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Manipulation of the motion of polyatomic molecules in the rotational ground state : microwave lens effect… Zhong, Wei 2013

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Manipulation of the Motion ofPolyatomic Molecules in theRotational Ground StateMicrowave Lens Effect by AC Stark Dipole ForcebyWei ZhongB.Sc., Wuhan University, 2011A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Physics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)October 2013c? Wei Zhong 2013AbstractThe main contribution of this project to the field of cold and ultracoldmolecules is we firstly demonstrated successful manipulation of the motionof polyatomic molecular beam in the rotational ground state, which hasthe lowest temperature of all possible states. Chapter 1 gives a summaryof this field, including the application of cold and ultracold molecules, themethods to obtain them, and each method?s advantages and disadvantages.Once we decelerate molecular ensembles, we would like to trap the coldand ultracold molecules in electric trap, megnetic trap and megneto-opticaltrap. Chapter 2 starts with an introduction of the concept of supersonicbeam and the basic knowledge of it, such as the specific features. Theexperimental setup will also be presented and explained in this chapter. Themain highlight of this project is that we are manipulating molecules in thereal ground state. Our molecular source is a Counter Rotating Nozzle(CRN),which can precool (or slow in alternate terminology) molecules in all statesincluding the rotational ground state. The principle and performance ofCRN will be presented and explained in Chapter 3. After obtaining a wellprecooled molecular beam, the microwave lens effect on various species ispresented in Chapter 4. Meanwhile, the principle of AC Stark shift, ACdipole force and the microwave standing wave modes, such as TE modes andTM modes, will be explained in this chapter as well. Finally, I?ll summarize,draw conclusion of this work and describe the future expectation of thisproject in Chapter 5.iiPrefaceStatement of relative contributionsThe construction of the experimental setup including the source chamber(Counter Rotating Nozzle), microwave chamber and detection chamber wasdone by Pavle Djuricanin. Some advice on the design of CRN came fromProfessor Frank Stienkemeier?s group and improvement was done by PavleDjuricanin. The microwave cylindrical tube was mainly designed by PavleDjuricanin, Katsunari Enomoto, Omid Nourbakhsh and Ilja Gerhardt. Thedetection chamber was designed by Pavle Djuricanin. The cooling system,liquid nitrogen tank was designed by Mr. Djuricanin, and was made byJorgen Hansen and Pritesh Padhiar at the Technical Services at UBC. Theion optics chamber was designed and assembled by Steffen Spieler. I didtheinitial analysis of molecular source beam features from CRN. The exper-imental parameters were optimized by Steffen Spieler, Pavle Djuricanin andI. I was responsible for conducting the experiments, improving the experi-ments, collecting and analyzing the data. The CH3CN lens effect simulationwith TM mode was done by Steffen Spieler. A notch filter was designed andmade by Steffen Spieler. I made and tested the shutter which improved thesystem vacuum. I carried on the simulation of CD3CN lens effect with TEmode based on previous work. The resulting publication[1] was written byProfessor Takamasa Momose.Publication arising from thesis workThis thesis work has produced the following publication:S. Spieler, W. Zhong, P. Djuricanin, O. Nourbakhsh, I. Gerhardt, K.Enomoto,F. Stienkemeier and T. Momose. Microwave lens effect for the J = 0 rota-tional state of CH3CN. Molecular Physics, 111:1823-1834, 2013iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Supersonic beam and experimental setup . . . . . . . . . . 32.1 Supersonic molecular beam . . . . . . . . . . . . . . . . . . . 32.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . 52.2.1 The shutter . . . . . . . . . . . . . . . . . . . . . . . 92.2.2 The rotor and nozzle . . . . . . . . . . . . . . . . . . 92.2.3 The microwave tube . . . . . . . . . . . . . . . . . . . 122.2.4 The detection . . . . . . . . . . . . . . . . . . . . . . 143 Molecular beam source: Counter Rotating Nozzle . . . . . 163.1 The principle of CRN in slowing molecular beams . . . . . . 163.2 Properties of molecular beams created by CRN . . . . . . . . 174 The microwave lens effect on polarized polyatomic molecularbeams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.1 The AC Stark shift . . . . . . . . . . . . . . . . . . . . . . . 244.2 The electromagnetic field resonant mode spectrum in the mi-crowave cavity . . . . . . . . . . . . . . . . . . . . . . . . . . 254.2.1 The TM01p field and induced AC Stark dipole forcedistribution . . . . . . . . . . . . . . . . . . . . . . . 25ivTable of Contents4.2.2 The TE11p field and induced AC Stark dipole forcedistribution . . . . . . . . . . . . . . . . . . . . . . . 284.3 The lens effect on CH3CN beam by AC electric field in TMmode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.3.1 The basic properties of CH3CN . . . . . . . . . . . . 324.3.2 The populations of CH3CN in |0, 0, 0? and |1, 0, 0?states . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.3.3 The AC Stark shift of CH3CN . . . . . . . . . . . . . 354.3.4 The experimental results . . . . . . . . . . . . . . . . 354.4 The lens effect on CD3CN beam by AC electric field in TEmode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.4.1 The basic properties of CD3CN . . . . . . . . . . . . 414.4.2 The AC Stark shift of CD3CN . . . . . . . . . . . . . 424.4.3 The experimental and simulation results . . . . . . . 424.5 Experimental lens effect demonstration of an acetone beamin TE mode . . . . . . . . . . . . . . . . . . . . . . . . . . . 535 Conclusion and future work . . . . . . . . . . . . . . . . . . . 54Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56vList of Figures2.1 Supersonic beam diagram . . . . . . . . . . . . . . . . . . . . 42.2 MW lens effect diagram . . . . . . . . . . . . . . . . . . . . . 62.3 Experimental setup schematic . . . . . . . . . . . . . . . . . . 82.4 The shutter under testing . . . . . . . . . . . . . . . . . . . . 102.5 The rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.6 The nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.7 The vibration with different frequencies . . . . . . . . . . . . 112.8 The copper cylindrical cavity . . . . . . . . . . . . . . . . . . 122.9 The TE11p mode spectrum . . . . . . . . . . . . . . . . . . . . 132.10 The ion-optics . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.11 The MCP detector . . . . . . . . . . . . . . . . . . . . . . . . 142.12 The nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.1 The Principle of CRN . . . . . . . . . . . . . . . . . . . . . . 163.2 The pulse train . . . . . . . . . . . . . . . . . . . . . . . . . . 173.3 The profile of the first pulse . . . . . . . . . . . . . . . . . . . 183.4 The intensity of each pulse in the train . . . . . . . . . . . . . 183.5 The krypton TOF with different rotation frequencies . . . . . 193.6 The slowed beam velocity with different rotation frequencies . 203.7 The krypton beam initial velocity with different rotation fre-quencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.8 The krypton beam longitudinal temperature with differentrotation frequencies . . . . . . . . . . . . . . . . . . . . . . . . 213.9 The calculated centrifugal effect on enhancement of pressureat the nozzle tip . . . . . . . . . . . . . . . . . . . . . . . . . 223.10 The oxygen beam . . . . . . . . . . . . . . . . . . . . . . . . . 234.1 TM014 mode electric field distribution . . . . . . . . . . . . . 274.2 TM014 mode AC dipole force distribution . . . . . . . . . . . 274.3 TE112 mode electric field distribution in y-z plane . . . . . . . 