it is difficult to the remove the other gas completely and whencooling to 10 K these gases will freeze and clog the nozzle. We have only had onenozzle clog from this, so switching between gases should be done very carefully.Ideally, the lines are pumped and then helium is run through the system overnightbefore a cool down. Alternatively, a cycle of pumping and purging is done withhelium while monitoring the other gas species and helium partial pressures on theRGA. This cycle is repeated three times over 30 min intervals (30 min of pumping,then 30 min purging with helium for one cycle). There should be no increase of theother gas (oxygen for example) on the RGA.The cold head (Sumitomo 408D2) is mounted onto an adaptor flange that con-tains an O-ring and allows for horizontal and vertical manipulation. This is shown inFigure 3.4. An O-ring in the ConFlat flange is squeezed between the cold head and abrass square (The ConFlat flange is visible in Figure 3.4, but the O-ring is not sinceit is on the vacuum side). Brass is chosen because it will more easily slide acrossthe O-ring and stainless steel flange. A thicker stainless steel square, marked withthe green arrow in Figure 3.4, is bolted on top of this and has large bolts mountedto its four sides. Loosening and tightening these is what causes translation of thecold head and 3 of them are visible in Figure 3.4 and highlighted with red arrows.The brass housing connecting these bolts to the square can be tightened to fix thecold head’s position. The moving parts are made of brass and can actually result inshavings inside the vacuum chamber from rubbing against the stainless steel, butthey have not affected the vacuum or caused other damage. A mount designed toattach to the bottom of the cold head manipulator and allow it to slide on to rails.These are also shown in Figure 3.4 and highlighted with the grey arrow. The railsmade opening the chamber much easier but also allowed the nozzle height to remainfixed when opening the chamber.At normal droplet operations, the chamber pressures are shown in Table 3.224Figure 3.4: Cold head manipulator. The ConFlat flange that contains theO-ring is marked in oragne, the adjustment bolts are marked in red,the square that moves the cold head is marked in green, and the railsinstalled that pull the ConFlat flange off of the chamber to open thesource chamber is marked in grey.Shutter StateSource Chamber(Torr)Doping Cham-ber (Torr)Science Cham-ber (Torr)Beam On 1.2∗10−4 3.4∗10−7 2.2∗10−7Beam Off 1.2∗10−4 6.7∗10−8 1.8∗10−7Table 3.2: Normal operating pressures when producing droplets withT0=14.5 K and P0=24 bar.3.2.1 Source ChamberThe source chamber is where the droplets are produced and is the first chamberon the left in Figure 3.3. It is pumped by a 1300 Ls−1 turbo pump (KYKY FF-200/1300E) and contains the cold head, nozzle, hard drive shutter, and skimmer.25A filter is mounted in between the line and the nozzle to prevent contamination.The nozzle and cryoshield are made of oxygen free copper, which is chosen forit’s thermal conductivity at low temperatures. Important design parameters in thischamber include the nozzle flux, the nozzle skimmer distance, the nozzle shutterdistance, and the pumping speed. As a rule of thumb, the pressure of the sourcechamber when producing droplets should not exceed 1∗10−3 torr in order to avoidextra heat load on the cold head and to avoid throttling the turbo pump. With ournozzle diameter and pumping speed, this indicates a maximum backing pressure ofabout 30 bar before the turbo cannot keep up and the beam is destroyed. At normaldroplet operations of 14.5 K and 24 bar the source chamber pressure is 1.2∗10−4torr.The nozzle was fabricated by a collaborating group at the University of FreiburgFigure 3.5: Nozzle mounted on the rail, with resistor and temperature sensorattached.using SEM apertures (Plano EM, Platinum) allowing for a small hole size of 5 µmand is shown in Figure 3.5. They roll the aperture into the end tube that is weldedinto a square body. This design can tolerate backing pressures of up to 80 bar,though that limit was never tested in our set up since the turbo pump can’t toleratethat gas load. This nozzle is received (and stored) in aluminum foil and a desiccant.Installation is straightforward but tricky because the aperture can be clogged soeasily - even just from the humid room air. It should not be cleaned like most26vacuum parts with a sonication bath in acetone or isopropanol because this will clogthe nozzle. It should be connected to the helium gas line quickly after removal fromthe desiccant in order to get flow running through the hole to decrease the liklihoodthat it clogs. After gas is flowing, it is important to check that the nozzle is workingand this is done by bubbling the output gas through water. Assuming the output ofthe nozzle gives an effusive beam through an ideal aperture, the theoretical flow ratethrough an aperture of this size is 0.011 mLs−1 for 1 bar. Linearly extrapolatingthis to 20 bar, we should measure flow rates around 0.22 mLs−1[35]. This canbe checked by measuring the volume of helium that bubbles through water in aninverted graduated cylinder, for example. Our tolerance for accepting the nozzle iscollecting 10 mL of He in 35 s to 45 s. Even a factor of 2 decrease in this flow ratecan result in a lower intensity, but working, molecular beam and a droplet beam thatis not operational.The nozzle is attached to the cold head on top of a rail. It bolts down alongthe grooves on it’s bottom and it’s position is etched into the rail using a utility knife.It is very important to place the nozzle at the same distance along the rail becauseof the potential for beam destruction. Some variance in the angle of the nozzlecan be compensated for with the cold head manipulator. On the nozzle’s side a47Ω resistor rated for 10 W is mounted and this allows the final nozzle temperatureto be controlled. This is done with a Neocera LTC-21 temperature controller thatmonitors the temperature sensor on top of the nozzle body. Both of these are shownin Figure 3.5, along with the particle filter that is attached to the gas line. Notethat the temperature sensor is technically about 10 mm away from the edge of thenozzle but is as close as it can conveniently be. We don’t expect this to produce anydiscrepancies even though the nozzle sticks out from the shield about 2 mm becauseit should be an accurate reading in steady state conditions.Another important component of the source chamber is the cyroshield. It is acylindrical tube that is mounted to the cold head and also actively cooled. It usedto shield the assembly shown in Figure 3.5 from the thermal radiation of chamberwalls that remain at room temperature. It is a typical design consideration usedin most low temperature vacuum designs. The shield is assumed to be uniformly27heated by the outer walls and needs to be made of a material that has high heat con-ductivity at low temperature (oxygen free copper) to transfer that radiation to a heatsink (the cold head). At normal operations the cyroshield reaches 40 K. Withoutthe cryoshield, the nozzle can only reach 20 K and therefore won’t be producingdroplets. With the cryoshield the nozzle can reach temperatures as low as 10 K inour set up, depending on the backing pressure. In order to minimize the footprintof the shield, it is made in two concentric cylindrical stages to accommodate thecoldhead and the rail that the nozzle is mounted to. There are shims placed atthe end of the cold head to make sure the apparatus is long enough to fit aroundthe nozzle assembly. As well, the top part of the first stage has an flat cut in it toaccommodate the source chamber profile. On the second stage of the shield, justabove the gas line filter, a second temperature sensor is placed.Because of the chamber geometry, the effective pumping area by the nozzle isvery low. This is because there is very little empty space in the cross sectionalarea. The pump and pressure gauge are on a different end of the chamber fromwhere the expansion takes place. The nozzle expands gas towards a skimmer that is0.3 mm (Model 2, Beam Dynamics) that is mounted in the center of the the backwall. Ideally, the expansion occurs in an open area of the chamber, away from walls,to avoid reflections and turbulence that can lead to beam destruction. This alsoensures that pressure readings are an accurate reflection of the nozzle environmentand that the effective pumping speed is maximum.Prior to installation or during maintenance, it is important to check the condi-tions of the skimmer and make sure that the tip is shiny and undamaged. Thiscan be inspected with a microscope and a bright light. It is delicate, difficult tomount, and difficult to clean. If the outside is dirty, it can be soaked in acetone orisopropanol and then blown out with nitrogen. It should remain in the chamber asmuch as possible to avoid dust from landing on it. However, if this happens a thinwire can be pushed through the opening to remove the dust without damaging it.The skimmer and the nozzle are mounted very close together and the final positionwas determined by checking for a droplet signal (described in Section 3.3) whilemoving the nozzle closer to the skimmer. The final distance was measured to be287.6 mm and was decreased from a distance of 10 mm. Moving the nozzle closer tothe skimmer meant that more gas would get through the skimmer before there wassignificant beam destruction which is caused by collisions due to a high chamberpressure and reflections from the back wall. The trade off is how much gain you canget from the free jet expansion and how sensitive your set up becomes to alignment.Our pumping speed is limited in this chamber, so closer was better. The distancebetween the nozzle and skimmer is difficult to measure accurately because theskimmer is press fit in the wall, the nozzle rail was filed so the nozzle hangs off ofit, and the final position depends on how tightly two different flanges are clampedtogether. The final distance is determined by measuring how far the skimmer mountsticks off the back wall using calipers, using the skimmer specifications from themanufacturer, and measuring the nozzle position from the back rail. It was criticalto know this space because a shutter had to be designed to block the beam in thissmall space.3.2.2 Hard Drive ShutterOriginally, a DC motor was used but it eventually burned out due to it’s inabilityto radiate heat away in vacuum. This lead us to using an optical hard drive voicecoil, as has been done in some groups that needed frequencies of up to 30 Hz with asharp rise/fall time in vacuum [39]. In our set up, the shutter is difficult to mountin the source chamber because there is no where to attach it, and due to machiningtolerances the back end of the source chamber is a bit bigger than the front end. Thismakes anything that has to be installed very difficult to squeeze in, but may wiggleand be loose at the end of the chamber near the skimmer. Typically, two rings are cutout of acrylic so that one can be pressed up against the back wall and the second canbe used to space the shutter away from the skimmer. Although acrylic is normallyavoided in high vacuum applications, the source chamber is normally around 10−4torr with the gas load and so the offgassing is not an important consideration inthis chamber. In fact, the electrical wiring to the shutter is held to the chamberside with scotch tape and pumping down has never been a problem. The shutteris held together using spacers and brass threaded rod. It is important that boltson the side that press against the chamber be filed flat so that the shutter moves29perpendicular to the beam path and does not hit the skimmer. The shutter skimmerdistance is minimized, since this a more reliable measurement, and is 1.8 mm. Thedistance from the back wall to the back side of the shutter flag should be 33.5 mmto accommodate this. The shutter and mount are depicted in Figure 3.6. In olderdesigns, a third plate was mounted using a longer threaded rod to help keep theshutter pressed into the back wall. This had to fit around the cryoshield and acted tostabilize the shutter. Since it was very difficult to install and lower frequencies wereused, it was omitted from the last round of shutter maintenance.The hard drive used was a 3.5” drive that was cut to remove the back plate.Figure 3.6: Left: Shutter mounted in the source chamber in front of the skim-mer. Right: Shutter mounted to be tested with a HeNe laser beam.The critical deciding factor in what hard drive to use is the size of the magnet dueto the limited space. This was an old Fujitso drive. Most 2.5” drives tend to fit,but were found to overheat at higher frequencies. The shutter was tested to operateat frequencies of 10 Hz to 20 Hz and a control circuit was designed and built byan undergraduate student in the lab to achieve this [49]. This circuit outputs alarge initial voltage pulse that decays to a lower holding voltage. The initial pulseprovides the high speed to the shutter and the lower holding voltage minimizes thepower dissipated by the shutter (details in [49] and [39]). The shutter is normallyused at a frequency of 0.1 Hz for applications involving image collection.30The shutter should be centered in the acrylic disks so that the arm and flag openand close with respect to the middle of the chamber, otherwise the beam will notbe fully blocked. When assembling the magnet and voice coil from the hard driveto the acrylic mount, the screws need to be undone that align the spacers betweenthe powerful magnets. This makes it difficult to keep the magnet seated properly,though is easy to tell if you have it aligned based on the friction felt when rotatingthe arm. It is important to get this seated properly, because if it is misaligned extraheat will be generated during operation. This can soften the rubber stoppers, usedto prevent recoil, and cause them to move. There are a few critical checks that needto be performed before installing the shutter in the chamber and both have to dowith the final assembly. In order to test the alignment, the holder can be mountedconcentric to a HeNe laser and the