Second-order number-conserving description of nonequilibrium dynamics in finite-temperature Bose-Einstein condensates

T. P. Billam, P. Mason, and S. A. Gardiner
Phys. Rev. A 87, 033628 – Published 27 March 2013

Abstract

While the Gross-Pitaevskii equation is well established as the canonical dynamical description of atomic Bose-Einstein condensates (BECs) at zero temperature, describing the dynamics of BECs at finite temperatures remains a difficult theoretical problem, particularly when considering low-temperature, nonequilibrium systems in which depletion of the condensate occurs dynamically as a result of external driving. In this paper, we describe a fully time-dependent numerical implementation of a second-order, number-conserving description of finite-temperature BEC dynamics. This description consists of equations of motion describing the coupled dynamics of the condensate and noncondensate fractions in a self-consistent manner, and is ideally suited for the study of low-temperature, nonequilibrium, driven systems. The δ-kicked-rotor BEC provides a prototypical example of such a system, and we demonstrate the efficacy of our numerical implementation by investigating its dynamics at finite temperature. We demonstrate that the qualitative features of the system dynamics at zero temperature are generally preserved at finite temperatures, and predict a quantitative finite-temperature shift of resonance frequencies which would be relevant for, and could be verified by, future experiments.

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  • Received 11 July 2012

DOI:https://doi.org/10.1103/PhysRevA.87.033628

©2013 American Physical Society

Authors & Affiliations

T. P. Billam*

  • Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin 9016, New Zealand

P. Mason and S. A. Gardiner

  • Joint Quantum Centre (JQC) Durham-Newcastle, Department of Physics, Durham University, Durham, DH1 3LE, United Kingdom

  • *thomas.billam@otago.ac.nz

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Vol. 87, Iss. 3 — March 2013

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