294.4 TE112 mode AC dipole force distribution in y-z plane . . . . . 294.5 TE112 mode electric field distribution in x-z plane . . . . . . . 30viList of Figures4.6 TE112 mode AC dipole force distribution in x-z plane . . . . . 304.7 TE112 mode electric field distribution in x-y plane . . . . . . 314.8 CH3CN molecular structure . . . . . . . . . . . . . . . . . . . 324.9 RGA mass spectrum of pure Kr . . . . . . . . . . . . . . . . . 334.10 Populations of CH3CN in |0, 0, 0? and |1, 0, 0? states . . . . . 344.11 CH3CN AC Stark shift with red and blue detunings of 12MHz 354.12 Focusing effect when applying red detuning microwave withpower of 5W . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.13 Focusing effect with different input powers . . . . . . . . . . . 384.14 Focusing effect when applying blue detuning microwave . . . 394.15 Focusing effect when switching off both of the sections . . . . 404.16 Focusing effect when switching off the first section . . . . . . 404.17 The populations of CD3CN in |0, 0, 0? and |1, 0, 0? states . . . 414.18 The AC Stark shift of CD3CN . . . . . . . . . . . . . . . . . 424.19 Background pressure fluctuation in detection chamber whenpulsing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.20 The calibration of output power after TWT amplifier . . . . . 444.21 Focusing effect with various input power . . . . . . . . . . . . 464.22 Simulated focusing effect with various input power . . . . . . 474.23 Simulated number of detected molecules . . . . . . . . . . . . 484.24 Simulated and experimental signal intensity increase by per-centage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.25 AC Stark shifts for different detunings . . . . . . . . . . . . . 504.26 Focusing effect with various detuning . . . . . . . . . . . . . . 514.27 Simulated focusing effect with various detuning . . . . . . . . 524.28 Lens effect on an acetone beam . . . . . . . . . . . . . . . . . 535.1 The superconducting microwave cavity attached to the cry-ocooler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55viiAcknowledgementsBefore I came to UBC and this laboratory, I have to say I was not wellprepared, neither for overseas life as an international student, nor researchbackground knowledge. Even though I encountered dozens of problems atthe beginning, assistance from friends, colleagues and supervisor help meout. As a result, this thesis has come out finally. First and foremost, I?dlike to thank Professor Momose for offering me an opportunity to conductresearch in his group and finish my Master?s degree in physics here. I appre-ciate his patience, trust and valuable advice to guide me on the research. Iappreciate he assisted me financially to attend the Gordon Rearch Confer-ence in 2012 and Canadian Association of Physists Congress in 2013, whereI broadened my view on physics science and acquired lots of new knowledge.These experiences are invaluable for a master student like me.Mr. Djuricanin is the technician of our lab, and probably the best tech-nician I have met or will meet in my whole life. With full-picture andcomprehensive knowledge of projects in our lab, he could always stand outwhenever problems rise. His solid backup, hard working and constructivedisscusion has accelerated the progress of this whole project.Our postdoc, Dr. Yang Liu, offered accurate theoretical assistance, tomake me understand the experimental results. Our discussion at lunch timeinspired me a lot to come up with solutions and improvments. I would liketo thank Eric?s help with my thesis and understanding of the native culture.Also, I appreciate the former work from Omid Nourbakhsh, Ilja Gerhardtand Katsunari Enomoto, without whose work, I couldn?t have received thiswell-prepared experimental setup.Finally, I appreciate the support from Technical Services at UBC.viiiDedicationI appreciate my friends? suggestion and spiritual encouragement in the pasttwo years. The time we spent together made the life here so enjoyable,and inspired me to think about the research and be active in preparing thisthesis.I would like to thank my family, Shihui Zhong, Xian Zhong, You Zhong,Huazhen Wang and Jikuan Zhong, for their support on my education finan-cially and spiritually.ixChapter 1IntroductionLast year, the Nobel Prize in physics was awarded to Dr. Serge Harocheand Dr. David J. Wineland for ?ground-breaking experimental methodsthat enable measuring and manipulation of individual quantum systems?.Dr. David J. Wineland traps electrically charged atoms, or ions, controllingand measuring them with light, or photons. In the opposite approach, Dr.Serge Haroche controls and measures trapped photons, or particles of light,by sending atoms through a trap[2]. Nowadays, lots of researchers aroundall over the world are working on cold(1mK-1K) and ultracold(<1mK)molecules, decelerating the molecular beam, trapping it, and conducting re-search on it. Then, why are cold and ultracold molecules so hot now? Theresearch field of cold molecules brings together two of three main thrusts ofmodern atomic, molecular and optical (AMO) physics: the ultracold and theultraprecise. It also brings together researchers from a variety of fields, in-cluding AMO physics, chemistry, quantum information science and quantumsimulations, condensed matter physics, nuclear physics and astrophysics[3].It is widely recognized that cold and ultracold molecules play an importantrole in basic scientific exploration[4?10]. Their application includes the real-ization of Bose-Einstein condensation [11], study of molecular collision andcross sections at ultralow temperatures[12, 13], knowledge of ultracold chem-ical rates[14, 15], measurement of the electron?s electric dipole moment[16],superchemistry[17], and quantum computation[18]. Considering the signif-icance of cold and ultracold molecules, researchers have developed severalmethods to obtain them; each of them has its own advantages and dis-advantages. Laser cooling of atoms technique is well developed, but notwell extended to molecules because of their complex internal stucture. Forlaser cooling, an almost closed transition is required, which can be foundin many atoms, but is very demanding in the case of molecules[19]. Re-cently, success of laser cooling of a diatomic molecule was reported and ithas bridged the gap between ultracold(submillikelvin) temperature and the1K temperature attainable with directly cooled molecules[20]. Another wayto obtain ultracold molecules is to laser cool atoms to ultracold regime andphotoassociate them into ultracold molecules[21, 22]. The direct cooling1Chapter 1. Introductionmethods includes Stark decelerator[23?25], Zeeman decelerator[26], sympa-thetic cooling[27, 28], Sisyphus cooling[29], buffer gas cooling[30, 31], and themethods we?ll discuss later, the CRN[32?38], and mcrowave decelerator[39?45]. In order to enhance the phase space density, guide technologies are ap-plied on the decelerated molecular beam[46, 47]. After deceleration, varioustraps[48?53] are need to hold the ensemble for further research as mentionedabove.In this thesis, CH3CN and CD3CN in ground states are the targetmolecules and their energy levels are explored. The sample is seeded inkrypton carrier gas with pressure of 3bar. The supersonic molecular beamis created after the open valve. First, we slow down the internal-cooledsupersonic beam?s translational velocity from 400m/s to about 100m/s byCRN. Then, when flying through the microwave resonator, a cylindrical cav-ity, the motion of molecular beam is manipulated by the AC Stark dipoleforce produced by standing wave, either focusing or deceleration. The focus-ing is realized with standing wave in both of TM01p and TE11p modes, anddeceleration could be realized with that in TE11p mode because of its three-dimensional potential trap[42]. A superconducting cylindrical tube is neededin the future for deceleration since the requirement of high quality factor.The achieved maximum electric field