signal read on a photodiode. The beam can beexpanded to ensure a large enough flag as well. This is shown in Figure 3.6. Thebeam size, assuming 45◦ expansion would be about 10 mm, so this can be visuallyinspected. Once the position is checked, the shutter can be installed in a roughvacuum chamber; meaning a chamber that reaches a pressure of about 1∗10−2 torr.This is enough to see if the temperature of the voice coil raises significantly. If thisis left to operate at 5 Hz overnight, it shouldn’t raise more than 6oC based on thelast round of overnight testing conducted. The shutter can then be placed in thesource chamber. If the flange between the source and doping chamber is open andthe skimmer is removed, it can be visually inspected whether or not the flag blocksthe nozzle. This is also a good time to run the shutter at, say, 5 Hz to ensure thevacuum feed through electrical connections are okay. Finally, the change in partialpressure measured by the RGA can be observed by changing the state of the shutter.The change should be quite dramatic, as shown in Figure 3.7. The rise and fall timeis limited by the collection rate of the RGA.The original hard drive shutter was operated for approximately one year until themagnet casing melted. It was unclear where the extra friction came from. The rubberstoppers may have shifted and caused the arm to heat up the magnet more thannormal. The vibrations of the cold head could also have made the arm shift in the31Figure 3.7: Normal Operations of Shutter seen by observing the M/Q = 4partial pressure on the RGA.holder and cause more friction. The hard drive was simply replaced and the controlcircuit was reused. Measuring the resistance and voltage drop across the shutter atthe control circuit gave the results of Table 3.3 before and after replacement.Shutter State Resistance (Ω) Voltage Drop (V)Working 9.47 0.85/-0.95Broken Overrange ±20.69Table 3.3: Useful electrical diagnostics for shutter.3.2.3 Doping ChamberThe skimmer holder mounted in the source chamber is made of Delrin that is pressfit into a hole at the back wall. It is made long enough to stick out into the dopingchamber. There is a hole drilled into this piece for 1/8” stainless steel tubing to goin. Crack resistance fluorinated Teflon tubing is press fit on top of this and locked inplace with a set screw. This is set up is shown in Figure 3.8 with the black arrow32and the Teflon tubing that supplies the doping gas to the beam.The doping chamber is effectively the backside of the skimmer and the inside ofFigure 3.8: Skimmer, doping line, and holder assembled on outside of sourcechamber.the holder, as highlighted in Figure 3.9. The holder length that sticks into the dopingchamber is 20 mm and has an inner diameter of 11 mm. This creates a high numberdensity of the dopant gas that the beam must travel through and simulates a cell,which is implemented in other set ups. Normally, a small cell is placed in the dropletbeam path that is filled up with the dopant gas and localizes it so that it doesn’t affectthe overall chamber pressure. There is not enough room for this type of constructionin the 27.3 mm of space until the science chamber. The gas line pressure can bekept low and adjusted precisely because it is filled with a sapphire crystal leak valve(Varian, 951-5106). The “T” in Figure 3.8 was water jetted to screw into the dopingchamber side of the source chamber in order to hold the skimmer holder in placeand provide on option for securing the doping line. When the fore vacuum lineswere separated there was a pressure differential at the beginning of a pump down33between the source and doping chamber large enough to cause the skimmer to popout and damage both the nozzle and skimmer.Placing the doping line right behind the nozzle is also critical in our chamberfor producing droplets because when the entire chamber is filled with gas, the num-ber density in the beam path is too low to have a reasonable pick up rate. Mountingthe leak valve directly to the chamber is not important either. If it is more convenientto keep it separate it is fine to have stainless steel tubing connecting it to the vacuumchamber. This also allows adaptors that have swagelok connection on the vacuumside so that the tubing cannot pop off with high pressures.Pumping speed requirements on the doping chamber are such that a pressure differ-ence between ≈ 10−6 and 10−7 torr can be maintained. Without adding any gas fordoping at normal droplet operations of 14.5 K and 24 bar the chamber pressure is3.4∗10−7 torr, as mentioned in Table 3.2 and droplet doping conditions bring theoverall chamber pressure up to about 5∗10−6torr.Figure 3.9: The effective doping “cell”. The gas line is inserted in the end ofthe skimmer holder and the doping gas can fill the path marked by theblue area. The droplets can collide with it on the path marked in red andpick up molecules.343.2.4 Science ChamberApproximately 31 mm away from the 2 mm aperture separating the doping andscience chamber is the laser beam interaction region in the imaging set up. The gasload is much lower in the science chamber since the beam density decreases like1/z2 and the beam has been skimmed already and so the pumping requirements aremuch lower. At normal droplet conditions with no doping, the chamber pressure is2.2∗10−7 torr. However, with doping due to the proximity to the doping chamberthere is a lot of effusive background gas that enters the imaging region. There isno room to place a liquid nitrogen, LN2, trap between the doping chamber andinteraction region, so one was installed another 24 cm downstream. It is used tolower the overall background chamber pressure and mounted to not obstruct thebeam from reaching the RGA, which is a Faraday cup detector. It can improvethe signal to background ratio by a factor of 3. This chamber will be discussed ingreater detail in the next chapter.3.3 Characterizing a Droplet BeamBefore the beam can be characterized, it is important to check all connections forleaks. After 1 day of pumping, the ConFlat flanges can be checked to make sure theknife edge/copper gasket seal is good. A rough check can be done by looking forpressure increases while spraying acetone at the flange. If the pressure increases,there is a leak and the chamber should be vented so that the flange can be tightenedagain. A more sensitive check can be done using the RGA. While monitoring thepartial pressure of He, a line with a needle at the end can be brought up to thechamber and placed inside the flanges to see if the signal increases. After about 3days of pumping down, the backing pressure can be increased going from 4 bar to24 bar, slowly to avoid damaging a turbo pump if there is a large leak. At 24 bar ofhelium with the nozzle at room temperature, the pressures expected for the source,doping and science chamber is 1.55∗10−5torr, 8.6∗10−8torr, and 1.47∗10−7torr,respectively. In the source chamber, leaks can happen in the gas line connecting thehelium tank to the nozzle either for the connections at the flange, filter, or nozzlebody. Same with in the doping chamber.35If the nozzle is replaced or if the source chamber is moved, the nozzle alignmentshould be checked. It can be dangerous to move the nozzle a lot because the O-ringmay not seal and will vent the chamber with atmospheric gas. Nozzle alignmentcan be observed with a decrease in source chamber pressure and increase in sciencechamber pressure, but we can more precisely monitor the quality of alignment usingthe RGA at the end of the chamber. The pressure increase is very dramatic - overtwo orders of magnitude from absolute pressures of 10−9 torr to 10−7 torr. Oncethe signal is maximized it’s important to check the sensitivity of the maximum totranslation. For our manipulator, moving the nozzle up/down or left/right by 1/4of a bolt rotation should take the signal decrease to half of the maximum. Whenthe nozzle or skimmer are partially clogged, this changes drastically and the nozzle-skimmer alignment is very sensitive to movement.Once these checks are passed, the nozzle is ready to be cooled. The source, dop-ing, and science chambers are monitored with respect to the nozzle temperatureas well as the He and He2 pressures on the RGA. As the metals contract, there ismovement of the nozzle with respect the the skimmer and seen quite dramaticallyin our chamber. It is a bit more dramatic due to the small nozzle - skimmer distance,with respect to other group’s chambers. This can be seen in Figure 3.10 in theyellow Science Chamber pressure curve between 100 K to 200 K. Once the nozzleFigure 3.10: Left: Chamber Pressure Cool down Curves Right: RGA PressureCool down Curves.temperature reaches about 20 K the flux of He decreases (beginning of clustering)36and the science chamber pressure and He RGA signal decrease. Most importantly,He2 begins to form and is the important benchmark for droplet production since itcan only form from droplets. As showing in Figure 3.11, it is 0 up to about 20 K. Asthe nozzle cools more, droplets begin to form and these pressures should increasequite dramatically as larger and larger clusters are produced. A clear increase isseen in the curves shown in Figure 3.10 at low temperatures and is marked withred arrows. It is not as dramatic because of the misalignment that happens duringcool down and because of the limited pumping speed that results in a higher overallchamber pressure. This is shown in Figure 3.11 in comparison to the expecteddroplet behaviour seen in other chambers[8]. The lowest dip in pressure, marked byorange arrows, is when droplets start to form. This is proportional to√P0d and justshifts to colder temperatures for our set up, but the qualitative behaviour should bethe same. In our chamber, we do not see a clear maximum around 30 K, markedwith green arrows, before the helium clusters into droplets, but we do see a dip andthen subsequent rise in pressure that also corresponds to an increase in the He2+signal. We see the He2+ signal dips after rising, which is not expected, as a result ofmisalignment and beam destruction from the high chamber pressure. This is fixedby realigning the nozzle and skimmer at the peak around 13 K. The increase insignal after the dip is marked by red arrows and is when helium droplets start to form.Figure 3.12 shows the partial pressure of He2 and He after the nozzle is alignedand the increase is more clear. Different backing pressures were supplied to thenozzle, which shows how the droplet formation temperature increases with higherbacking pressures. When the turbos start to be throttled or there is beam destruction,the increase abruptly stops as is seen for the curves of He at P0 = 20 bar and 24 bar.As well, the lowest temperature achievable increases with an increase of backingpressure which is likely a result of extra friction from the additional gas.The nozzle should be aligned to the maximum flux into the science chamber at thedesired operating temperature and it can take up to 20 min for the signal to stabilize.The heater can be turned on to maintain the nozzle temperature to within ±0.1 Kbut can take up to 1 min to stabilize when changing the shutter state between onand shutter off. When the nozzle is clogged, the shutter state between on and off37Figure 3.11: Comparison of our RGA Partial Pressures (normalized) with thedroplet signature seen in other chambers, shown in the lowest panel.Adapted from [8].becomes less square, as shown in Figure 3.13, and will be very erratic. Heatingthe nozzle does not work and the chamber has to be opened for maintenance if thishappens.The fragmentation in the time of flight spectrum can be observed with the femtosec-ond probe at high intensities. This is done using the probe because an electron gun isnot available for comparison to literature; 100 eV is often used in comparison to the1.5 eV per photon we have to reach the ionization energy of He at 24 eV. The timeof flight signal observed in our chamber shows cluster peaks up to about 16 AMUwith probe intensities that begin to reach the limit of damaging the detection equip-ment. In other set ups, helium oligomers can be a concern (for background) upto 32 AMU. Our time of flight spectrum is shown in Figure 3.14. The peak at18 AMU is just background water and not due to the droplet beam. It is clear fromthe non-linear increase in ion signal with probe energy that there are some dropletsthat are ionizing from plasma ignition and is an indication of droplets forming[20].38Figure 3.12: The effect of changing the backing pressure on the cool downcurve. The effect is a change in the coldest temperature that can bereached in the system. Pushing this system to operate at colder nozzletemperatures results in producing larger helium droplets and a largerpressure load in the source chamber. We are at the limit of throttlingthe turbo pump and it can be seen that the beam starts to be destroyedwith the jumps down in pressure for P0 = 20 and 24 bar.It is unclear what impact our inability to produce larger helium fragments hason the beam quality. It could suggest that we have fewer droplets successfullyclustering in our beam which would lead to a lower count rate than anticipated.The ratio of the the peak heights can be evaluated from the curve ionized with100 µJ of probe energy to compare against other experiments where the intensitieswere measured using an electron gun and is shown in Table 3.4. The ratio of He8to He12 is comparable, but the other ratios are off by an order of magnitude. Itis more important for us to efficiently produce medium - small droplets (< 5000)because it can be difficult to ionize molecules inside large droplets and because ofcollisional effects that prevent us from determining the molecular position. Thiswill be discussed in the next chapter.39Figure 3.13: Partial Clog of Skimmer: the shutter switched from beam on tobeam off at 72.5 min and remains off. We do not observe the anticipatedsquare wave.Experiment I8/I12 I16/I8 I16/I12Vilesov 6.7 0.027 0.294UBC 3 0.67 2Table 3.4: Ratio of Peaks; comparing our measurements to another experimentat 14 K found in [45].The final check to verify that droplets are being produced, and that they arebeing doped