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arXiv:cond-mat/0503581 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Quantum backreaction in dilute Bose-Einstein condensates

Ralf Schützhold, Michael Uhlmann, Yan Xu, Uwe R. Fischer

Published Nov 8, 2005• 44 citations
arXivHTMLPDF

Abstract

For many physical systems which can be approximated by a classical background field plus small (linearized) quantum fluctuations, a fundamental question concerns the correct description of the backreaction of the quantum fluctuations onto the dynamics of the classical background. We investigate this problem for the example of dilute atomic/molecular Bose-Einstein condensates, for which the microscopic dynamical behavior is under control. It turns out that the effective-action technique does not yield the correct result in general and that the knowledge of the pseudo-energy-momentum tensor $⟨{\stackrel{^}{T}}_{\ensuremath{\mu}\ensuremath{\nu}}⟩$ is not sufficient to describe quantum backreaction.

DOI
10.1103/physrevd.72.105005

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For many physical systems which can be approximated by a classical background field plus small (linearized) quantum fluctuations, a fundamental question concerns the correct description of the backreaction of the quantum fluctuations onto the dynamics of the classical background. We investigate this problem for the example of dilute atomic/molecular Bose-Einstein condensates, for which the microscopic dynamical behavior is under control. It turns out that the effective-action technique does not yield the correct result in general and that the knowledge of the pseudo-energy-momentum tensor ⟨{\stackrel{^}{T}}_{\ensuremath{\mu}\ensuremath{\nu}}⟩ is not sufficient to describe quantum backreaction.
In this paper, with the full field operator expressed in terms of a particle-number-conserving mean-field ansatz, we investigate the dynamical behaviour of Bose–Einstein condensates from microscopic physics. Including the first-order term correction from single-particle excitation and the remaining higher-order term correction from collective excitations simultaneously, we obtain the formulation for a closed local expression of quantum backreaction Q , and discuss the influence on static Bose–Einstein condensates. Even though the quantum backreaction is small, it still has some influence on its dynamics.
Bose-Einstein condensates are suitable systems for studying fundamental aspects of quantum backreaction. Here, the backreaction problem in one-dimensional condensates is considered from the perspective of energy and momentum conservation. By assuming the validity of Bogoliubov theory, the backreaction equations are used to identify the contributions to the system energy and momentum coming from quantum fluctuations and condensate corrections. The backreaction is solved for a condensate trapped in a ring configuration such that particle interactions are gradually switched on. It is shown that the energy in the condensate cannot be addressed without taking into account how the system entered the interacting regime, and even for homogeneous condensates the power transferred to the condensate by quantum fluctuations showcases an intricate nonmonotonic pattern.
We provide a number-conserving approach to the backreaction problem of small quantum fluctuations onto a classical background for the exactly soluble dynamical evolution of a quasi-one-dimensional Bose-Einstein condensate, experimentally realizable in the ultracold gas laboratory. A force density exerted on the gas particles, which is of quantum origin, is uniquely identified as the deviation from the classical Eulerian force density. The backreaction equations are then explored for the specific example of a finite-size uniform density condens- ate initially at rest. By assuming that the condensate starts from a noninteracting regime and in its ground state, we fix a well-defined initial vacuum condition, which is driven out of equilibrium by instantaneously turning on the interactions. The assumption of this initial vacuum accounts for the ambiguity in choosing a vacuum state for interacting condensates, which is due to phase diffusion and the ensuing condensate collapse. As a major finding, we reveal that the time evolution of the condensate cloud leads to condensate density corrections that cannot in general be disentangled from the quantum depletion in measurements probing the power spectrum of the total density. Furthermore, while the condensate is initially at rest, quantum fluctuations give rise to a nontrivial condensate flux, from which we demonstrate that the quantum force density attenuates the classical Eulerian force. Finally, the knowledge of the particle density as a function of time for a condensate at rest determines, to order N0{N}^{0}N0 (where NNN is the total number of particles), the quantum force density, thus offering a viable route for obtaining experimentally accessible quantum backreaction effects.
Weakly interacting, dilute atomic Bose-Einstein condensates (BECs) have proved to be an attractive context for the study of nonlinear dynamics and quantum effects at the macroscopic scale. Recently, weakly interacting, dilute atomic BECs have been used to investigate quantum turbulence both experimentally and theoretically, stimulated largely by the high degree of control which is available within these quantum gases. In this article we motivate the use of weakly interacting, dilute atomic BECs for the study of turbulence, discuss the characteristic regimes of turbulence which are accessible, and briefly review some selected investigations of quantum turbulence and recent results. We focus on three stages of turbulence – the generation of turbulence, its steady state and its decay – and highlight some fundamental questions regarding our understanding in each of these regimes.
Weakly interacting, dilute atomic Bose-Einstein condensates (BECs) have proved to be an attractive context for the study of nonlinear dynamics and quantum effects at the macroscopic scale. Recently, weakly interacting, dilute atomic BECs have been used to investigate quantum turbulence both experimentally and theoretically, stimulated largely by the high degree of control which is available within these quantum gases. In this article we motivate the use of weakly interacting, dilute atomic BECs for the study of turbulence, discuss the characteristic regimes of turbulence which are accessible, and briefly review some selected investigations of quantum turbulence and recent results. We focus on three stages of turbulence- the generation of turbulence, its steady state and its decay- and highlight some fundamental questions regarding our understanding in each of these regimes. 1.
© Published under licence by IOP Publishing Ltd. Weakly interacting, dilute atomic Bose-Einstein condensates (BECs) have proved to be an attractive context for the study of nonlinear dynamics and quantum effects at the macroscopic scale. Recently, weakly interacting, dilute atomic BECs have been used to investigate quantum turbulence both experimentally and theoretically, stimulated largely by the high degree of control which is available within these quantum gases. In this article we motivate the use of weakly interacting, dilute atomic BECs for the study of turbulence, discuss the characteristic regimes of turbulence which are accessible, and briefly review some selected investigations of quantum turbulence and recent results. We focus on three stages of turbulence-the generation of turbulence, its steady state and its decay-and highlight some fundamental questions regarding our understanding in each of these regimes.