in the tube is about E0/2=11kV/cm.Two different detection techniques are used. One of them is RGA (ResidualGas Analysis) detection, and the other one is MCP (Microchannel Plate)detection. Also, the trajectory and time-of-flight simulation results by afourth order Runge-Kutta algorithm support experimental data very well.2Chapter 2Supersonic beam andexperimental setupThe object we are studying is the molecular beam essentially. Therefore,we?ll briefly introduce supersonic molecular beam and the questions whichneed to be answered in this chapter: for exmaple, how to create supersonicbeam, what?s the feature of it, and the reason why supersonic molecularbeam is choosen, in order to show a basic picture of supersonic molecu-lar beams. After that, the whole experimental setup will be presented, aswell as the function of each part, including the source chamber(CRN), themicrowave chamber, the detection chamber, the microwave generator, thevacuum system, the control system and so on.2.1 Supersonic molecular beamThe cooling methods we mentioned in Chapter 1 are mainly about how tocool the translational degrees of freedom. However, before that, the veryfirst step is to make an internally cooled molecular beam source. During theexpansion of a gas through a supersonic nozzle, rotational cooling occursthrough equilibration with the geometrically cooled translational degreesof freedom via collisional energy transfer[54]. The following diagram, Fig-ure 2.1[55], shows the features of supersonic beam in space dimension.A free-jet molecular beam can be produced by supersonic expansion fromhigh pressure to low pressure, provided the ratio of p0/pb exceeds the criticalvalue[55], where p0 is pressure in the gas line and pb is that of background.G = (? + 12)???1 (2.1)? is defined as ?=cp/cv, where cp is molar heat capacity of ideal gas atconstant pressure and cv is that at constant volume. A supersonic beamhas several important characteristic properties. First, the beam velocity, in32.1. Supersonic molecular beamFigure 2.1: There are separate zones distinguished by velocities of themolecular beam. The Zone of Silence is the desired one in our experiments.42.2. Experimental setupdimensionless unit of M , increases during the expansion. Second, the beamparameters in the zone of silence are independent of boundary conditions[55],which means the velocity of molecules in the zone of silence will be muchlarger than the speed of sound regardless of background pressure pb.Third,the longitudinal velocity distribution width of the beam is very narrow.Fourth, the beam maintains a good directionality, with small transversevelocity.2.2 Experimental setupIn this thesis, our first goal was the manipulation of motion of polyatomicmolecules in rotational ground state. How does it actually be achieved? Infigure 2.2, a cartoon of lens effect on the molecular beam is shown. Themolecular beam comes out from the nozzle moving backward with velocityof 300m/s . The slowed molecular beam colored in green is focused by theAC stark dipole force. The red and blue disks reprensent the standing wavenodes where the maximum of field strength is obtained.Experimental setup is illustrated in Figure 2.3, which consists of threesections: A CRN, a microwave cavity, and a detector. A titanium nozzlewith an orifice of 200?m was attached to one end of a carbon-fiber tube withan inner diameter of 2.5mm and a outer diameter of 4.0mm, and rotatedby a brushless DC-Servomotor (Faulhaber, 2057S012BK179) in a vacuumchamber. The center of the rotor was attached to a ferrofluidic feedthroughfor the introduction of gases inside the tube. The arm of the carbon-tubethat did not have the titanium nozzle was plugged with a carbon-fiber rodin order to prevent any gas flow into this side of the arm, while keeping thebalance of the rotor. The frequency of the spindle rotation was monitoredby a diode laser. The rotor tip speed was continuously variable between10m/s and 320m/s.One advantage of our source chamber is that we have installed a pulsedvalve instead of utilizing a continuous gas inlet in order to reduce the back-ground pressure during operation, so that the pumping requirement is re-duced dramatically. A pulsed valve (General Valve, 9 Series) was attachedat the inlet of the ferrofluidic feedthrough to allow for a pulsed rotatingsource so that the gas load to the turbo pump is minimized. The valve wasoperated with an opening time of 450?s at repetition time of 5s and backingpressure of 3bar.Our source chamber is pumped by a 800l/s turbo pump and detectionchamber is pumped by a 300l/s turbo pump.The background pressure in52.2. Experimental setupFigure 2.2: The microwave field is polarized and motion trajectories of poly-atomic molecules are deflected due to the AC dipole force, the so-called lenseffect62.2. Experimental setupsource chamber can maintain as low as 10?7 torr between successive pulsing.The range of pressure change is from 10?7 to 10?4 torr when pulsing.The source chamber and the microwave cavity were sperated by a skim-mer (Beam Dynamics, 3mm orifice). A home-made shutter was installedbefore the skimmer to pick up only the first pulse after the introduction ofthe gas into the tube and block the rest of the beam in order to reduce thegas load.The microwave cavity is made of copper. The cavity was constructedfrom a 400mm long, 12.6mm inside diameter copper tube and two copperend caps with a thickness of 4mm, Each end cap had a hole at the center tolet molecular beam pass. The diameter of entrance hole is 6mm and that ofexit hole is 4.5mm. A teflon disk with a thickness of 3mm was additionallyplaced at the center of the cavity to separate the cavity into two sections.The teflon disk had a hole of 5mm in diameter at the center in order toenhance the signal of the J = 0 ground state.There are another two holes in the side of the copper tube for the place-ment of coupling loop antennas made from semi-rigid coaxial cable (Coax,SC-219/50-SCN-CN). One of them transmitted high power into the mi-crowave cavity while the other monitored the resonant frequency. The depthof insertion of both antennas is adjustable to find the best coupling condi-tion and high Q-factor. The loss of the MW power due to the coaxial cablewas estimated to be about 50%?60%. The cavity was cooled by a liquidnitrogen tank to reduce the surface resistance and thereby to increase theQ-factor of the cavity as high as 1?1.5?104 for each mode.The microwave signal was generated by a synthesizer (Anritsu MG3693C),and amplified by a traveling wave tube amplifier (Hughes 1277H04F000).The maximum output power of the amplifier is 10W .72.2. Experimental setupFigure 2.3: The experiment system consists of three chambers, the CRNsource chamber, the microwave chamber and the detection chamber.82.2. Experimental setup2.2.1 The shutterIn order to improve the vacuum in MW chamber and detection chamber,a shutter has been installed. The skimmer can prevent molecules off theaxis from going into the next chamber. The problem is, when valve is open,each rotation of nozzle will generate a beam pulse going into the MW cavity.However, we found the first pulse had the best characheristic properties of asupersonic molecular beam, stronger intensity and narrow velocity spread.The home-made shutter completed this mission essentially. It?s made ofa hard drive magnetic switch as shown in figure 2.4. Once the first pulsecame through the skimmer, the shutter was closed in front of the skimmer,blocking the following beam pulses and keeping them in the source chamberwhere a stronger turbo pump was located. According to the testing, theshutter can close the entrance completely in about 10ms. By varying thedelay time compared to the synchronization or pulsing timing, it can allowthe first pulse to go through and block the second one perfectly. With thiswork, the background pressure remained at 10?8 torr in detection chambereven when pulsing.2.2.2 The