effectively, is to measure the CS2 dimer signal. Dimers form insidethe helium droplets or in a seeded gas expansion when they get cold[37]. Theyare detected by observing CS2 molecule repulsion in an ion image, as shown inFigure 3.15. Without droplets in the Beam Off image, only background CS2+ isobserved. The line at the right is the effusive jet that forms from the 2 mm aperture40Figure 3.14: Droplet signal TOF for various probe energies.leading to the science chamber. A circle is expected because the molecules areoriented isotropically when ionized by the probe. The asymmetry is because thedetector is overwhelmed by the strong signal or partial damage and is not respondinglinearly. With droplets in the Beam On image, ions are detected out to the large bluering, which marks the expected repulsion energy.Figure 3.15: CS2 Dimer Doping 13.6 K at PD = 1∗10−6 torr.413.4 Molecular Jet DilutionThe number density of a doped droplet beam is significantly lower than the densityof a pure molecular jet. The two can be compared using the formula for numberdensity, n = F/vA, and the flux of a beam, F = ∆PS/kBTΩ [44]. Combining thetwo and taking the ratio for the number density between two species yields thefollowing formula:n(X)n(Y )=∆PX SvX AkBTΩvY AkBTΩ∆PY S=∆PXqX vXqY vY∆PY(3.2)where n is the density, v is the velocity, A is the area of the chamber, F is the flux, Sis the pumping speed, and Ω is the angle subtended at the end of the chamber by theaperature and skimmer. If we take the ratio of n(O2) and n(Hen), the molecular jetand singly doped beam densities, we don’t care about A because it is the same. Theflux of molecules is given by the pressure increase, ∆P, corrected for the sensitivityof the ion gauge, q. The velocity of the oxygen jet is 736 ms−1 and the droplet beamvelocity depends on the exact operating point, but we can calculate using 476 ms−1.The speeds are taken from the St. Venant Wantzel equation:v =√2kk−1kBTM(3.3)where k is the adiabatic exponent or ratio of specific heats (5/3 for monatomics, 7/5for diatomics, and 4/3 for triatomics), kB is the Boltzmann constant, T is the temper-ature, and M is the mass. This form of the equation assumes the gas expands intoperfect vacuum. At the operating conditions we expand the helium at, we shouldbe producing clusters of 5000 atoms and assuming the doping is set according toPoissonian statistics, 30% of those nanodroplets contain a single oxygen molecule.When we calculate the ratio from Equation 3.2, we get n(Hen)n(O2) = 0.0053, which isclose to the same values from other nozzles used in this chamber. Clearly this posesa challenge in terms of collection since the signal density is≈ 2 orders of magnitudelower than a molecular jet of pure oxygen, and simultaneously the added dopinggas will lower the S:B by 3 orders of magnitude. This number isn’t terribly usefulto diagnose the beam, but it gives a good indication for how to simulate the number42density of a droplet experiment. It also highlights the importance of beam align-ment and minimizing beam destruction, since the pressure increase is the importantfactor in number density and not overall chamber pressure, although they are related.Because of the CS2 and He dimer signals, we are confident that we are producingdoped helium droplets. The other metrics suggest that we are not producing themas efficiently as conventional set ups but there is no scaling parameter to help usdetermine by how much. By producing CS2 doped droplets, preliminary resultswere able to be measured and explored.43Chapter 4Detection Techniques4.1 Velocity Map ImagingAn ion focusing scheme is utilized that maps different initial velocity vectors ontodifferent points of a detector plane when the probe ionizes the molecule, known asvelocity map imaging (VMI) [13]. The three dimensional velocity distribution maybe recovered from the two dimensional ion image and allows the molecule’s rota-tional energy and orientation to be inferred. Ions are created through laser inducedCoulomb explosion, which is a process that rips electrons from a molecule rapidlywith an intense probe pulse. This creates a positive, highly charged “parent” molec-ular ion that fragments from the huge Coulombic repulsion the ions experience afterthe electrons are ripped away. The axial recoil approximation assumes the fragmentions recoil along the bond axes of the parent molecule, which allows the molecularorientation to be inferred[11][41]. Different ion fragments can result dependingon the charge of the parent molecule and these break up via different pathways,or channels, creating distinct rings in an ion image due to different amounts ofenergy released. These rings are used to determine the transitions of the excitedmolecule and thus the VMI technique allows insight into these parameters whereconventional time of flight (TOF) methods do not[12]. We use VMI to monitor theorientation of a molecule excited by the CF because the rotational excitation pullsthe molecule into the plane of rotation. We compare a bare molecule’s angulardistribution to the angular distribution from inside a helium nanodroplet. Changes44in the distribution would allow insight into the coupling strength and degree ofsuperfluidity of a nanodroplet.A basic VMI consists of a three electrode set up: a repeller plate VR, an extrac-tor plate VE , and a ground plate, as shown in Figure 4.1. The extractor and groundplates have open holes in the center to allow the ions through while the repelleris a closed disk that provides a uniform field to accelerate the ions. The ions areaccelerated to a multichannel plate (MCP Tectra, MCP-50-D-FV-P46) that creates acascade of electrons that then hit a phosphor screen. A photomultiplier tube (PMT)can be used to collect this ion signal and is useful for TOF measurements. Aswell, the light is focused onto a CCD camera sensor with a 40 mm condensing lensand this allows the ions to be tracked via pixel locations. The voltages applied tothe electrodes are always in the order VR > VE > 0 and the ratio VE/VR is fixeddepending on the geometry of the electrodes. This ratio fixes the focal plane and theshape of the trajectories are independent of the mass to charge ratio, m/q. So, anytwo particles that are created at the same point with the same kinetic energy andvelocity vector will follow the same path though their TOF will be different if theyare different masses [13][6]. This means that an energy scale can be applied to theimage radii that is independent of the mass and can be extended to other masses.In order to recreate the full three dimensional velocity distribution, an inverse Abeltransform must be done. This is a unique transformation that can map between 2Dand 3D velocity distributions as long as there is cylindrical symmetry and what isdone to reconstruct the full 3D distribution. This is not always possible to attaincylindrical symmetry and it has become common practice to use the raw ion imageand characterize the alignment from the 2D distribution[47]. The raw ion imagecan still be used to recreate the 3D distribution if “time slicing” is implemented[46].This means gating the MCP and only collecting ions that arrive within a certain,very narrow, time window. Ideally, this time window correlates to one shell of the3D velocity distribution from the Newton sphere and improves the resolution. Weused this principle to extract the ions in the middle of the TOF peak and increasedthe resolution of the distribution.45Figure 4.1: VMI Configuration.A few general relationships are outlined in [6] and are useful to recall here. Whenions are created in a VMI, they will give rise to a spherically symmetric cloud thatexpands at a velocity, v, and will create a ring on the detector with radius, R, calledthe Newton Sphere. R is related to the tTOF by:R = AvtTOF (4.1)where A is the magnification factor and depends on the specific VMI geometry. Asin conventional time of flight mass spectrometers, tTOF is determined by the initialacceleration set by the repeller voltage[6]:tTOF ∝√mqVR(4.2)46The velocity can be expressed as the kinetic energy release EKE = 12 mv2 and can besubstituted into Figure 4.1 to show how the radius scales[6]:R ∝ A√EKEqVR(4.3)4.1.1 Velocity Map Imaging CalibrationThe ratio for our set up was determined to be 0.718 (VR = 4500 V and VE = 3230 V)experimentally. The MCP and phosphor screen voltages are set to 800 V and 4100 Vto 4500 V. These were decided by finding a linear regime of operation by monitor-ing the increase in ion response as the voltages were increased and staying withingthe limits of operation. Using a molecule with known Coulomb channels, suchas CS2 which releases about 3 eV per S+ fragment[48] or N2 with 4.8 eV per N+fragment[52] (the exact energy depends on the intensity of the pulse), ions arecreated using a probe that is polarized perpendicular to the TOF so that there is ananisotropic ion distribution. This distribution is illustrated in Figure 4.2 for N2. VRis then determined such that the size of the distribution fills the detector in orderto maximize the spatial resolution that can be achieved with the sensor or can beselected in order to optimize mass selection with the TOF. After, VE is changed tooptimize the ion focus which means maximizing the ion signal and making it assharp as possible. VR is also important because it determines the energy at whichions impinge the MCP and this changes the collection efficiency. Typically, the bestachievable efficiency is 65%[34].Once the voltages are fixed, the arrival time of the ions can be scaled to al-low for mass gating of the MCP. Mass gating is done using a high voltage trigger(Photek, GM-MCP-2) that pulses the back of the MCP up an additional 500 V fromwhat the power supply is set to (800 V+500 V) in order to turn the detection on.Although the trigger can be set to 10 ns, we are limited to a gate as narrow as 20 nsbecause of the pulse generator and coupling into the system. The calibration of thisgate requires knowing two different masses; an easy selection is the ionization ofN+, as shown in Figure 4.2, and it’s parent ion N2+, which will just be a bright spot.47Figure 4.2: N+ ion distribution for a probe polarized perpendicular to theTOF path. The circle had a radius of 250 pixels. The ions were createdby ionizing a jet of N2 expanded at 20 bar with the fs probe set to anintensity of 2.1 ∗ 1015Wcm−2 and the VMI set at VR = 4500 V, VE =3230 V, VMCP = 800 V and the Phosphor Screen = 4300 V.In principle, it’s important to use a probe that is polarized parallel to the detectionplane to avoid having to select between ions that are accelerated towards the planeand away from the plane (forward and backward ions) as would be the case with aprobe that is polarized parallel to the TOF path. This isn’t very important for our setup because at VR = 4500 V the difference in arrival time between the forward andbackward ions made from N2 is expected to be 18.8 ns (from SIMION simulationsof our VMI detector) but the smallest mass gate possible is 20 ns. It is also importantto note that there can be a background signal from water that hasn’t been completelypumped out of the chamber, M/Q = 18 AMU. We can distinguish this ion signalfrom the N2 related signal using the shutter.We can set a simple time calibration for M/Q from the TOF at a specific repellervoltage by scaling the time axis with the assumption tTOF ∝√M/Q. From t = 0 inthe MCP trigger, there can be some dead time, which means there is an offset thatneeds to be accounted for. We use two known masses to fit M/Q = A(tTOF +B)2,where A is the scaling factor and B is the offset (M = 0 corresponds to tTOF = B). If48we use two data points, (tTOF ,M/Q) = (LX ,LM) and (tTOF ,M/Q) = (UX ,UM) wecan solve for A and B as follows:LM = A(LX +B)2A =LM(LX +B)2(4.4)UM = A(UX +B)2B =√UMA−UX (4.5)Substituting Equation 4.4 into Equation 4.5 and isolating B:B =√UMLM(LX +B)−UXB =√UMLMLX −UX(1−√UMLM)(4.6)Finally, Equation 4.6 can be used to solve for A from Equation 4.4. Normal practiceis to assign the lower mass to be LM = 14 for N+ and the upper mass to be UM = 28for N2+. Then, for LX and UX we record the leading edge of the MCP trigger (setto the narrowest gate possible, 20 ns) and calculate A and B for the available triggerrange. For a fixed set of voltages, an energy scale is assigned to the image radiithat is independent of the particle mass and once this is done for one species, thecalibration would apply for all other masses. We assume that we can scale the radiusof the ion image in a simple way according to[6]:EKE =C(qR2) (4.7)where C is the scaling factor that we need to determine. Note that this C is valid forone VR and would need to be remeasured for different electrode voltages. Normally,this is done using a well known photoelectron energy channel. We do not havethe ability to measure photoelectrons because a flight tube was not installed thatwould shield the electrons from stray electric and magnetic fields, so we had touse a well known ion kinetic energy release channel. Another group tested their49photoelectron calibration versus their calibration according to the dimer repulsionfelt by two CS2 molecules, and we implemented this procedure [37]. It is importantto do this after the mass calibration is known because the CS2+ signal comes froma seeded jet and can be weak (and the dimer signal weaker) and data collectionhas to be done over a long period of time, up to 30 min to 45 min to see a signal.The following ion image was collected using a probe pulse parallel to the TOFpath (for cylindrical symmetry) with the mass gate set to M/Q = 76 AMU and isshown in Figure 4.3. The radial distribution is found with respect to the center ofFigure 4.3: Determining the scaling in eV/pixel2 for CS2 dimers.Coulomb energy (CE) and is plotted in the bottom right of Figure 4.3. The centeris considered the point of maximal intensity of the parent ion because this processhas no kinetic energy release and therefore no repulsion. As well, background CS2can build up in the chamber. These are removed from Figure 4.3 because they aremuch brighter than the dimer ring, which is plotted on the left. It is not importantfor the energy calibration, but the outer ring indicates trimers