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arXiv:1002.1740 · Journal of Physics B Atomic Molecular and Optical Physics

Simulating quantum transport for a quasi-one-dimensional Bose gas in an optical lattice: the choice of fluctuation modes in the truncated Wigner approximation

Bo Xiong, Tao Yang, Keith A. Benedict

Published Jul 5, 2013• 3 citations
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Abstract

We study the effect of quantum fluctuations on the dynamics of a quasi-one-dimensional Bose gas in an optical lattice at zero temperature using the truncated Wigner approximation with a variety of basis sets for the initial fluctuation modes. The initial spatial distributions of the quantum fluctuations are very different when using a limited number of plane-wave (PW), simple-harmonic-oscillator (SHO) and self-consistently determined Bogoliubov (SCB) modes. The short-time transport properties of the Bose gas, characterized by the phase coherence in the PW basis, are distinct from those gained using the SHO and SCB basis. The calculations using the SCB modes predict greater phase decoherence and stronger number fluctuations than the other choices. Furthermore, we observe that the use of PW modes overestimates the extent to which atoms are expelled from the core of the cloud, while the use of the other modes only breaks the cloud structure slightly, which is in agreement with the experimental observations by Fertig et al (2005 Phys. Rev. Lett. 94 120403).

DOI
10.1088/0953-4075/46/14/145307

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We study the effect of quantum fluctuations on the dynamics of a quasi-one-dimensional Bose gas in an optical lattice at zero temperature using the truncated Wigner approximation with a variety of basis sets for the initial fluctuation modes. The initial spatial distributions of the quantum fluctuations are very different when using a limited number of plane-wave (PW), simple-harmonic-oscillator (SHO) and self-consistently determined Bogoliubov (SCB) modes. The short-time transport properties of the Bose gas, characterized by the phase coherence in the PW basis, are distinct from those gained using the SHO and SCB basis. The calculations using the SCB modes predict greater phase decoherence and stronger number fluctuations than the other choices. Furthermore, we observe that the use of PW modes overestimates the extent to which atoms are expelled from the core of the cloud, while the use of the other modes only breaks the cloud structure slightly, which is in agreement with the experimental observations by Fertig et al (2005 Phys. Rev. Lett. 94 120403).
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We study quantum dynamics of a Bose-Einstein condensate in a one-dimensional optical lattice in the limit of weak atom-atom interactions within the truncated Wigner approximation for a system with one dynamically unstable mode. This extends previous classical studies of a pulsating dynamical instability in which atoms periodically collect together and subsequently disperse back into the initial homogeneous state. We observe that the quasiperiodic behavior still persists in the presence of quantum fluctuations for a single realization that represents a typical experimental outcome, but ensemble averages show various manifestations of quantum statistics. Quantum effects become more prominent when the effective interaction strength is increased.
This dissertation studies the dynamics of atomic Bose-Einstein condensates (nEes) and Bose gases in a suddenly modified potential.\nFirstly, we investigate the correlation between vortex formation and interference in merging Bose-Einstein condensates. This inherent correlation can explain some experiments in which vortices are formed in interfering condensates. Furthermore, we show the interference properties of merging condensates, particularly the relation of interference among colliding, expanding, and merging condensates, which can explain some complex interference phenomena in recent experiments.\nSecondly, using the truncated Wigner approximation, we investigate the role of quantum fluctuations in different forms on the transport properties of bosonic atoms in a ID optical lattice. The dynamics of transport with respect to quantum fluctuations in the plane-wave modes is distinct from that in the single-harmonic-oscillator modes. The discrepancies are demonstrated in detail. Quantum fluctuations in Bogoliubov modes lead to stronger damping behaviour of the centre-of-mass motion than quantum fluctuations in the plane-wave and single-harmonic-oscillator modes, which is in agreement with the experiment.\nThirdly, the role of the relative phase variation and velocity of two low-density condensates, and quantum noise on interference properties are discussed. In particular, the incoherent atoms have significant effect on the interference visibility and microscopic dynamics. Although the interference pattern is not broken by quantum fluctuations, indicating the robust character of this interference, the process of inner correlations and dynamics is very complex and cannot he understood purely with mean-field theory.\nFinally, we investigate the elementary excitation spectrum and mode functions of a trapped Bose gas by numerically solving the Bogoliubov-De Gennes equation. The characteristic form of the Bogoliubov matrix, determined by the interatomic interactions, and the interaction between atoms and confining potential, specifies excitation spectra and mode functions. The role of these interactions on the properties of spectra and mode functions are shown.
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