rotor and nozzleIn our experiment, the rotor will be sped up to about 300m/s, close tothe speed of sound, so a rotor made of carbon fiber was chosen for its highstrength. The length from the tip to the spindle is about 19cm. It was gluedonto the shaft and a titanium ferrule was attached to the long end, whileopposite end had carbon fiber rod inserted and glued. The position of rod isadjusted for careful static balancing of rotor. Titanium ferrule incorporateda step such that the nozzle output diameter might be changed by gluing anaperture over the 250um hole as shown in figure 2.6. The step also helpedalign the nozzle perpendicular to the spindle. The length of the carbon fibertube is about 36cm.A large brass block sits on an aluminum housing piece to dampen vi-bration. Figure 2.7 shows the vibration noise when increasing the rotationspeed. There is a minima appearing around 260Hz which we have focusedon. The valve and ferrofluidic feedthrough are coupled through aluminumferrule that fits closely into housing. The spindle (titanium) O-ring is sealedto ferrofluidic shaft. The opposite side of spindle is coupled to motor withsoft silicone tubing. A large copper block attached to the motor is water-cooled to remove excess heat from motor.92.2. Experimental setupFigure 2.4: The shutter under testingFigure 2.5: The rotor102.2. Experimental setupFigure 2.6: The nozzleFigure 2.7: The vibration with different frequencies112.2. Experimental setup2.2.3 The microwave tubeThe core part of the microwave cavity is the cylindrical cavity tube of copperas shown in figure 2.8. The length of this cavity is about 408mm at roomtemperature and the radius is about 7mm.Figure 2.8: The copper cylindrical cavityA strong electrical field with amplitude of up to about 600kV/m is ap-plied in the tube with input power of 20W . In order to obtain such strongfield, a liquid nitrogen cooling system is attached to the tube to decrease thesurface resistance. When temperature is down to 77K, the tube is about6.3mm in radius and 400mm in length. The quality factor of a cavity isdefined generally as Q = 2pivW/P , where v is the microwave frequency, Wis the total energy stored in the cavity and P is the power loss of the cavity.The Q-factor is up to about 104. We focused on TM01p and TE11p modesand figure 2.9 shows the spectrum of TE11p modes for our microwave cavity.Since a travelling-wave tube (TWT) amplifier was utilized to increase inputpower, the possible frequency shift after the amplifier was considered. It122.2. Experimental setupshowed the frequency shift is not observable up to order of 1MHz, so theeffects could be ignored in this situation.Figure 2.9: The TE11p mode spectrumThe mode was assigned by fitting the length and radius to equation 2.2,and the nodes number p was aquired.v =c2?(xlmapi)2 + (pL)2 (2.2)where c is the light speed, xlmis 2.4048 for TM01p modes and 1.8412 forTE11p modes, p is the node number of standing wave, a is the radius andL is the length of the microwave tube. When calculating the nodes, wemust take the contraction of the cavity caused by the low temprature(77K)into consideration. Take the length for example: it contracted by 8mmfrom 408mm to 400mm. This layout change is considered in the simulationsection as well.132.2. Experimental setup2.2.4 The detectionTwo different detection techniques are utlized in our experiment. The firstone is MCP detection and the other one is RGA detectionThe MCP detectorWhen molecular beam arrives at the laser focal point, the molecules willbe ionized and charged. An electric field for accelerating charged particlesis built using ion optics. The arriving timing of particles with differentcharge-to-mass ratios are different. Each time when the charged particlehits the wall of the microchannel of MCP detector, more electrons will beejected like an avalanche so that a weak signal will be detectable.Figure 2.10: The ion opticsFigure 2.11: The MCP detector142.2. Experimental setupThe RGA dectorRGA1 is a mass spectrometer with small physical dimensions that can beconnected directly to a vacuum system and whose function is to analyzethe gases inside the vacuum chamber. It can distinguish charged particlesaccording to the different charge-to-mass ratio.It consists of three modules. First is an ion source, which can convert gasphase sample molecules into ions. Second is a mass analyzer(filter), whichsorts the ions by their charge-to-mass ratio by applying electromagneticfields. The last is a detector, which measures the value of an indicatorquantity and thus provides data for calculating the abundances of each ionpresent. Here is the way how it works: when a sample is loaded into theRGA and undergoes vaporization, the components of the sample are ionized,and the ions are separated according to their mass-to-charge ratio in ananalyzer by electromagnetic fields. Finally the ions are detected, usually bya quantitative method, and then processed into mass spectra.Figure 2.12: The RGAThe ionization section of the RGA was placed about 6cm behind theexit hole of the microwave cavity. The advantage of the RGA is that it hasa large detection area which can enhance the detected signal. It is even abetter choice when considering the non-trivial alignment of the molecularbeam produced by CRN.A trasimpedance amplifier followed by a voltage amplifier (StandfordResearch, SR570 and SR560) was connected to the RGA. The amplifiedsignal was record in real time by an oscilloscope (Agilent DSO5034A). Ahome-made notch filter was used to reduce the noise.1We used a Model SRS100 RGA15Chapter 3Molecular beam source:Counter Rotating NozzleThe highlight of this work is the beam source we use, CRN. In order tomanipulate the molecular beam, we need to precool and slow the beamdown to about 100m/s. The Stark decelerator was used in Gerard Meijer?sgroup[44]. According to Earnshaw?s theorem, there are no local minimaor maxima of the field potential in free space by static field. Therefore,the target molecular states are limited to the low field seeking state (LFS),which is not the rotational ground state. Our advantage is that CRN canslow target gas-phase molecules in all states regardless of the molecular mass.3.1 The principle of CRN in slowing molecularbeamsThe CRN is a mechanical method to produce intense cold, slow beams ofatoms and molecules, which utilizes the peripheral backward velocity of ahigh-speed rotating nozzle to offset the beam?s velocity. By changing therotating speed of the nozzle, velocity of the beam can be easily tuned.Figure 3.1: The Principle of CRN163.2. Properties of molecular beams created by CRNAs the nozzle moves backward relative to the molecular beam motion,the beam velocity is reduced to V=X-Vrot, where X is the initial velocityof the molecular beam and Vrot is the velocity of nozzle. The difficulty forexisting systems which use a continuous gas inlet is the requirement of alarge pumping capacity[35, 38]. To overcome this issue, a pulsed valve wasinstalled at the spindle in order to reduce the background pressure duringoperation as mentioned above.3.2 Properties of molecular beams created byCRNFigure 3.2 shows the original signal of the Argon pulse train with a rotationrate of 100Hz. When the valve was open, one beam pulse was produced perrotation. As the time went by, the pressure in the nozzle became lower sothat the intensity of pulses decreased. The background pressure increasedat the beginning, then decreased as the gas was pumped out.30x10-320100Signal( A.U.)300250200150100500TOF(ms) Argon 100HZFigure 3.2: The pulse trainThe first pulse, with the strongest intensity and the lowest backgroundpressure, is enlarged and depicted in figure 3.3. We noticed a high frequencyoscillation which showed up in the baseline. This noise source was due tothe vibration of the turbo pumps and the rotor.After the first pulse, the intensity of following pulses decreased exponen-tially as illustrated in figure 3.4173.2. Properties of molecular beams created by CRN30x10-32520151050Signal( A.U.)151050TOF(ms) First Argon Pulse at 100HZFigure 3.3: The profile of the first pulseFigure 3.4: The intensity of each pulse in the train183.2. Properties of molecular beams created by CRNThe velocity of the slowed beam is related to the rotation frequency ofthe nozzle as shown in figure 3.5. As the rotation frequency increased, theTOF peak shifted to a later time. The inlet backing pressure was 3bar, andvalve opening time was 450?s. The TOF measurements were fitted by thefollowing equation 3.1 from[35]:D(t) =Ct(Lt? Vrot)e?