that are known tocluster in these experiments as well and it should not be mistaken for the dimerring. We find the peak of the outer ring in the radial distribution, which is 98.44 pix,and assign it to the 2 eV of kinetic energy release expected by the dimers. Thisgives a scaling factor of C = 2.064∗10−4eV/pix2 for q = 1. This scale is appliedto the radial distribution and then plotted in the top right of Figure 4.3. As well, the50intensity is scaled by the radius so that I→ I/R. The resolution can be determinedby fitting the scaled distribution to a Gaussian and using the standard deviation ofthe fit: σ =0.2 eV (equivalently, 6.5pix). The resolution would then be reportedas ∆E/E = 20.5% (∆R/R = 7%). For reference, other detectors typically haveresolution ∆E/E < 5%[26][54]. The specifications for our set up that have beenexperimentally determined and/or simulated are summarized in Table 4.1.Feature VR =4500 V VR =2500 VSimulated Reso-lution∆E/E = 10.6%(∆R/R = 4%)∆E/E = 4.5%(∆R/R = 3%)ExperimentalResolution∆E/E = 20.5%(∆R/R = 7%) N/AScaling Factor[eV/pix2]C =2.064∗10−4 forq = 1C =1.391 ∗ 10−4 forq = 1 (sim)Scaling Factor[(ms−1)/pix2]C = 22.89 forq = 1,M = 76C = 18.79 forq = 1,M = 76(sim)SimulatedEnergy Accep-tance23 eV 13 eVMaximumRadius300 pix 300 pixTable 4.1: Detector Specifications.4.1.2 Interpretting Ion ImagesIn a VMI ion image, the jet or droplet beam is shifted with respect to the centerof the background, which is located at 0 ms−1. This is because the molecular jet(or droplet beam) is travelling at 250 ms−1 to 1750 ms−1, and so the parent ionis shifted along the direction of propagation. This is shown with the red circlesin Figure 4.4 for a droplet beam. In order to experimentally measure the speedof the molecular jet or estimate the center of the droplet beam, the scaling factorfor velocity can be reformulated to accommodate mass by dividing out√76, soC = 199.56√AMU(m/s)/pix. The center for CE is located at this shifted spot,51Figure 4.4: The shift of the jet with respect to the background.where the parent ion is. In general, the larger the shift of the parent ion spot isaway from the background center, the easier background subtraction is. This isbecause we focus on measuring the channel, which means we analyze that ions thatlie in a radial range around the peak at 100 pix in the bottom right of Figure 4.3,for example. Since the background ions will be at the same radius from a differentcenter (the background centre), the contribution of background ions will be less inthis bin.The angular dependence of the velocities allow the orientation of the moleculeto be directly observed for many different ionization pathways. This is quantifiedby the metric, 〈cos2 θ2D〉, where θ2D is the angle between the molecule and laserpolarization axes projected onto the plane of the detector, as illustrated in Figure 4.5.When the molecules are excited by the CF, they are following it’s polarization vectorand are pulled into the plane of rotation, which we call planar confinement. Thismeans that the angle the molecular axis makes with the plane of rotation goes to0,pi . When the molecules are ionized without the CF and a probe that is polarizedparallel to the time of flight axis, the probe is along the same direction as the planeof rotation and so the ion image has anisotropy as well.52By changing the arrival time of the probe relative to the pump pulse, the dynamicalbehaviour of the molecule can be studied as well. Before the CF arrives, the dis-tribution is a ring and 〈cos2 θ2D〉= 0.5. As the probe moves to arrive after the CF,〈cos2 θ2D〉 → 1 and this squeezing into a horizontal line is maintained long after theCF leaves.The VMI technique is useful for understanding how the motion of the moleculeFigure 4.5: Illustration depicting the angle important in quantifying how muchthe molecule is squeezed into the plane of the centrifuge. For high Jstates, the molecule is squeezed into a line so that that θ2D→ 0,pi .changes in the helium environment and lends an easy way of studying the dissipationof rotational energy into the helium molecules since the decay of the excitationcan be measured. However, because of the effusive doping gas, the backgroundhas to be taken care of. This is done using a shutter and collecting ions for a fixedtime and subsequently subtracted the on and off states. As mentioned briefly above,the velocity center can also be used to discriminate against the background. Fora droplet beam, this isn’t the case. The parent ion signal from the cold beam istoo weak to detect against the background because the mean velocity is between250 ms−1 to 450 ms−1 which translates into 2.5-4.5 pix for Helium and 7.1-12.8pix for S+ and is on the edge of our resolution but we should be able to distinguishthe different angular features of the distributions.534.2 Resonance Enhanced Multiphoton IonizationThe ionization signal is used to investigate the rotational spectra of molecules whichis created through resonant transitions with a tunable laser and known as resonanceenhanced multiphoton ionization (REMPI). This means the angular momentumstate of the molecule can be directly probed, since the ion current measured isproportional to the population of the initial level and the transition probability to theexcited state. This pump probe scheme is depicted in Figure 4.6. The moleculeswere expanded and cooled in our UHV chamber and the ion signal was detectedusing the VMI imaging set up.In oxygen the (2+1)C3Πg(ν ′ = 2)←← X3Σg(ν” = 0) transition is studied becauseof the high ionization cross section and ability to reproduce the rotational spectrumof [24] where the line assignment is discussed in detail. The two photon energyrequired for this transition was scanned over the range 69400 cm−1 to 71000 cm−1(279 nm to 288 nm). It was sufficient for our purposes to choose one CF truncation(rotational state) instead of scanning through these in order to develop the techniquefor use in droplets. Observing these rotational resonances indicated correct beamalignment, sufficient ionization intensity, and proper focusing. The power of theREMPI technique lies in it’s ability to measure small signals and obtain a high degreeof spectral resolution.4.2.1 Dye Laser SystemThe tunable laser used to resonantly probe molecules is a Sirah Cobra Stretchpumped by a Quanta Ray 50 Hz Nd:YAG laser with a frequency doubling unit fromSpectra Physics. The gain curve of the dye should match the molecule of interest;for oxygen we frequency doubled light from Rhodamine 6G. Rhodamine 6G wasdissolved in ethanol with a concentration of 0.09 gL−1 and 0.01125 gL−1 for theresonator and amplifier cells, respectively. This output was directed to a BBOcrystal for second harmonic generation to deliver a wavelength range of 279 nmto 288 nm. The crystal angle was computer controlled to follow the optimal phase54Figure 4.6: CF and (2+1)REMPI excitation scheme of Oxygen.matched position and deliver maximum power. These pulses are≈ 10 ns in durationand have a linewidth of 0.1 cm−1. Typically, the energy delivered by the laser at287 nm was 3 mJ per pulse. This light was directed to the UHV chamber with 4Pellin Broca prisms in order to minimize the amount of losses to the beam andbecause the Al mirrors were burning. The light was directed into the chamber, andcombined with the CF, using a dichroic mirror (Thorlabs DMLP900L). Typicallythe energy incident on the dichroic was ≈1.2 mJ, leading to an energy of about0.7 mJ to 1 mJ going into the UHV chamber for 287 nm. If the energy going intothe chamber was <500 µJ we would not be able to detect a signal.Synchronization of the CF and the UV pulses required triggering the Nd:YAGlaser with a trigger from the femtosecond laser. The Legend is equipped with acontroller that can output a 50 Hz pulse synchronized with the 1 kHz output. This55Figure 4.7: The timing diagram that shows how the YAG laser is triggeredwith respect to the Legend laser.allowed the flashlamps and the Q-switch to be triggered independently by a pulsegenerator in order to optmize power with the CF pulses. We set the Q-switch triggerto be with “the next” expected pulse of the 1 kHz trigger signal (around 1 ms) inorder to allow us to pre-trigger the flashlamps of the YAG. This couldn’t be donearound t = 0 because the delay generator did not allow negative delay times (it alsomeant we added 1 ms to the mass gate timing for the MCP which had a completelydifferent calibration for the 50 Hz signal). The flashlamps were triggered ≈180 µsbefore this, and the exact position was determined by optimizing the power fromthe YAG. So, the Q-switch trigger was set to a delay of 999.997 µs (pulse width5 µs) and the flash lamp trigger was set to 818.397 µs (pulse width 5 µs). The timingdiagram in Figure 4.7 illustrates this scheme.The output of Sirah is a slightly expanding beam that normally has an elon-gated profile vertically. Near the entrance to the UHV chamber, the beam wouldlook like the left image in Figure 4.8. However, once this beam goes to the refocus-ing mirror in the chamber, it does not focus to the center of the molecular jet beam.This was deduced from spatial map imaging (SMI) mode and seeing that the UVbeam was focused to a different spot than the fs beam. A telescope was installedafter the first set of Pellin Broca prisms, with one lens on an adjustable rail. This56changed the angle of the beams enough to shift the focal spot of the beam in theUHV chamber. With the telescope in the beam path, when the beam is reflectedfrom the entrance of the UHV chamber onto a wall ≈5 m away we see the spoton the right in Figure 4.8. The beam shape is far from ideal, but could be focusedsufficiently to get a strong ion signal. The telescope installed in the UV beam pathFigure 4.8: Output beam profile of the Sirah at the UHV chamber without atelescope left and in far field with the telescope right.had the first lens with a focal length of −30 mm and the second lens had a focallength of 125 mm. They were set a distance of 13.5 cm apart. This distance wasdetermined by aligning the fs probe and the UV probe in what’s called SMI mode.This means that instead of the velocity vectors being mapped onto the detector, theions origin position is (like normal imaging). This requires us to change the ratio ofVE/VR from 0.718 to ≈ 0.9[42]. The mass gate on the MCP has to be extended by100 ns to accommodate the different arrival positions based on where the ions areborn. Then, if the fs probe is focused to a position that gives the optimal ionizationsignal from O2+, the UV probe can be adjusted using the telescope and dichroicmirror to align with the fs probe spot. This adjusts the focus closer/further fromthe refocusing mirror and along/against the direction of beam propagation. Howwell the beams are aligned vertically could not be determined in SMI mode becausethe MCP gate delay had to be opened up by 100 ns in order to view both the UVand fs probe spots together. It was suspected that the difference in TOF was due tovertical misalignment but we were not able to substantially correct the timing byadjusting the beams vertically. Meanwhile, other imaging set ups actually report thata misalignment of 2 mm results in a TOF different of ≈100 ns for VR =3000 V[16].It is possible that this is occurring because we are not in “true SMI” mode for ourset up, which could be confirmed with SIMION simulations. Additionally, our57electrodes are very small and ions that are born far away from the middle of thedetector may not be properly focused which would change the expected behaviourin SMI mode. The UV probe focal spot is quite large due to the bad profile andthis is certainly the case. Further investigation is required to pin down why thisdidn’t work, but the beams were aligned without the need of this tool. The verticalalignment was done by directing the beam to the far field and adjusted the beam’svertical position and then by optimizing the ionization signal from fs probe + UVprobe. Assuming the CF is aligned with the fs probe, the UV probe will be closeto overlapping with the CF though this procedure only gets one close to alignment.The final vertical adjustments should be done in VMI mode looking at a particularwavelength where only rotational excitation will be observed, like 285.94 nm forthe CF truncated to 10 nm/arm, until the signal is maximized.58Chapter 5Experimental Results5.1 Direct Measurement of Molecular Orientation5.1.1 Kick Alignment as a Benchmark ExperimentThere have been studies already conducted on impulsively aligning molecules em-bedded in helium nanodroplets[10][40][9][36]. While many of these moleculeswould be difficult to spin with the CF because they are heavy or not linear, thekick technique can still be used for rotational excitations and as a benchmark ex-periment to compare to the work done in droplets already. Fortunately, we caneven compare with a molecule that will also spin well in the CF - CS2. If we canmeasure a response in the alignment of this molecule with a kick, we will know thatdoping conditions are good and the droplet beam is produced sufficiently well forCF experimentation since the results are known. With kick alignment, the timescaleof the excitation is important. As previously described, the helium nanodroplet canact as a bath that counteracts rotational excitation (similar to centrifugal distortion).This can also act as a sort of barrier or “rotational speed limit” for superfluidity. Ifthe molecule can be spun fast enough to reach this barrier before the nanodropletcan equilibrate this rotational energy with phonons, the molecule “breaks free” fromthe helium bath and can spin without friction[10]. When measuring the molecularorientation of the molecule as quantified by < cos2 θ2D >, we would reproduce theoscillations measured in [10] whose behaviour is qualitatively shown in Figure 5.159with respect to the free particle, or gas phase, behaviour. The oscillations have aperiod of about 60 ps and almost totally decay by the time the full alignment revivalis expected at 152.9 ps, as calculated according to Equation 2.29. These features areentirely washed out by the helium nanodroplet interactions. It was also found thatif the fluence was too high, the