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Beyond mean-field investigations of Bose-Einstein condensates: principles and applications in ultracold atomic gases

Banff International Research Station for Mathematical Innovation and Discovery

Bose-Einstein condensation, theoretically known to appear at ultralow temperatures since the 1920s, was achieved in the laboratory only 20 years ago, in dilute bosonic gases at temperatures close to absolute zero. The wide range of applications and controlabillity of the system parame- ters has made them unprecedented tools for exploring novel quantum phases and behavior. The most common theoretical method employed to tackle these complex systems, typically consisting of tens of thousands of interacting particles is the celebrated mean-field Gross-Pitaevskii model. Even though it has been proven successful in describing various types of nonlinear excitations it does not take into consideration fragmentation and correlations that can develop in time. I will briefly present a systematic theory, the MultiConfigurational Time-Dependet Hartree for Bosons (MCTDHB) [1] that has been developed in order to solve the many-body Schroedinger equation beyond the mean-field approach and can be in principle exact, and the latest numerical imple- mentation (solver) that is freely distributed in the web [2]. I will then discuss some particular applications in Bose gases possessing angular momentum and interacting vortices and discuss the novel concept of phantom vortices. The latter are topological defects in rotating gases that evade detection in the density of the gas but give their signature in the correlation function. Last I will present recent theoretical and experimental investigations in nearly-1D gases where periodic modulation of the scattering length might give rise to beyond-mean-field phenomena. [1] Alexej I. Streltsov, Ofir E. Alon, and Lorenz S. Cederbaum, Role of Excited States in the Splitting of a Trapped Interacting Bose-Einstein Condensate by a Time-Dependent Barrier, Phys. Rev. Lett. 99, 030402 (2007); Ofir E. Alon, Alexej I. Streltsov, and Lorenz S. Cederbaum, Mul- ticonfigurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems, Phys. Rev. A 77, 033613 (2008). [2] A.U.J. Lode, M.C. Tsatsos and E. Fasshauer, The Multiconfigurational Time-Dependent Hartree for Indistinguishable particles software (2016), http://ultracold.org.

Mathematics; Partial differential equations; Dynamical systems and ergodic theory

video/mp4

Author affiliation: Institute of Physics Sao Carlos

2017-01-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60048

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/