(Lt ?V?v )2(3.1)where C is the total flux intensity, L is the flight distance, Vrot is the rotationvelocity of nozzle with negative sign indicating slowing, ?v represents thevelocity spread(full width at half maximum ), V is the effective velocity ofthe beam in the laboratory frame.10x10-386420TOF Signal(A.U.)3.0x10- TOF(sec)        Krypton 100HZ 120HZ 140HZ 160HZ 180HZ 200HZ Fitting LineFigure 3.5: The krypton TOF with different rotation frequenciesThe beam velocity was slowed down from about 380m/s to about 140m/sas shown in figure 3.6. The velocity of the beam was fitted with a straightline, which matched the expectation as predicted by V=X-Vrot.193.2. Properties of molecular beams created by CRN280260240220200180160140Slowed Velocity (m/s)200180160140120100Freq of Nozzle(HZ)Figure 3.6: The slowed beam velocity with different rotation frequenciesOne interesting point is that the supersonic expansion velocity of kryptonat room temperature is supposed to be about 400m/s, while the initialvelocity of the krypton beam shown in figure 3.7 was about 380m/s. Oneexplanation about this phenomenon was the detector RGA?s response timedelayed the real arrival time, which resulted in slower beam velocities as wesaw.400380360340320300Initial Velocity(m/s)200180160140120100Freq of Nozzle(HZ)Figure 3.7: The krypton beam initial velocity with different rotation fre-quenciesDue to the centrifugal effect of rotating the nozzle, the pressure at the tipof the nozzle is higher than the inlet backing pressure. This effect becomes203.2. Properties of molecular beams created by CRNmore significant when increasing the rotation frequency. The other issue isthat the pressure change will directly change the longitudinal temperatureof the molecular beam, which is related to velocity spread by equation 3.2?v = (2kbT0/m)1/2(T||/T0)1/2 (3.2)where kb is the boltzmann constant, m is the particle mass, T0 is the backingenviroment temperature, T|| is the longitudinal temperature. Temperature(K)200180160140120100Freq of Nozzle(HZ)Figure 3.8: The krypton beam longitudinal temperature with differentrotation frequenciesAccording to figure 3.8, the longitudinal temperature of krypton beamdropped when increasing the rotation speed. The reason was that the pres-sure P0 at the tip of the nozzle increased due to the centrifugal effect de-scribed by equation 3.3[35]P0Pin= exp[mV 2rot/(2kBT0)] (3.3)where P0 represents the pressure at the tip of the nozzle, Pin is the inletbacking pressure, m is the mass, Vrot is the velocity of the nozzle tipThe pressure would increased exponentially when increasing the rotationfrequency as illustrated in 3.9. Supersonic expansion with a higher pressureat the tip of the nozzle cooled the internal temperature of the beam by abouta factor of two.213.2. Properties of molecular beams created by CRNFigure 3.9: The calculated centrifugal effect on enhancement of pressure atthe nozzle tip223.2. Properties of molecular beams created by CRNThe valve opening time is another factor which affects the longitudi-nal temperature besides pressure. Basically, if the valve opening time waslonger, more gas went into the nozzle, and a higher pressure was obtainedinside. This effect was proved by slowing the oxygen beam seeded in argonas shown in figure 3.10.Figure 3.10: TOF measurements of slowed oxygen beams seeded in argonat a rotation frequency of 100HzThe longitudinal temperatures were about 4.5K and 1K, correspondingto the red and green curves respectively. The longer opening time mainlycontributed the lower longitudinal temperature.23Chapter 4The microwave lens effect onpolarized polyatomicmolecular beamsIn this chapter, we will demonstrate a MW lens effect for the J=0 rotationalground state of cold polyatomic beams, including CH3CN and CD3CN, cre-ated by the CRN. In order to observe any effect induced by the dipoleforce, precooling is necessary since the potential depth that the electromag-netic fields can generate is at most 1K. For the true rotational groundstate, precooling has to be achieved without using a static field accord-ing to Earnshaw?s theorem. In this study, slowed CH3CN and CD3CNbeams created by the CRN were introduced into a waveguide MW cav-ity, in which a TM01p or TE11p mode MW standing wave nearly resonant tothe |J,K? = |1, 0? ? |0, 0? pure rotational transition was maintained. Wehave observed a difference in the number of molecules exiting the cavity bychanging the condition of the MW standing wave such as the ON-durationtime, the field strength and the detuning frequency, which indicated thatthe translational motion of a cold polyatomic beam in the J=0 rotationalstate was successfully influenced by the MW dipole force.4.1 The AC Stark shiftThe microwave lens effect we observed is due to the AC Stark shift associ-ated with a molecular rotational transition. In our work, the discussion isconfined to the effect of the MW field on two rotational states, |J,K? = |1, 0?and |0, 0? of CH3CN and CD3CN. A linearly polarized electric field is builtin the MW cavity. For dipole transitions induced by linearly polarized ra-diation, the optical selection rule of ?J = ?1, ?K = 0, and ?M = 0applies for symmetric top molecules. Therefore, |1, 0, 0? is the only statethat is accessible from the ground |0, 0, 0? rotational state by one photontransition. The total Hamiltonian of the system is given by H? = H?rot + H??,244.2. The electromagnetic field resonant mode spectrum in the microwave cavitywhere H??= ?? ? E is the interaction between the electric dipole moment? of the molecule and the electric field E. According to the dressed stateformalism, the Hamiltonian matrix between the two basis sets |0, 0, 0?|n?+1?and |1, 0, 0?|n?? for linearly polarized radiation is approximated byH =((n?+ 1)hv 12??1012??10 2B + n?hv)(4.1)where ? = |E| is the electric field amplitude, n? is the number of photons inthe field, hv is the photon energy with frequency of v and ?10 is the tran-sition dipole moment between the resonant states, |1, 0, 0? and |0, 0, 0?. ForCH3CN, ?10 = ?100|?|000? = ?10?100|cos?|000? = 3.92/?3 = 2.26debye.For CD3CN, ?10 = 3.31/?3 = 1.91debye. By diagonalizing the Hamiltonianmatrix for the two-state model given in 4.1, the energy shift for the |0, 0, 0?state by the AC Stark effect is found to be?U000 = ??2?12??2 + ?2?102 (4.2)The energy shift of |1, 0, 0? state is?U100 = +?2?12??2 + ?2?102 (4.3)where ? = h(v ? v10) is the detuning when the MW radiation frequencyis v and the resonant transition frequency between the |0, 0, 0? and |1, 0, 0?states is v10 = 2B/h. The upper sign is for the blue detuning ? > 0 case,and the lower sign is for the red detuning ? < 0 case.4.2 The electromagnetic field resonant modespectrum in the microwave cavityWe established TM01p and TE11p mode electric fields in the microwave cav-ity. The index p denotes the number of nodes in the longitudinal direction ofthe cavity. These two different series of modes provide a linearly polarizedradiation.4.2.1 The TM01p field and induced AC Stark dipole forcedistributionThe distribution of the electric field of TM01p modes in a cylindrical cav-ity is completely concentric. The azimuthal component, E?, is zero. The254.2. The electromagnetic field resonant mode spectrum in the microwave cavitylongitudinal component of electric field along central axis direction Ez, andradial component Er, in cylindrical coordinates with the domain (0 ? z ?L, 0 ? r ? a, 0 ? ? ? 