oscillations would die out which is different fromthe gas phase behaviour where the alignment would be stronger, since the numberof J states populated is proportional to the fluence. This would also act as a way tocalibrate the actual intensity in the interaction region and be useful to distinguishbetween an effusive background signal and a doped droplet signal.It is not clear if the CF will be able to excite the molecule fast enough to al-low it to spin freely. We don’t know if we should look for small changes in planarconfinement or if the lack of a large change indicates a problem. The idea of usingboth the kick alignment pulse and the CF pulse is to compare an effect that is knownto the new effects excited by the CF in droplets, and therefore, in the marginalconditions of the experimental apparatus. Besides the background in the detectionregion, the other major hurdle is the interplay between ease of spinning a moleculewith the centrifuge and the degree to which the molecular fragments will scatterwith the helium droplet atoms upon Coulomb explosion. The centrifuge spins lightdiatomic molecules, like N2 and O2, very well in a molecular jet but these moleculeswill have their initial orientation inside the droplets lost upon Coulomb explosion.Larger, heavier molecules are also spun well by the centrifuge but can sometimesbe ionized by the centrifuge alone giving rise to an anisotropic background signal,like with CS2, for example. These molecules will maintain their initial orientationwithout recoil from collisions, but it can make interpreting results less clear due tothat anisoptropic ionization. This forces “a race to the bottom” where the signalis lowered by making the droplets smaller, making the CF less intense, and bytruncating the centrifuge so that only small changes in 〈cos2 θ2D〉 are expected.The gas phase dynamics had to be reproduced in our set up before moving tonanodroplets and this was explored for the original heavy CS2 rotor and also lightrotors like N2 and O2 in order to extend the original study of [10]. To recover theexpected behaviour of our light rotors, a ≈90 fs kick pulse was used because they60Figure 5.1: An illustrative sketch of the dynamics of CS2 doped helium nan-odroplets found in [10] in comparison to their gas phase kick dynamicsfound in [27]. This highlights how the helium interactions change theresponse of the rotor to the kick alignment pulse. The gas phase CS2molecules go through alignment/anti-alignment peaks and show charac-teristic half and full revivals at 76.5ps and 152.9ps, respectively, whereasthe response of the CS2 doped helium droplets look like an exponentiallydecaying sinusoid with a period that is less than the half revival time.The difference in the dynamics will be extremely useful in distinguishingthe background (gas phase, revivals) to the signal (droplet, oscillations)response.have a much shorter rotational period and the pulses should have a correspondinglyfaster rise time to be non-adiabatic. The full revivals of these molecules are 8.4 psand 11.3 ps, respectively, which are close because of the similarity in their rotationalconstants. The results for N2 are shown in Figure 5.2 in comparison to CS2. Thevertical axis has the same scale to highlight the difference in response while thehorizontal axis changes to accommodate the different timescales. The absolutevalue of the peak alignment is expected to be closer to 〈cos2 θ2D〉 = 0.7 for bothmolecules[27][32]. The alignment in CS2 is not quite as expected, whereas the61behaviour of N2 is very good. For the experiment with CS2, a 300 fs pulse wasused and the jet was seeded using 5 bar and 60 bar of He. The max alignmentof 0.7 was achieved in the 60 bar jet and had a maximum anti-alignment dippingbelow 0.5 to 0.41. The 5 bar jet had a weaker response to the kick and oscillatedbetween 0.6 and 0.48 for the alignment/anti-alignment response. The change inresponse observed in the left plot of Figure 5.2 is close to the response observed forthe 5 bar expansion even though our experiment was done using 30 bar, which wasincreased from the normal 20 bar expansion and had a slight improvement. Thissuggests that our jet expansion is not cooling the CS2 molecules as effectively aspossible, which could be optimized by diluting the mixture further. The pulses weused were also much shorter at 90 fs and so the intensity was also very close tothe ionization threshold of the molecule. In order to limit the intensity, the beamdiameter could be adjusted before the refocusing lens in the vacuum chamber tomake the focal volume larger, since it was about the same as the probe. Whenthe pump beam is focused to the same size as the probe, this could lead to sam-pling a region not rotationally excited if the overlap is not perfect. As well, ifthe pump pulse is close to the intensity required to ionize the molecule this couldlead to ions being created along an anisotropic polarization vector that are notactually rotationally excited - or are but cannot be distinguished. This effect is seenin the shift of 〈cos2 θ2D〉 before the initial alignment from 0.5 to 0.55 at t = 0 in CS2.In addition to the above, in order to try and increase the maximum alignmentin CS2 and to move towards a pulse that could be used to reproduce the oscillationsin Figure 5.1, I attempted to use one arm of the centrifuge truncated to 15 ps. Thispulse would have less peak intensity in the focus and would still have a sharp enoughrise time with respect to the revival time (whereas it wouldn’t be fast enough tokick N2). The difference in behaviour is shown in Figure 5.3 at the full revival. Thefull revival is chosen to highlight field-free behavioural responses. The alignmentand anti-alignment was worse for the 15 ps kick. Without ionizing the moleculemore, the peak alignment could not be optimized to something more than ≈ 0.55,while 0.7 seems reasonable to expect based on the response of the molecule tosimilar pulses (or similar molecules to this pulse). Perhaps the alignment is smallfor the same reason as with the fs pulse - the molecules are not cooling efficiently62Figure 5.2: Left: Non adiabatic alignment of CS2 showing the initial align-ment along with the half and full revivals. This was collected froma seeded CS2:He jet expanded from 30 bar, gating the MCP to 25 nsaround S+, and the VMI set at VR = 4500 V, VE = 3230 V, VMCP = 815 Vand the Phosphor Screen = 4300 V. The ions were excited by a pumppulse with a fluence of 12 Jcm−2 (ω0 = 6 µm) and ionized with a probeof intensity 7.2 ∗ 1014Wcm−2 (ω0 = 6 µm, τ = 90 fs Gaussian pulse).Right: Non-adiabatic alignment of N+ showing the behaviour up totwo full revivals from the initial alignment. This was collected from apure N2 jet expanded from 20 bar, gating the MCP to 20 ns around N+,and the VMI set at VR = 4500 V, VE = 3230 V, VMCP = 815 V and thePhosphor Screen = 4300 V. The ions were excited by a pump pulse witha fluence of 7 Jcm−2 (ω0 = 6 µm) and ionized with a probe of intensity1.2∗1015Wcm−2 (ω0 = 6 µm, τ = 90 fs Gaussian pulse).in the seeded mixture because the concentration of CS2 is too high. This, of course,wouldn’t be an issue in the helium nanodroplets. It is not clear if the behaviourwould be proportionally worse in droplets and that the oscillations would be muchsmaller because a “gentle” kick is required to see the oscillations at all.Without a direct comparison in the gas phase experiment, it seems the best wayforward is to move to the helium nanodroplet measurements. Before doing thisbenchmark experiment, it would be good to measure the alignment at the full revivalwhile varying the signal to background. This means diluting the seeded gas mixture(and seeing if this indeed does improve the alignment) to a level that is about afactor of 1000 less in number density in comparison to a pure molecular beam while63Figure 5.3: Non-adiabatic alignment of CS2 using a 15 ps and 90 fs pulse. Thecollection parameters for the fs pulse are the same as in Figure 5.2. Forthe ps pulse, the VMI collection parameters are the same but the jet wasexpanded at 20 bar and the fluence was increased to 36 Jcm−2 (ω0 =8 µm) to try and increase the maximum alignment. The probe intensitywas set to 2.9∗1015Wcm−2.adding background gas that is appropriate to doping a helium nanodroplet. Thistype of study is described in detail in Section 5.2.2 and should be repeated here toensure the sensitivity is sufficient to extract the alignment effect from the signal tobackground (S:B).5.1.2 Planar Alignment with the Optical CentrifugeSimulation and TechniqueAs already discussed, the nested configuration of the vacuum chamber leads to aneffusive background of the dopant gas in the detection region of the VMI system.The dopant gas pressure, and therefore background gas signal, is determined bywhat pressure will give singly doped droplets. This is a maximum of about 30% ofall droplets, but is normally chosen to be less in order to minimize the amount ofdoubly and triply doped droplets. In order to determine whether or not the chosen64metric of planar confinement, < cos2 θ2D >, can be measured for some ion fragment,we need to understand the effects that the background gas has on measuring theplanar confinement. In order to do that, we can study a Monte Carlo simulationof different ion images and compare the ion images measured from a O2 jet andbackground gas in order to simulate the conditions that occur for helium droplets.The purpose of this study is to validate the technique and to indicate what alterationsin the data collection parameters (pressure, time, etc) need to be made in order toimprove the measurement. Improving the measurement means recovering a smallchange of < cos2 θ2D > in a reasonable amount of time.In order to recover the signal the “beam on” 〈cos2 θ2D〉 from the ion image wastreated as a distribution composed of the signal and the background with someweight. Then, measuring the beam off (background) distribution, the signal contri-bution could be determined with the following formula:〈cos2 θ2D〉S+B = F〈cos2 θ2D〉S+(1−F)〈cos2 θ2D〉B〈cos2 θ2D〉S = (NS+B〈cos2 θ2D〉S+B−NB〈cos2 θ2D〉B)(NS+B−NB) (5.1)where F is the weight and can be described by the ratio of the number of ions of thesignal or background to the total number of ions measured, NS/NS+B for example.The error bars are added to the measured variables by bootstrapping the ions (randomsampling with replacement) to create different distributions of 〈cos2 θ2D〉. The meanand standard deviations are the estimate for the populations true mean and standarderror. Reporting the error on 〈cos2 θ2D〉S is done by propagating this error accordingto:δ 2〈cos2 θ2D〉S = δ2CS =dCSdNS+B2δ 2NS+B +dCSdNB2δ 2NB +dCSdCS+B2δ 2CS+B +dCSCB2δ 2CB (5.2)where 〈cos2 θ2D〉 has been shortened to C for readability. In general, shrinking errorbars is done by collecting more data and using the central limit theorem to state thatthe fluctuations should go like√N =√Rt, where N is the number of ions detected,R is the count rate, and t is the collection time. When looking at the standard error,65we divide by this number so the error will shrink. An important assumption is thatthe count rate is constant and there are no large fluctuations during the collectiontime such that the number of ions detected can no longer be modelled as a Poisso-nian distribution. For this type of distribution, the mean is N, the standard deviationis√N, and it approaches a Gaussian distribution as N becomes large. This is anexperimental point that helps set the collection time appropriately small for eachbeam on/beam off cycle.The S:B ratio is measured by looking only at the ions that affect the measurementof 〈cos2 θ2D〉. This means in some radial bin that corresponds to the appropriateCoulomb channel (energy range). Assuming, in the large number limit, that the S:Bratio can be represented by the ratio of two Gaussian distributions, there cannot beany error bars calculated because that ratio is a Cauchy distribution whose momentsare undefined.The purpose of representing the data this way is to show a difference betweenthe mean value of the signal 〈cos2 θ2D〉 values and the background 〈cos2 θ2D〉. Thisis why we use standard error for the error bars. To be complete in our analysis, thep−value should be calculated to determine whether or not the difference betweenthe means is statistically significant at the 95% confidence interval. This was calcu-lated by generating a null hypothesis of ions distributed isotropically in the sametechnique described below from a sample size of 200,000 for a one-sided tail test.The S:B was 3±5 and the measured 〈cos2 θ2D〉 was 0.505±0.058.Ions were randomly generated in pairs to compose ion images that would be similarto a CS2 molecule. This means that there was 6 eV of rotational energy (RE) addedto 3 eV of CE energy to give the total energy (TE), where the radii distances wereset according to the MCP calibration outlined in Section 4.1.1. Figure 5.4 depictsthe main parameters of the simulation that were changed. The angular width isthe degree of confinement but it could also have to do with ionization channel ordynamic alignment from probe. In the simulation, two ions are generated 180 degfrom one another (assuming the axial recoil approximation and a linear molecule)and are chosen from around 0 deg along the x-axis based on a Gaussian with the66Figure 5.4: Simulating an Ion Image. The import parameters is the angularwidth and rotational energy of the rotating ions created. This will directlychange 〈cos2 θ2D〉 measured. Another important parameter is the separa-tion of the signal and the background due to the difference of velocities.Seeded jets travel at 1500 ms−1 and droplet beams travel at 200 ms−1to 400 ms−1.angular width. This is tuned to give some 〈cos2 θ2D〉 when there are no backgroundions. There is also an option to add some recoil width that randomizes where the“pair” ion is generated, but this is not considered in the following results. The radialwidth is chosen to represent a cross section of a few of the velocity spherical shellsand the poor resolution of the raw image process. It was chosen to be a Gaussianspread since, in terms of vectorial velocity, the Boltzman distribution is Gaussian(whereas the speed is a Chi distribution). So the radial width, R(r), is then randomlysampled from a distribution of the form:R(r) =1σR√2pie−(r−µR)2)2σ2R (5.3)where µR is where the radius should be based on the input energy, calculated from√T E/C, and σR is the channel resolution. For example, for the null distribution CE= 3 eV, RE = 3 eV, and C = 2.064∗10−4eV/pix2 so TE = 4.25 eV and µR = 143.64.Although the measured experimental resolution would be≈0.9 eV at this energy, σRis typically chosen to be smaller in order to decouple physical effects and the effectof the detector. For the null distribution it was set to σR = 0.02. The backgroundwas shifted with respect to the center of the image based on how fast the jet should6730 h Collection Time 3 h Collection TimeS:BTrue〈cos2 θ2D〉 Smallest〈cos2 θ2D〉p value Smallest〈cos2 θ2D〉p value101 0.51 0.511±0.004 0.003 0.528±0.007 0.00003100 0.51 0.513±0.006 0.02 0.59±0.04 0.0110−1 0.56 0.56±0.02 0.001 0.70±0.05 0.0000310−2 0.72 0.7±0.1 0.02 N/A N/ATable 5.1: Table describing background subtraction sensitivity and collectiontime for 95% confidence intervals (p < 0.05 is significant) with respect toa null distribution of 〈cos2 θ2D〉= 0.5.be moving, and in this case, assumed to be an isotropic distribution. Alternatively,the distribution could have the same angular width as the signal but be shifted.The total number of ions used in the simulation is what dictates the data collectiontime, and was calculated assuming a (low) count rate of 3 ions per frame. Thisis important so that ions do not overlap for peak counting which would result inerrors in the counting algorithm (saturation effects). As well, the trajectories of theparticles could be distorted if there were space charge effects from multiple ionsbeing created at the same time[50].Table. 5.1 shows the simulated results for distributions equivalent to two dif-ferent times of data collection for various S:B ratios. The smallest 〈cos2 θ2D〉 meansthe significant level of the mean 〈cos2 θ2D〉 measured for the signal is differentfrom the null hypothesis within 95% confidence intervals. So, with p < 0.05, themeasurement is different than an ion image with 〈cos2 θ2D〉= 0.505. The lower theS:B, the bigger 〈cos2 θ2D〉 has to be before the measurement is significantly differentfrom something isotropic. When S:B is high, smaller differences can be resolvedfor the equivalent experimental time. Note that if N/A is the result, it means theerror bars were too large to resolve any difference from the background. Theseresults show that if we want to measure 〈cos2 θ2D〉= 0.7, we can do so in 3 h (≈ 3million ions) of data collection when the S:B is 10−1. If S:B is 10−2, we would need30 h (≈ 31 million ions). The data collection time is determined using the 3 ion-68s/frame with a collection speed of≈ 97 fps to give the total number of ions collected.The collection speed is determined by the laser repetition rate and camera frame rate.From the simulation results of in Table. 5.1, it seems that 〈cos2 θ2D〉 is a goodmetric to measure the planar confinement in droplet like conditions. However, theystill needed to be experimentally verified and this is discussed in the followingsection.ExperimentIn various S:B conditions, 〈cos2 θ2D〉 was measured in an O2 jet using the imagesubtraction technique discussed in the previous section over 1 h and 3 h. The S:Bwas varied by adding more effusive background gas through the doping chamberto a pure molecular jet of O2. The “true 〈cos2 θ2D〉” expected was 0.57 and 0.864.They were measured in the case with no added background gas over 3 h using theCF and probe.Analyzing Figure 5.5 suggests that these techniques are successfully recover-ing the signal since the percent difference is less than 10% and the error bars aresmall. As the S:B approaches 10−1 the error bars grow and the mean shifts furtheraway from the true value, though the error bars do not blow up. This would beinterpreted as both techniques working to recover this signal. However, the errorbars are too small to cover the systematic error. The drift of the mean value of〈cos2 θ2D〉 away from the true value doesn’t necessarily suggest that the backgroundis high enough to cause an error. The probe overlap with the centrifuge can drift andactually cause a lower value of 〈cos2 θ2D〉 than expected. In other words, althoughthe mean drifts from the true value measurement in “ideal conditions” as the back-ground is increased, we may be recovering the proper 〈cos2 θ2D〉. In other words,the error is actually in the definition of true 〈cos2 θ2D〉. Since this effect didn’t causethe error bars to blow up, we conclude that the drift doesn’t affect the measurementsover the timescale of 1.5 hours.69Figure 5.5: Left: The image subtraction results for 1 hour of measurements(30 minutes per pump/probe delay) and for 3 hours of measurements(1.5 hours per pump/probe delay). Right: The accuracy (or percent dif-ference) between the measured value and the true value. 10% differencewould need error bars of 0.06 and 0.09 for 0.570 and 0.864 to cover thedifference of means. As well, the measurements capture the true valuebetter for the 3 hr measurements (red and pink points) except for the 3 hrmeasurement with low S:B. See below for discussion.After this confirmation of the technique, we moved to a CS2 doped droplet beamusing only the probe polarized perpendicular to the TOF path. This was done todecouple any effects (or lack thereof) due to rotation. These results are illustratedin Figure 5.6 and seem to be successful - we measured 〈cos2 θ2D〉= 0.651±0.005which is around the expected value of 0.7-0.75 (the 〈cos2 θ2D〉 of S+ in the seededjet using the probe). In fact, in the beam on image (containing both signal and back-ground) 〈cos2 θ2D〉= 0.73, and so measuring 0.651 would be an effect of scatteringwith the helium nanodroplets after ionization. Our ability to extract this value is inagreement with the simulations from Table 5.1 because the S:B = 0.1−0.6 and thechange in 〈cos2 θ2D〉 ≥ 0.2.From this positive result, we decided to proceed to the experiments with theCF. With considerations for ionization from the CF pulse and field alignment, the CFwas truncated to 30 ps. This length of CF should excite molecules to 〈cos2 θ2D〉≈ 0.6as measured in the seeded molecular jet with no added background, so if the helium70Figure 5.6: Image subtraction technique used to extract the signal. Left toright: Beam On = Doped droplets and background, Beam off = back-ground, BS = Beam On - Beam Off. The red rings indicate the regionconsidered for measuring 〈cos2 θ2D〉 and correspond to the energy range0.5 eV to 2.5 eV, which was chosen because helium droplets shiftedthe kinetic energies to lower values, or the center of the image. In BS,〈cos2 θ2D〉= 0.651±0.005 and in Beam On/Beam Off 〈cos2 θ2D〉= 0.73.In contrast, the purple rings show the typical region measured for aseeded molecular jet experiment and correspond to an energy range of6.3 eV to 8.3 eV. There were much fewer counts in the BS image, and〈cos2 θ2D〉= 0.66±0.03.interactions are strong the signal will have 〈cos2 θ2D〉< 0.6. Based on the simula-tion and experimental verification of the technique so far, we would expect ≈3 h ofdata collection be enough to resolve the effect.The measurement is shown in Figure 5.8 with the CF working and the CF bro-ken for beam on (with droplets) and beam off (no droplets) measurements on theleft, and the signal calculations on the right. The signal calculations are very promis-ing and look like a result that indicates some rotation. The top panel shows thebehaviour of 〈cos2 θ2D〉 for the warm background gas with the CF working and theCF broken. When the CF is broken, there is no planar confinement and with the CFworking 〈cos2 θ2D〉 ≈ 0.6. On the bottom panel, the signal in droplets is plotted.The broken CF gives some alignment effect that decays away after the pulse is gone,as does the working CF. The working CF has strong planar confinement that lastsabout 10 ps longer than the broken CF. This would be expected if we did not rotatethe molecules fast enough and the alignment decayed away. From the plot on theleft, we can conclude that we are successfully measuring an anisotropic effect in71the signal that is statistically different from the background, at least during the CFexcitation pulse. However, we do not know if this is just an effect of alignmentsince the behaviour between the broken CF and working CF are so similar.The problem with interpreting these results is that the broken CF excites anFigure 5.7: Example of the anisotropic effect that the broken CF has in com-parison to the working CF in a molecular jet experiment of O2 expandedat 20 bar. In molecular jet experiments, we know that the CF is workingto spin molecules because there is a lasting effect past≈100 ps, but at thebeginning between 0 ps to 20 ps it is difficult to distinguish. Collectedwith the full, untruncated CF set to 1.3 ∗ 1013Wcm−2 (average energy2.1 mJ) and the probe set to 2.3∗1015Wcm−2 and VMI settings for O+at VR =4500 V.anisotropic effect during the pulse, as shown between 20 ps to 80 ps in Figure 5.7,which means that we cannot directly conclude that CS2 is rotating because thiscould be an effect of alignment. The strongest response in alignment is when thefield is present, and we do not know if we can resolve the decay accurately forthese time steps. In the previous study in Figure 5.6 we were only looking at an72alignment effect and our verification technique was only tested to distinguish againstan isotropic signal (no effect). The technique has not been characterized in a waythat we know we can reliably distinguish against two similar anisotropic signals.Outside of droplets in the molecular jet experiments the broken CF can elicit thesame type of response in CS2 or O2 that is typical of adiabatic alignment pulses,where the molecules are aligned while the field is present[27], though the pulse isshort and more like a kick, but there are no revivals. The circularly polarized lightrotates too quickly for the molecules to follow but the molecules are still pulled tothe rotational plane, as shown in Figure 5.7. We distinguish against this “alignment”effect by observing the lasting planar confinement, which can be seen by looking atthe lasting effect that is observed in the background signal on the left of Figure 5.8and clearly in Figure 5.7. We cannot do the same test in droplets though.There are some problems with the error bars in the signal calculation becausethey can get quite large when contribution above the background count is small(essentially dividing by zero). When the signal is stable, they are as shown inFigure 5.8, and are found via bootstrap sampling. This can make the brokenCF give a higher degree of anisotropy than the working CF that is statisticallysignificant. An example of this is shown in Figure 5.9. The curves plotted are〈cos2 θ2D〉workingCF −〈cos2 θ2D〉brokenCF . In the plot on the left, the variation be-tween 2 different runs on the same day are shown, along with the data consolidatedinto one run. In the plot on the right, the day to day variation is plotted. When∆〈cos2 θ2D〉> 0 this means the working CF has achieved more planar confinementor excited a more anisotropic signal than the broken CF. These plots highlight thevariance of the measurements whereas the error bars plotted are the standard errorand represent the statistical error in the average of the mean. The error bars do notcover the spread of the data and it seems that for reliability purposes, systematicerror should be accounted for in order to diagnose operational problems. This couldinclude accounting for changes in the doping chamber pressure or laser energychanges. As a note, the problem of the broken CF giving a higher 〈cos2 θ2D〉 wasmore prevalent in 20 ps and 10 ps CF which are not shown here, whereas the 30 psCF worked quite well.73Figure 5.8: Droplet Measurements with Centrifuge. The difference in thedroplet vs no droplet curves agrees with the conclusion from Figure 5.6 -we are successfully extracting a signal. However, if the signal disappearswe wouldn’t be sensitive to this in these measurements. These exper-iments were done for droplet conditions of TN =15 K and P0 =24 bar.The doping was set so that the CS2+ signal counted 2 ions/frame witha probe polarized perpendicular to the TOF axis with an intensity of2.9 ∗ 1015 Wcm−2(the ion gauge was broken). The CF was set to the6 nm/arm settings from Table 2.2 with an average energy of 0.5 mJ. Theprobe was polarized parallel to the TOF axis and had an intensity of2.9 ∗ 1015 Wcm−2. The VMI settings were VR = 4500 V, VE = 3230 V,VMCP = 850 V and the Phosphor Screen = 4300 V.In order to shrink the error bars data would have to be collected for longer,in line with the results from the simulation. In order to simulate more collectiontime, it is typical to use bootstrap sampling which we employed. However, that onlyworks if the system is behaving well and implementing this strategy was difficultbecause of drifts and fluctuations in the system. The error bars may underestimatethe true fluctuations of the system. We thought this was the case because we couldnot reproduce the results of Figure 5.8 reliably. Maintaining a steady doping cham-ber pressure was problematic because of the long line leading up to the back ofthe skimmer and because CS2 is a liquid, meaning we rely on the vapour pressurefilling up the line and being constant. We tried to stabilize this by placing the smallvial of CS2 connected to the system into a water bath so that room temperaturefluctuations have a smaller effect. This source is also being constantly consumed,74Figure 5.9: A dissection of the results plotted in Figure 5.8 for the 30 ps CF.Left: Variance of the data in one day over subsequent data collectionruns. Right: Variance of the data day to day.which means the experiment needs to be stopped at some point in order to proceed.We collect in such a way that the fluctuations can be “tracked” by the beam on/beamoff subtraction and we know that we are doing a good job of this if the ion count ratehas error bars that can be described by a Poissonian distribution (√λ ). These effectswere attempted to be minimized by increasing