2pi) are given byEz = ?0J0(x01ra)cos(kz) (4.4)andEr = ?0kax01J1(x01ra)sin(kz) (4.5)where a is the inner radius of cylindrical cavity, 6.29mm, L is the length,400mm, ?0 is the magnitude of the electric field, k = ppi/L, Ji(x) is the i-thorder Bessel function of the first kind, x01 = 2.4048 is the first zero of J0(x)modes.TM01p modes in a cylindrical cavity have a concentric radial electric fielddistribution, and are ideal for demonstration of the lens effect of a molecularbeam. The translational motion of the beam is affected by the AC dipoleforce, F , given by F = ??(?U000), where ?U000 is the energy shift givenin equation 4.2. Since a/L  1, the approximation of the dipole forcedistribution at a postion (r, z) in our cavity is:Fr(r, z) = ???U000?r? ??210?20x012a??2 + E2z?210J0(x01ra)J1(x01ra)cos2(kz) (4.6)The upper sign is for ? > 0(blue detuning), and the lower sign is for? < 0(red detuning). For a red-detuned MW frequency, there is always aforce towards the centric axis of the cavity.The electric field distribution is as shown in figure 4.1. The scale of theradial direction, r, is exaggerated relative to the longitudinal direction, z.The force distribution is as shown in figure 4.2. The magnitude of theradial component of the force Fr, is for the|0, 0, 0? state.264.2. The electromagnetic field resonant mode spectrum in the microwave cavityFigure 4.1: TM014 mode electric field distributionFigure 4.2: TM014 mode AC dipole force distribution274.2. The electromagnetic field resonant mode spectrum in the microwave cavity4.2.2 The TE11p field and induced AC Stark dipole forcedistributionCompared to TM01p modes, which provide a two-dimensional radial con-finement harmonic potential for HFS states, the TE11p modes provide athree-dimensional trapping potential for HFS states at every antinode[42],which can be used for deceleration applications in the future. Here wepresent the electric field distribution of TE112 mode in y-z plane.The electric field component along longitudinal direction Ez is 0, whilethe azimuthal component E? and radial component Er are given byEr = E0J1(x?11r/a)x?11r/asin?sin(kz) (4.7)andE? = E0[J0(x?11ra)?J1(x?11ra )x?11ra]cos?sin(kz) (4.8)where x?11 is 1.8412. According to F = ??(?U000), where ?U000 is the ACStark energy shift, each component of dipole force is given byFr = ?12?210E20sin2(kz)??2 + ( ~E2r + ~E2? )?210{J20 (x11ra)/r + J21 (x?11ra)[2a2(x?11)2r3?cos2?r]+J0(x?11ra)J1(x?11ra)[x?11acos2? ?ax?11r2(1 + 2cos2?)]}(4.9)F? = (?1r) ? ?12?210E20sin2(kz)sin?cos???2 + ( ~E2r + ~E2? )?210[2J1(x?11ra )x?11ra? J0(x?11ra)]J0(x?11ra)(4.10)Fz = ?12?210??2 + ( ~E2r + ~E2? )?210{ ~Er[E0kJ1(x?11ra )x?11rasin?cos(kz)]+ ~E?[E0k[J0(x?11ra)?J1(x?11ra )x?11ra]cos? cos(kz)]}(4.11)284.2. The electromagnetic field resonant mode spectrum in the microwave cavityBy projecting the cylindrical coordinates onto Cartesian coordinates, theforces along x-direction and y-direction are derived as:Fx = Fr ? cos? ? F? ? sin?;Fy = Fr ? cos? + F? ? sin?;(4.12)The electric field distribution in y-z plane is as shown in figure 4.3Figure 4.3: TE112 mode electric field distribution in y-z planeThe AC dipole force distribution in y-z plane is as shown in figure 4.4Figure 4.4: TE112 mode AC dipole force distribution in y-z plane294.2. The electromagnetic field resonant mode spectrum in the microwave cavityIt is observed that the field and force distribution is non-centrosymmetricrelative to the longitudinal axis. The electric field distribution in x-z planeis as shown in figure 4.5Figure 4.5: TE112 mode electric field distribution in x-z planeand the AC dipole force distribution is as shown in figure 4.6Figure 4.6: TE112 mode AC dipole force distribution in x-z plane304.2. The electromagnetic field resonant mode spectrum in the microwave cavityThe electric field distribution in x-y plane, the cross section plane, is asshown in figure 4.7Figure 4.7: TE112 mode electric field distribution in x-y plane314.3. The lens effect on CH3CN beam by AC electric field in TM mode4.3 The lens effect on CH3CN beam by ACelectric field in TM mode4.3.1 The basic properties of CH3CNCH3CN is a prolate symmetric top molecule with a permanent electric dipolemoment of ?0 = 3.92debye, which is linearly polarized, and a mass of 41u.The structure is as shown in figure 4.8.Figure 4.8: CH3CN molecule structureThe black, white, blue balls represent carbon, hydrogen, nitrogen atoms,respectively. Its lowest pure rotational transition frequency|J,K? = |0, 0? ?|1, 0? is 18.398GHz.The sample was introduced by bubbling in a stainless steel tube containerat room temperature. The vapor pressure of CH3CN is about 75torr andthe concentration when seeded in the krypton carrier gas is about 3.3% withbacking pressure of 3bar.Since the molecular beam was detected by a RGA detector, located about6cm behind the exit hole of the MW cavity, we calibrated the mass settingof the RGA very carefully. Krypton possesses isotopes of varying massesincluding 82Kr(11.5%), 83Kr(11.5%) and 84Kr(58.0%). When these isotopeslose two electrons and Kr2+ is created, the charge-to-mass ratio is closelyoverlapping that of the target ion CH3CN+. The RGA mass spectrum ofpure Kr supersonic beam is illustrated in figure 4.9324.3. The lens effect on CH3CN beam by AC electric field in TM mode250x10-12200150100500Signal Intensity(torr )4846444240383634Mass(amu)Figure 4.9: RGA mass spectrum of pure Kr334.3. The lens effect on CH3CN beam by AC electric field in TM modeBy detecting the pure Kr in the same condition, we confirmed that thesignal of mass 41 produced by 82Kr2+ and 83Kr2+ were much weaker thanthat when CH3CN seeded in the beam.4.3.2 The populations of CH3CN in |0, 0, 0? and |1, 0, 0? statesThese two states follow the Boltzmann distribution:NiN=gie?Ei/(kB)T?igie?Ei/(kBT )(4.13)where kB is the Boltzmann constant, T is rotational temperature, gi is thedegeneracy, N is the total number of particles, Ni is the number of particlesin i-state and Ei is the energy level of i-state.The energy levels are Ei = ?J,K,M |H?rot|J,K,M? = BJ(J + 1) +(A ? B)K2. The rotational constants of CH3CN are: A=158.3GHz andB=9.2GHz.Each rotational state has a degeneracy of 2(2J+1) for K =\ 0 and 2J+1for K = 0. Due to the symmetrical configuration of the three protons,there are two spin modifications: I = 3/2ortho-CH3CN for K = 3n, andI = 1/2para-CH3CN for K = 3n?1 (n is an integer) with a statistical ratioof 2 : temperature(K) |0,0,0>  |1,0,0>Figure 4.10: Populations of CH3CN in |0, 0, 0? and |1, 0, 0? states344.3. The lens effect on CH3CN beam by AC electric field in TM modeBy considering this statistical ratio, the populations of CH3CN in the|J,K,M? = |0, 0, 0? and |1, 0, 0?states are expected to be 5.7% and 4.8%respectively in molecular beam with a rotational temperature of 5K.4.3.3 The AC Stark shift of CH3CNThe resonant transition frequency between |0, 0, 0? and |1, 0, 0? states arev10 = 18.389GHz. The transition dipole moment is ? = 2.26debye. Assum-ing the electric field of about 460kV/m, the detuning frequency of -12MHzand 12MHz, the AC Stark shift were depicted in figure 4.18. It?s interest-ing that certain states such as |0, 0, 0? can be either HFS with red detuningor LFS with blue detuning. It applies to excited state such as |1, 0, 0? aswell. The solid lines are blue detuning cases, and the dashed lines are reddetuning cases. The AC Stark shift with these conditions is about 2GHz20151050AC Stark shift(GHz)5004003002001000Electric field(kV/m) J=0 with blue detuning J=0 with red detuning J=1 with blue detuning J=1 with red detuningFigure 4.11: CH3CN AC Stark shift with red and blue detunings of 12MHz4.3.4 The experimental resultsFrom the equations 4.9, 4.10 and 4.11, we know that the motion of molecu-lar beam, or the AC dipole force is dominated by the strength of the electricfield and the detuning frequency, therefore these two factors? effects