the diameter of the tubing (to preventcondensation and pressure pockets), which seemed to stabilize the partial pressureof the CS2 signal over the course of an hour, according to the RGA measurementsdone in the Science Chamber with the doping chamber filled. However, this doesn’tchange what happens to the signal when the doping chamber pressure changes evena small amount - if it increases then the droplets can pick up more molecules andthis can destroy planar confinement or if it decreases than the signal disappearsaltogether. The doping chamber fluctuations could not be tracked at the time ofthese measurements externally because the ion gauge was broken. At the sametime, the CF and probe alignment drifts, seemingly as the mirrors heat up, and theexperiment needs to be stopped to adjust this as well. This is difficult to exactlyreproduce the same alignment since the background gas pressure is increased so theroom temperature planar confinement can be optimized. This effect is difficult tosee and then the system needs time to relax into steady state after this change butit would also be challenging and expensive to build a feed back system that could75maintain the beam alignment.From the results of Figure 5.8, we can conclude that the technique for isolating thesignal with respect to the background is working. We are measuring somethingstatistically different than the background. However, we cannot drawn conclusionsfrom the measurements regarding whether or not the molecules are rotating yetsince the effect must be small in comparison to the broken CF. More understandingof the broken CF behaviour is needed in order to use this as a method to discriminateagainst rotation. An intermediate study, before returning to droplets, could beperformed on a diluted jet using the broken CF and the working CF but truncatedto a different duration. If the broken CF behaves like a circularly polarized kick,the different dynamics should be clear on shorter timescales and this would allowus to discriminate between rotation and alignment. This study would then need tobe repeated in the low S:B limits expected in the droplet experience to confirm thatthe behaviour can be detected with our sensitivity. We may be at the limit of ourdetection sensitivity, but the results are promising!5.2 Direct Measurement of Angular Momenta5.2.1 Resonance Enhanced Multiphoton Ionization Spectroscopy ofCentrifuged OxygenThe REMPI spectrum of oxygen excited by the centrifuge has previously been in-vestigated by our group[24]. This technique used the CF to rotationally excite themolecule and then use a resonant probe to excite a transition between the groundstate, X3Σ−g , and the excited state C3Πg. This is typically called a (2+1) REMPIprocess because 2 photons are used to excited the intermediate state C3Πg andanother photon is needed to ionized. A diatomic the term symbol characterizes theelectron spin and orbital angular momentum and is written as 2S+1ΛΩ, where Λ isthe projection of angular momentum on the molecular axis, S is the total electronicspin angular momentum, and Ω = Σ+Λ which is the sum of the projections ofelectron spin (Σ) and orbital angular momentum. In a simple rigid rotor, where only76the rotational structure is important because Λ= 0 and S = 0, the spectra is mucheasier to interpret because the peaks correspond to rotational transitions. Oxygen ismore complicated because the ground state has Λ= 0 and S 6= 0 and follows Hund’sb rule. This means the ground state is a triplet and that for each of these levels thereare 3 possible J states. The excited state has Λ= 1 and S 6= 0 and follows Hund’s arule. This means there are, again, three different sets of J states for each Ω= 0,1,2.The CF was used to control the rotational excitation of oxygen already for levelsbetween 0 and ≈ 120.By truncating the spectrum of the CF, accurate control of the final rotational state ispossible. In order to fit the excitations of each branch from the ground state, the CFtruncation can be scanned along with the photon energy of the nanosecond probeused to resonantly ionize the excited oxygen and the ions peaks can be fit to theexpected Fortrat. A 2D REMPI spectrogram was measured and analyzed in [24]and was the guide for our preliminary studies. One CF truncation scan is shown inFigure 5.10 in comparison to the nanosecond probe only. The horizontal axis is theenergy of the 2 photons used to excited the intermediate oxygen state convertedfrom the laser wavelength and the vertical axis is just the normalized intensity, withthe scans shifted in order to show the differences. The 6 nm/arm CF should be ableto rotate molecules to J ≈ 33, and one of the branches has a J = 34 transitions at69976.56 cm−1. The scan with no CF and just the nanosecond probe showed thatthe molecular jet has a temperature of 10 K and has a maximum rotational state ofJ = 6, which is located at 69620 cm−1. The location of these J states are marked inFigure 5.10. When the laser wavelength is resonant with one of these transitions,an ion signal can be measured. Seeing peaks between 69600 cm−1 to 70000 cm−1indicates that the CF is working and we are populating rotational states betweenJ ≈ 20 and 40. The clear difference in the two plots is a result of the CF workingand redistributing the initial ground state population to higher J states in the tripletbranches. These results were reproduced to have ensure that the detection andalignment were working and to allow us to chose strong transitions that could beused to study in helium nanodroplets.77Figure 5.10: Reproducing a slice of the 2D Spectrogram in [24]. The ionsignal was measured as a function of the nanosecond probe wavelengthfor the CF truncated to 6 nm/arm and without the CF. These scans weremeasured with an average energy of the nanosecond probe set to 500 µJat 287 nm and the average energy of the CF was 0.76 mJ. The MCP wasgated for O+ signal was collected with 100 averages of images takenwith 30 ms of exposure time. VR = 4500 V, VE = 3230 V, VMCP = 800 Vand the Phosphor Screen = 4300 V.5.2.2 Measurements Limiting the Signal to Background RatioUsing the predictions made for the doped helium beam density, oxygen was dilutedwith helium down to about a factor of 1000x less than in a pure jet. We did this inorder to determine if our detection technique was sensitive enough to recover thelow count rate in the high background using both the CF and probe to study a rota-tionally excited state and using just the nanosecond probe to study the dependencedecoupled from effects due to rotation.There are few ways to beat the background when processing an ion image: choose arotational state that can only be excited by the CF (not thermally) and observe thepixels in the ion image that correspond to the jet velocities or count long enough78to avoid the noise from image subtraction (and collect beam on/off). Becausethe helium droplets move slower than a supersonic jet; at 200 ms−1 to 400 ms−1depending on the expansion conditions, we cannot set a crop that would only corre-spond to the jet based on the velocity because of the background. The most probablevelocity according to the Maxwell Boltzmann distribution is given by:vmp =√2kBTM(5.4)where M is the mass in kilogram and T is the temperature of the reservoir in kelvin.For oxygen, vmp = 393 ms−1. This means that the jet spot, easily identifiable in amolecular jet experiment, will lie within the background spot and be impossible toreliably identify. So, we cannot use velocity to discriminate against the background,but it may be possible to discriminate against the background using rotational exci-tation.Figure 5.11 shows the triplet branch of the ground state in oxygen, cold fromexpansion in a molecular jet, in comparison to warm effusive gas leaked into thescience chamber. The cold jet was measured using the normal 20 bar expansionthrough the nozzle at room temperature and the warm distribution was measured byblocking the jet and leaking in a lot of gas into the doping chamber so that the sci-ence chamber increase was 3.32∗10−7torr. The spectra are much different becauseat room temperature, when higher rotational states are populated, the bandheadin O2 becomes apparent. The bandhead exists because the rotational constant isdifferent for excited states (B→ Bν ) and the spectral lines bunch together. Thismeans the spacing is not linear and that the next J state may actually be lowerin energy [19]. This is why the spectra from the warm sample looks only a littlebit broader than the spectra from the jet although many more rotational states arepopulated.Ideally, the CF would excite the molecules to J > 21. Because the moleculesstarts out cold and in the ground rotational state, more of them will be capturedby the CF in comparison to the molecules rotating 10 < J < 21, for example. Nota lot of this population will be transferred to higher J states by the CF and so the79ion signal will be much less there. The molecular jet is 10 K whereas the inside ofhelium nanodroplets will be 0.4 K.In molecular jet experiments, it was very useful to use wavelength and rotation toFigure 5.11: Cold Oxygen, 10 K in blue, vs Warm Oxygen, 298 K in red.Ionization signal from the nanosecond probe only set to an energy of500 µJ at 287 nm. The cold distribution is from 20 bar expansion ofpure O2 and the warm distribution is from adding 3.32∗10−7torr O2to the science chamber via the doping chamber. VR = 4500 V, VE =3230 V, VMCP = 1000 V and the Phosphor Screen = 4300 V.discriminate against the background. Moderately truncating the CF and observing aJ state that cannot be reached through thermal excitation (or background excitation)allowed us to observe a noise free signal when the jet density was reduced by afactor of 0.039. These results are shown in Figure 5.12 for a molecule excited bythe 7 nm/arm CF (≈ 38} truncation) and the diluted O2 jet had no background gasadded. The signal is diluted by adding more Helium gas and the dilution level iscompared to a pure jet of oxygen. The ion signal is recorded using peak counting,so the noise level is low and ≈ 1 ion over the course of the measurement. Thisexperiment was only done for a dilution level of 0.039, whereas a level of 0.005380is the dilution level expected to compare to a droplet experiment. As well, thistechnique relies on our ability to actually rotate molecules that are embedded inhelium and we don’t know if this will happen yet (or if it will be excited to the sameJ state). However, this served as a good preliminary study since the sensitivity canbe increased by increasing the collection time without increasing the noise. Thismeans we can detect a background free CF signal that is 100x less dense than themolecular jet and it has the potential to be pushed further to observing a signal thatis 1000x less dense like in the droplet experiment.In the worse case scenario, the molecules will not be rotating in a superfluidFigure 5.12: A peak counting experiment observing the ion signal theCF+probe truncated to 7 nm/arm (≈ 38}) as a function of decreas-ing O2 density and the probe was set to λ =285.26 nm. A total of 1500frames (at 50 Hz, ¡1 min of collection time) were collected for eachdata point and the MCP was gated to observe the O2+. VR = 4500 V,VE = 3230 V, VMCP = 800 V and the Phosphor Screen = 4300 V. Thediluted gas was expanded through the nozzle at room temperature withP0=20 bar.environment and so the CF will not be able to excite the high rotational levels thatare easily distinguishable from the warm background. This means studying resonantpeaks that are within the warm distribution of Figure 5.11 instead of outside of81it. In order to recover this signal, we will have to rely on our ability to increasemeasurement time and do background subtraction. Towards this direction, 5 mea-surements were taken at wavelengths near the middle triplet peak of oxygen. Theseare shown in Figure 5.13. At the transition corresponding to a two photon energyof 69420 cm−1 in the middle of the triplet (the J′ = 2← J = 0 transition of the F2branch for N = 1), a pure molecular jet of oxygen (signal dilution = n/nMJ = 1)has ≈ 104 counts in 10,000 frames, or 3.5 min of collection time. As the signaldensity was lowered by an order of magnitude, the ion signal also decreased byabout an order of magnitude. When a dilution was reached that was equivalentto the number density expected in the helium nanodroplet experiment, effusivebackground gas was added to simulate dimer doping (the purple dot). The error barsadded are the 1 standard deviation value between 5 different measurements. Whenthe beam is blocked and the effusive background gas is still there, we measure theblue dotted line which is plotted to show the difference between beam on and beamoff. With these few statistics, we can see that there is a clear difference betweenbeam on and beam off and we can tentatively conclude that we are successfullymeasuring the O2+ signal from the doped droplets since the ion signal from theeffusive background is negligible.This technique is confirmed to be working in the molecular jet but at the time of thisthesis, no signal was recovered in nanodroplets. This could indicate that the dropletdensity is much lower than expected. This could be the case if the droplets with 5000atoms are not forming, which we assume in the density calculations. If the beamis less dense than expected, a different detection technique should be employedbecause it is near it’s limit of sensitivity. However, the collection time should beincreased and the doping pressure can be increased to verify the presence of somesignal to diagnose this problem but was not pursued here. Regardless, the sensitivityof the REMPI technique has been demonstrated to be capable of recovering an O2+ion signal that is 1000x less dense than what is measured in a pure molecular jetfrom a background ion signal that is comparable to what is present when doublydoping helium nanodroplets.82Figure 5.13: Using the nanosecond probe only, the transitions were investi-gated by lowering the signal density and added background gas. Ourdetection set up was sensitive enough to capture a small signal 0.0007times lower than a pure molecular jet.83Chapter 