wereexplored in this section. In these experiments, in order to improve the vac-354.3. The lens effect on CH3CN beam by AC electric field in TM modeuum of the microwave cavity and enhance the signal of the J = 0 groundstate, we put a teflon disk at the center of the cavity to separate the cav-ity into two sections as mentioned. Most of the molecular beam would beblocked by the disk so that the vacuum in the second section would obtainan improvement to avoid high collision rates. By controlling the microwavegenerator, we can switch off the microwave in the first section or both of thesections.Power-dependent experimental resultsIn this experiment, we applies the TM015 mode at 18.386GHz to the cavity,with a red detuning of 12MHz. The loaded quality factor is about 10800.The MW power generated by the amplifier is about 5W , while the actualpower introduced into the cavity was about half of these values due to theloss of the coaxial cable. The electric field amplitude is about 123.7kV/mwith consideration of the power loss. The signal intensity increase of CH3CNbeam is about 7% by height shown in figure 4.12The blue trace shows the subtraction of the observed signals of CH3CNseeded in Kr when MW is on and off in both sections, which is multipliedby a factor of 15.By varying the input power generated by amplifier from 5W to 10W ,we find the observed RGA signal intensity increase is roughly doubled. Theresults are shown in figure 4.13, where the two traces are the subtractionsof MW-ON signals and MW-OFF signals.364.3. The lens effect on CH3CN beam by AC electric field in TM mode0.0500.0450.0400.0350.0300.025Signal Intensity(A.U.)86420Time of Flight(ms)000_ON_Aveaverage 496 traces out of 501 MW--OFF MW--ON (MW--ON-OFF)*15 Figure 4.12: Focusing effect when applying red detuned microwave withpower of 5W374.3. The lens effect on CH3CN beam by AC electric field in TM mode1.4x10- increasing of CH3CN signal(A.U.)86420TOF(ms)MW Power 10W 5WFigure 4.13: Focusing effect with different input powers384.3. The lens effect on CH3CN beam by AC electric field in TM modeExperimental result with blue detuningFigure 4.14 shows the CH3CN signal when applying the TM016 MW fieldat 18.410GHz. The loaded Q-factor is QL = 1.07? 104. This frequency isslightly blue detuned from the resonant frequency of the target transition.With a blue detuned MW field, molecules in |0, 0, 0? state are deflectedaway from the central axis, while molecules in |1, 0, 0? is deflected towardsthe central axis. Since the populations of molecules in these two states areclose to each other and the focusing effect is dominant, the intensity increasestill shows up when applying blue detuned microwave.0.0520.0500.0480.0460.0440.042RGA14121086420msec000_ON_Aveaverage 501 traces out of 501 OFF ONFigure 4.14: Focusing effect when applying blue detuning microwaveThe signal increased by about 7% when the blue detuned microwave wasswitched on.Experimental results of switching on one or both microwavesectionsBy changing the duration the microwave was applied on the molecular beam,we found the longer duration gave us stronger focusing effects. The mi-crowave frequency was set to 18.343GHz(TM014). The power generated bythe MW amplifier was 10W with a loaded Q-factor of QL = 1.34? 104Figure 4.15 shows the result when switching off the microwave generatorin both of sections. The signal intensity decreases by about 16%, while thesignal intensity decreases by about 10% when switching off just in the firstsection as shown in figure 4.16. We subtracted the baseline caused by thebackground pressure change since we pulsed the molecular beam.394.4. The lens effect on CD3CN beam by AC electric field in TE mode8x10-36420Signal Intensity(A.U .)86420 Time of Flight(ms) OFF ONFigure 4.15: Focusing effect when switching off both of the sections8x10-36420Signal Intensity(A.U .)86420 Time of Flight(ms) ONOFF ONFigure 4.16: Focusing effect when switching off the first section404.4. The lens effect on CD3CN beam by AC electric field in TE mode4.4 The lens effect on CD3CN beam by ACelectric field in TE mode4.4.1 The basic properties of CD3CNThe mass of CD3CN is 44u. It is a symmetric top molecule with the samestructure as CH3CN. The vapor pressure at room temperature is about96 torr. The concentration when seeded in krypton carrier gas is about4.2%. The energy level ?J,K,M |H?rot|J,K,M? = BJ(J + 1) + (A?B)K2?DJJ2(J + 1)2 ?DJKJ(J + 1)K2. The rotational constants of CD3CN are:A=78.9GHz, B=7.9GHz, DJ=2.76KHz and DJK=110.7KHzThe populations of molecules in |0, 0, 0? and |1, 0, 0? states are as shownin figure temperature(K) |0,0,0> |1,0,0>Figure 4.17: The populations of molecules in |0, 0, 0? and |1, 0, 0? statesAssuming a rotational temperature of 5K, the populations of |0, 0, 0?and |1, 0, 0? states are about 3.9% and 3.3% respectively.414.4. The lens effect on CD3CN beam by AC electric field in TE mode4.4.2 The AC Stark shift of CD3CNAccording to the equations 4.2 and 4.3, the AC Stark shifts of CD3CN areas shown in figure 4.18Figure 4.18: The AC Stark shift of CD3CNThe resonant transition frequency between these two states is v10 =15.716GHz. The transition dipole moment is ? = 1.91debye. Assuming theelectric field of about 460kV/m, the detuning frequencies of -300MHz and300MHz, the AC Stark shift is obtained in figure 4.18. The AC Stark shiftwith these conditions is about 2GHz4.4.3 The experimental and simulation resultsThe repetition time between pulses is 5s to maintain the high vacuum insidethe system. The background pressure change during pulses in detectionchamber is as shown in figure 4.19424.4. The lens effect on CD3CN beam by AC electric field in TE mode2. Signal43210 Time(s) Valve Marker Signal when pulsing Signal when no pulsingBackground Pressure in detection chamberFigure 4.19: Background pressure fluctuation in detection chamber whenpulsingThe background pressure recovered to original conditions after 2.5s.However, considering the reading showed the pressure in the detection cham-ber, not in the microwave cavity, we lengthened the repetition time to 5s tomake sure the vacuum inside the cavity restored properly since a large partof the molecular beam was blocked inside the cavity.Power-dependent Experimental and simulation resultsTM1118 at a frequency of 15.542 MHz was chosen for this experiment. Thered detuning frequency was about 174MHz. The amplifier type we usedwas a traveling-wave tube (TWT) amplifier. Due to nonlinearity features ofthe amplifier and the energy loss during transmission with the new antenna,we calibrated the output power after the TWT amplifier corresponding todifferent input power from microwave generator. The relation between theinput power in units of dBm and the output power after the TWT in unitsof W is depicted in figure 4.20According to equation 4.15 and 4.14[42], we can calculate the amplitudeof the electric field in the microwave cavity once we know the power inputinto the cavity.434.4. The lens effect on CD3CN beam by AC electric field in TE mode2015105Power(W)-18 -16 -14 -12 -10 -8 -6 -4 -2dBmFigure 4.20: The calibration of output power after TWT amplifier444.4. The lens effect on CD3CN beam by AC electric field in TE modeW =PinQLpiV(4.14)W = 0.029840E20V (4.15)where Pin is the power inputed into the cavity, QL is the loaded Q factor,E0 is the amplitude of the electric field, V is the volume of the microwavecavity, and 0 = 8.8? 10?12F/m is the permittivity.For example, if the output power of the TWT amplifier is 7.7W , thepower loss after the antenna is 11% according to the parameters in theantenna manual. The actual input power into the microwave cavity is about6.8W . The dimension of the cavity is 400.0mm in length and 6.3mm inradius. Therefore the volume is about 50cm3. The QL is about 12000. Theelectric amplitude is 355kV/m for this case.We varied the input power from 4W to 16.8W , corresponding to a electricfield of 256kV/m to 525kV/m. The TOFs for several cases are as shown infigure 4.21454.4. The lens effect on CD3CN beam by AC electric field in TE mode5x10-343210Signal Intensity(A.U.)86420 TOF(ms) MW--OFF 4W 16.8WFigure 4.21: Experimental focusing effect with various input powerThe longitudinal velocity of the CD3CN beam created by the CRN wasabout 120m/s with velocity spread of about ?20m/s.We noticed that the faster molecules were focused better than slowermolecules. The main reason for this phenomenon is that slower ones areeasier to over-focus.The simulation results are as shown in figure 4.22. By assuming therotational temperature of 5K, the population ratio is about 1.15:1. Thenumber of simulated molecules is 1?106 for each state and we added bothof the TOFs together by ratio of 1.15:1.The simulation results also showed that the peaks of the TOFs shiftedto earlier time for higher microwave by fitting with Gaussian distribution.The TOF peak of 4W case appeared at 4.79ms, while at 16.8W the peakshifted slightly earlier to 4.72ms.464.4. The lens effect on CD3CN beam by AC electric field in TE mode5004003002001000Signal Intensity(A.U.)10x10-39876543 TOF(second) MW--OFF 4W 16.8WFigure 4.22: Simulated focusing effect with various input power474.4. The lens effect on CD3CN beam by AC electric field in TE mode12x103108642Num of molecules1614121086420Power(W) J0 J1 rotational temperature of 5K: J0*1.18+J1Figure 4.23: Simulated number of detected molecules with various powerWe once expected the focusing effect was proportional to the input poweror proportional to the square root of the power. However, as shown infigure 4.23, the number of detected |0, 0, 0? state molecules and |1, 0, 0? statemolecules supported neither of these cases. Since the motion of moleculeswas complicated in the microwave cavity and the detected signal dependedon the combination of them, the relationship between the focusing effect andthe input power was mainly dominated by the focusing of |0, 0, 0? when weapplied red detuning and that of |1, 0, 0? when we applied blue detuning.484.4. The lens effect on CD3CN beam by AC electric field in TE modeFigure 4.24: Simulated and experimental signal intensity increase by per-centageThe average intensity increase was about 8% with 4W and 23% with16.8W . The red markers with error bars showed the experimental intensityincrease by area when increasing input power. It was noticed that the in-tensity increase became saturated compared to the simulated black markerswhen applying higher power. Also the error bars were larger with higherpower. One of the possibilities could be that collisions between the moleculesand between molecule and cavity wall were more intense with higher power,which resulted in the saturation and larger error bar.494.4. The lens effect on CD3CN beam by AC electric field in TE modeDetuning-dependent experimental and simulation results-2-1012AC st ark energy shift(GHZ)5004003002001000 Electric field strength (kV/m)Red detuning frequency ?=-333MHz ?=-1010MHz ?=158MHz wave8Figure 4.25: AC Stark shifts for different detuningsThe input power we chose for detuning-experiments was 16.8W , corre-sponding to an electric field with amplitude of about 462kV/m shown asdashed vertical line in figure 4.25. The AC Stark shift of red detuning of333MHz was 2.0GHz, that of red detuning of 1010MHz was 1.8GHz, andthat of blue detuning of 158MHz was 2.1GHz. Even though the AC Starkshift depended on both the electric field and detuning frequency, the detun-ing frequency changes contributed much less than the electric field strengthchanges.504.4. The lens effect on CD3CN beam by AC electric field in TE mode6x10-3420Signal Intensity(A.U.)86420Time Of Flight(ms)MW POWER: 13WRed detuning MW_OFF ?=-333MHZ ?=-1.01GHZ ?=158MHZFigure 4.26: Focusing effect with various detuningAs mentioned above, the focusing effect dominated compared to the de-focusing effect. Therefore, for both red and blue detuning experiments, weexpected to see focusing of the molecular beam. Three different conditionswere chosen for this experiments: two red detuning and one blue detun-ing. The red detuning of 333MHz gave about an 27% intensity increase,while the red detuning of 1010MHz gave about an 20% intensity increaseinstead. Smaller detuning gave us stronger lens effect. The very interestingobservation is that even though 158MHz of blue detuning was closer to thetransition frequency than 333MHz of red detuning, the focusing effect was514.4. The lens effect on CD3CN beam by AC electric field in TE modesmaller for blue detuning. The signal intensity increased by 22%. The rea-son was that the population of |0, 0, 0? state was slightly larger than that of|1, 0, 0? state. Therefore, the focusing of |1, 0, 0? state contributed less whenapplying blue detuning, comparing to the focusing of |0, 0, 0? state whenapplying red detuning.3002001000Signal Intensity(A.U.)12x10-310864TOF(s) MW--OFF ?=-333MHZ ?=-1010MHZ ?=158MHZFigure 4.27: Simulated focusing effect with various detuningThe simulation results are as shown in figure 4.27, which matched withthe experimental results very well. The blue detuning of 158MHz gavelarger focusing than red detuning of 1010MHz, and smaller than red de-tuning of 333MHz.524.5. Experimental lens effect demonstration of an acetone beam in TE mode4.5 Experimental lens effect demonstration of anacetone beam in TE modeBesides CH3CN and CD3CN samples, We also conducted microwave lensexperiments with molecules like acetone CO(CH3)2, which has more com-plicated molecular structure. Its two-state transition spectrum in the mi-crowave range (around 15GHz) is quite sophisticated because of the two-rotor structure resulting in large amount of degeneracies. Figure 4.28 showsa demonstration of the lens effect on an acetone beam.20151050x10-3  141210864AcetoneMW frequency: 14.9554GHZQ-factor:10071Power:19.2WFigure 4.28: Lens effect on an acetone beam53Chapter 5Conclusion and future workIn this thesis, we have presented our observations of the focusing effect onCH3CN and CD3CN molecular beams. The relation between the focus-ing effect and microwave power and frequency-detuning was explored. Thebeam intensity change due to our changes to experimental conditions provedthat we successfully manipulated the motion of the beam. We found thatthe intensity of faster molecules in the beam increased more than that ofslower molecules because the slower molecules experienced more time inthe standing wave and were easily over-focused. We found the focusing ef-fect saturated as we increased the power up to 16.8W , which was mainlybecause most accessible molecules in the rotational ground states alreadysucceed in exiting the microwave cavity. When applying the blue detuningto the molecular beam, we expected to see defocusing effect initially. How-ever, we found that the focusing effect always appeared even with a bluedetuning, which meant the focusing effect was dominant in these manipula-tion experiments. Since the RGA detector detected molecules in all states,the focusing of J = 1 state molecules not only compensated the defocusingof J = 0 state molecules, but also enhanced the total intensity of the molec-ular beam at the detector. This was confirmed by both experimental andsimulation results.Now, we are working on the construction of a half meter long supercon-ducting cylindrical cavity coated by the lead-tin as shown in figure 5.1, forwhich we expect to achieve a PQ-factor as high as 107 and a electric fieldwith a strength of 2MV/m when cooled down to around 3K. For a CH3CNbeam with an initial speed of 80m/s, TE1150 with 50 nodes can succeed indecelerating the beam to a standstill.54Chapter 5. Conclusion and future workFigure 5.1: The superconducting microwave cavity attached to the cry-ocooler55Bibliography[1] Steffen Spieler, Wei Zhong, Pavle Djuricanin, Omid Nourbakhsh, IljaGerhardt, Katsunari Enomoto, Frank Stienkemeier, and Takamasa Mo-mose. 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