6ConclusionIn this work, techniques were developed that would allow the rotational excitationof molecules in helium nanodroplets to be studied using an optical centrifuge. Thedetection limitations in this unique droplet machine were characterized and address-ing these limitations will be the first step in pushing the project forward.Two different experimental techniques were proposed: direct measurement of molec-ular orientation and direct measurement of angular momenta. These were exploredfor two different rotors (heavy and light) that are expected to have a different typeof interaction with the helium environment. For the molecular orientation techniquethat used VMI, the 〈cos2 θ2D〉 signal was measured down to a S:B ratio of 10−1 andsuccessfully recovered 〈cos2 θ2D〉 = 0.57. When the S:B reaches 10−2 problemsstart to occur in the signal recovery and we are only sensitive to larger changes in〈cos2 θ2D〉. Using this technique, a CF pulse that had a value of 〈cos2 θ2D〉= 0.6 ina CS2 molecular jet was applied to CS2 doped helium nanodroplets, but no lastingrotation was observed. For the angular momenta technique that used REMPI, theion signal was measured in a seeded jet of O2 for one of the ground state triplettransitions. The O2+ signal from this transition range was measured while the jetwas diluted with more helium to 0.0007x the pure O2 jet, whereas a decrease innumber density to the droplet experiment is 0.0053x.This work explored different options to study superfluidity and proposes an outline84for the future investigation. This means using two different “calibration” or “bench-mark” experiments that we realized are crucial to interpreting results.The first experiment to implement and understand is the kicked rotor in heliumnanodroplets. This is the most efficient experiment to start with because it ensuresthat an appropriate operating point of the droplet machine can be achieved that willreproduce the results from conventional droplet machines. Chamber modificationsmay need to be made and these are time consuming because of the pump downtime required to eliminate background gases. This gives proof that the system isstable enough to measure over the time needed to recover the signal. It will alsodemonstrate any discrepancies that may result due to the set up since it can bedirectly compared to understood physical behaviour.The second experiment that needs to be performed is the calibration of the broken CFusing REMPI spectroscopy. This allows an in-situ characterization and correlationbetween the J state measured (or depleted) and 〈cos2 θ2D〉 which we only had accessto indirectly before (through Raman in a different gas chamber). This will allow usto discriminate more confidently against rotation with the broken CF, since thereare some alignment effects during the field, and could ultimately allow the decayof rotational excitation to be characterized. This can be done in a seeded gas jetinitially and will directly give the dependence of 〈cos2 θ2D〉 on the excited J states(rotational wavepacket).In conclusion, we are producing some droplets despite the unconventional vac-uum system. Some preliminary measurements have been done, but more sensitivetests are required to understand the superfluid nature inside the nanodroplets.85Bibliography[1] E. Andronikashvili. A direct observation of two kinds of motion in helium ii.Journal of Physics, USSR, 10:201, 1946. → page 1[2] P. Atkins and R. Friedman. Molecular Quantum Mechanics. OxfordUniversity Press, 5th edition, 2011. → page 4[3] C. A. Balanis. Antenna theory: analysis and design. Wiley, 4th edition, 2016.→ page 8[4] M. Bitter. Quantum coherent control of laser-kicked molecular rotors. PhDthesis, The University of British Columbia, 2016. → pages 8, 10, 14[5] N. B. Brauer, S. Smolarek, E. Loginov, D. Mateo, A. Hernando, M. Pi,M. Barranco, W. J. Buma, and M. Drabbels. Critical Landau velocity inhelium nanodroplets. Physical Review Letters, 111, 2013.doi:10.1103/PhysRevLett.111.153002. → page 3[6] A. Braun. Photodissociation studies of CH3I and CF3I in fluid 4HeliumNanodroplets. PhD thesis, Ecole Polytechnique Federale de Lausanne, 2004.→ pages 45, 46, 47, 49[7] H. Buchenau, E. L. Knuth, J. Northby, J. P. Toennies, and C. Winkler. Massspectra and time-of-flight distributions of helium cluster beams. The Journalof Chemical Physics, 92, 1990. doi:10.1063/1.458275. → page 21[8] O. Bu¨nermann. Spektroskopie von Alkali- und Erdalkaliatomen, - moleku¨len,Alkaliclustern und Komplexen organischer Moleku¨le aufHeliumnanotro¨pfchen. PhD thesis, Universita¨t Bielefeld, 2006. → pagesx, 37, 38[9] A. S. Chatterley, C. Schouder, L. Christiansen, B. Shepperson, M. H.Rasmussen, and H. Stapelfeldt. Long-lasting field-free alignment of large86molecules inside helium nanodroplets. Nature Communications, 10, 2019.doi:10.1038/s41467-018-07995-0. → page 59[10] I. N. Cherepanov, G. Bighin, L. Christiansen, A. V. Jørgensen, R. Schmidt,H. Stapelfeldt, and M. Lemeshko. Far-from-equilibrium dynamics of angularmomentum in a quantum many-particle system. arXiv:1906.12238, 2019. →pages xii, 2, 59, 60, 61[11] L. Christensen, L. Christiansen, B. Shepperson, and H. Stapelfeldt.Deconvoluting nonaxial recoil in coulomb explosion measurements ofmolecular axis alignment. Phys. Rev. A, 94, 2016.doi:10.1103/PhysRevA.94.023410. → page 44[12] C. Ellert, H. Stapelfeldt, E. Constant, H. Sakai, J. Wright, D. M. Rayner, andP. B. Corkum. Observing molecular dynamics with timed coulomb explosionimaging. Philosophical Transactions of the Royal Society A: Mathematical,Physical and Engineering Sciences, 356, 1998. doi:10.1098/rsta.1998.0168.→ page 44[13] A. T. J. B. Eppink and D. H. Parker. Velocity map imaging of ions andelectrons using electrostatic lenses: Application in photoelectron andphotofragment ion imaging of molecular oxygen. Review of ScientificInstruments, 68, 1997. doi:10.1063/1.1148310. → pages 44, 45[14] B. Friedrich and D. Herschbach. Alignment and trapping of molecules inintense laser fields. Phys. Rev. Lett., 74:4623–4626, Jun 1995.doi:10.1103/PhysRevLett.74.4623. → page 10[15] R. Fro¨chtenicht, J. Toennies, and A. Vilesov. High-resolution infraredspectroscopy of SF6 embedded in he clusters. Chemical Physics Letters, 229,1994. doi:https://doi.org/10.1016/0009-2614(94)01026-9. → page 1[16] M. A. M. Garcı´a. Optimization of voltages for spatial map imaging andvelocity map imaging. Master’s thesis, Center for Free-Electron LaserScience, 2017. → page 57[17] S. Grebenev, J. P. Toennies, and A. F. Vilesov. Superfluidity within a smallhelium-4 cluster: The microscopic andronikashvili experiment. Science, 279,1998. ISSN 0036-8075. doi:10.1126/science.279.5359.2083. → page 1[18] O. F. Hagena and W. Obert. Cluster formation in expanding supersonic jets:Effect of pressure, temperature, nozzle size, and test gas. The Journal ofChemical Physics, 56(5), 1972. → page 2187[19] R. Hanson, R. Spearrin, and C. Goldenstein. Diatomic Molecular Spectra,pages 9–49. 01 2016. ISBN 978-3-319-23251-5.doi:10.1007/978-3-319-23252-2 2. → page 79[20] A. Heidenreich, D. Schomas, and M. Mudrich. Dopant-induced ignition ofhelium nanoplasmas—a mechanistic study. Journal of Physics B: Atomic,Molecular and Optical Physics, 50, 2017. doi:10.1088/1361-6455/aa92da.→ page 38[21] F. D. Jan Harms, J. Peter Toennies. Density of superfluid helium droplets.Physical Review B, 58(6), 1998. → page 21[22] J. Karczmarek, J. Wright, P. Corkum, and M. Ivanov. Optical Centrifuge forMolecules. Physical Review Letters, 82, 1999.doi:10.1103/PhysRevLett.82.3420. → pages 2, 14[23] A. Korobenko. Control of molecular rotation with an optical centrifuge. PhDthesis, The University of British Columbia, 2016. → pages ix, 14, 15[24] A. Korobenko, A. A. Milner, J. W. Hepburn, and V. Milner. Rotationalspectroscopy with an optical centrifuge. Phys. Chem. Chem. Phys., 16, 2014.doi:10.1039/C3CP54598A. → pages xv, 54, 76, 77, 78[25] S. A. Krasnokutski and F. Huisken. Low-temperature chemistry in heliumdroplets: Reactions of aluminum atoms with o2 and h2o. The Journal ofPhysical Chemistry A, 115, 2011. doi:10.1021/jp112423v. → page 1[26] S. Kregel, G. Thurston, J. Zhou, and E. Garand. A multi-plate velocity-mapimaging design for high-resolution photoelectron spectroscopy. The Journalof Chemical Physics, 147:094201, 09 2017. doi:10.1063/1.4996011. → page51[27] V. Kumarappan, S. S. Viftrup, L. Holmegaard, C. Z. Bisgaard, andH. Stapelfeldt. Aligning molecules with long or short laser pulses. PhysicaScripta, 76, 2007. doi:10.1088/0031-8949/76/3/n09. → pages xii, 61, 73[28] Y. Kwon, P. Huang, M. V. Patel, D. Blume, and K. Whaley. Quantumsolvation and molecular rotations in superfluid helium clusters. The Journalof Chemical Physics, 2000. → page 2[29] M. Lemeshko. Quasiparticle approach to molecules interacting with quantumsolvents. Phys. Rev. Lett., 118, 2017. doi:10.1103/PhysRevLett.118.095301.→ page 288[30] M. Lemeshko and R. Schmidt. Molecular impurities interacting with amany-particle environment: from ultracold gases to helium nanodroplets,page Low Energy and Low Temperature Molecular Scattering. 2016.doi:10.1039/9781782626800-00444. → page 2[31] I. MacPhail-Bartley, A. Milner, W. Wasserman, and V. Milner. Laser controlof molecular rotation: Expanding the utility of an optical centrifuge. 12 2019.→ pages ix, 3, 9, 10, 14, 15, 17[32] M. Meckel. Strong-Field Ionization of Aligned Oxygen. PhD thesis, Institutfur Kernphysik Johann Wolfgang Goethe Universitat Frankfurt am Main,August 2006. → page 61[33] A. A. Milner, J. A. M. Fordyce, I. MacPhail-Bartley, W. Wasserman,V. Milner, I. Tutunnikov, and I. S. Averbukh. Controlled enantioselectiveorientation of chiral molecules with an optical centrifuge. Phys. Rev. Lett.,122, 2019. doi:10.1103/PhysRevLett.122.223201. URLhttps://link.aps.org/doi/10.1103/PhysRevLett.122.223201. → page 3[34] J. Oberheide, P. Wilhelms, and M. Zimmer. New results on the absolute iondetection efficiencies of a microchannel plate. Measurement Science andTechnology, 8:351, 1999. doi:10.1088/0957-0233/8/4/001. → page 47[35] H. Pauly. Atom, Molecule, and Cluster Beams I: Basic Theory, Productionand Detection of Thermal Energy Beams, volume 28. Springer BerlinHeidelberg, 2000. doi:10.1007/978-3-662-04213-7. → page 27[36] D. Pentlehner, J. H. Nielsen, A. Slenczka, K. Mølmer, and H. Stapelfeldt.Impulsive laser induced alignment of molecules dissolved in heliumnanodroplets. Phys. Rev. Lett., 110, 2013.doi:10.1103/PhysRevLett.110.093002. URLhttps://link.aps.org/doi/10.1103/PhysRevLett.110.093002. → page 59[37] J. D. Pickering, B. Shepperson, L. Christiansen, and H. Stapelfeldt. Alignmentof the CS2 dimer embedded in helium droplets induced by a circularlypolarized laser pulse. arXiv:1901.03184 [physics], 2019. → pages 40, 50[38] E. Polyakova. Multiphoton Ionization Of Molecules Embedded In SuperfluidLiquid Helium Droplets. PhD thesis, University OF Southern California, 2005.→ page 21[39] K. Schneider. Implementation and characterisation of a new shutter forhelium nanodroplet isolation spectroscopy. Master’s thesis, University ofFreiburg, 2017. → pages 29, 3089[40] B. Shepperson, A. A. Søndergaard, L. Christiansen, J. Kaczmarczyk, R. E.Zillich, M. Lemeshko, and H. Stapelfeldt. Laser-induced rotation of iodinemolecules in helium nanodroplets: Revivals and breaking free. Phys. Rev.Lett., 118, 2017. doi:10.1103/PhysRevLett.118.203203. → pages 2, 59[41] H. Stapelfeldt and T. Seideman. Colloquium: Aligning molecules with stronglaser pulses. Rev. Mod. Phys., 75, 2003. doi:10.1103/RevModPhys.75.543.→ pages 13, 44[42] M. Stei, J. von Vangerow, R. Otto, A. Kelkar, E. Carrascosa, T. Best, andR. Wester. High resolution spatial map imaging of a gaseous target. TheJournal of chemical physics, 138, 06 2013. doi:10.1063/1.4807482. → page57[43] F. Stienkemeier and K. Lehmann. Topical review: Spectroscopy anddynamics in helium nanodroplets. Journal of Physics B-atomic Molecularand Optical Physics - J PHYS-B-AT MOL OPT PHYS, 39, 04 2006.doi:10.1088/0953-4075/39/8/R01. → page 1[44] R. Tanyag, C. Jones, C. Bernando, S. O’Connell, D. Verma, and A. Vilesov.CHAPTER 8: Experiments with Large Superfluid Helium Nanodroplets. 012018. doi:10.1039/9781782626800-00389. → pages ix, 20, 42[45] A. F. Toennies, J. Peter; Vilesov. Superfluid helium droplets: A uniquely coldnanomatrix for molecules and molecular complexes. Cheminform, 35(27),2004. → pages viii, 1, 21, 40[46] D. Townsend, M. Minitti, and A. Suits. Direct current slice imaging. Reviewof Scientific Instruments, 74:2530–2539, 2003. doi:10.1063/1.1544053. →page 45[47] J. Underwood, I. Procino, L. Christiansen, J. Maurer, and H. Stapelfeldt.Velocity map imaging with non-uniform detection: Quantitative molecularaxis alignment measurements via coulomb explosion imaging. The Review ofscientific instruments, 86, 2015. doi:10.1063/1.4922137. → page 45[48] X. Wang, J. Zhang, S.-A. Zhang, and Z.-R. Sun. Coulomb explosion of CS 2molecule under an intense femtosecond laser field. Chinese Physics B, 25,2016. doi:10.1088/1674-1056/25/5/053301. → page 47[49] W. W. Wasserman. Implementation of a mechanical shutter for studying thecritical velocity in superfluid helium nanodroplets. Master’s thesis, TheUniversity of British Columbia, 2018. → page 3090[50] B. J. Whitaker. Imaging in molecular dynamics : technology and applications: a user’s guide. Cambridge University Press, 2003. → page 68[51] D. Williams, editor. Molecular Physics: Methods of Experimental Physics,Part 2, volume 3. Academic Press, Inc., 2 edition, 1974. → page 19[52] C. Wu, Y. Yang, Z. Wu, B. Chen, H. Dong, X. Liu, Y. Deng, H. Liu, Y. Liu,and Q. Gong. Coulomb explosion of nitrogen and oxygen molecules throughnon-Coulombic states. Physical Chemistry Chemical Physics, 13, 2011.doi:10.1039/C1CP21345H. → page 47[53] S. Yang and A. M. Ellis. Helium droplets: a chemistry perspective. ChemicalSociety Reviews, 42(2), 2013. doi:10.1039/C2CS35277J. → page 19[54] A. Zhao, P. Sa´ndor, and T. Weinacht. Coincidence velocity map imagingusing a single detector. The Journal of Chemical Physics, 147, 2017.doi:10.1063/1.4981917. → page 5191
Thesis/Dissertation
eng
Physics
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Towards rotational control of molecules in helium nanodroplets
Text