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Physical Review A

Subsonic critical velocity of a Bose-Einstein condensate at finite temperature

Patrick Navez, Robert Graham

Published Apr 19, 2006• 11 citations
Publisher

Abstract

Based on the dielectric formalism in the generalized random phase approximation, we generalize the description of a Bose-Einstein condensed gas to allow for a relative velocity between the superfluid and normal fluid. In this model, we determine the critical velocity dynamically as the transition point between stable and unstable dynamics. Unlike the zero temperature case, at finite temperature the relative critical velocity of a dilute Bose-Einstein gas is lower than the sound velocity. The requirement of Galilean invariance essential to obtain an invariant result necessitates the use of a gapless and conserving approximation.

DOI
10.1103/physreva.73.043612

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Based on the dielectric formalism in the generalized random phase approximation, we generalize the description of a Bose-Einstein condensed gas to allow for a relative velocity between the superfluid and normal fluid. In this model, we determine the critical velocity dynamically as the transition point between stable and unstable dynamics. Unlike the zero temperature case, at finite temperature the relative critical velocity of a dilute Bose-Einstein gas is lower than the sound velocity. The requirement of Galilean invariance essential to obtain an invariant result necessitates the use of a gapless and conserving approximation.
Based on the dielectric formalism in the generalised random phase approximation, we generalise the description of a Bose condensed gas to allow for a relative velocity between the superfluid and normal fluid. In this model, we determine the critical velocity dynamically as the transition point between stable and unstable dynamics. Unlike the zero temperature case, at finite temperature the relative critical velocity of a dilute Bose gas is lower than the sound velocity. This result illustrates one relevant difference that exists between a conserving and gapless approximation and other approaches.
We discuss the superfluid properties of a uniform, weakly interacting Bose-Einstein condensed gas with spin-orbit coupling, realized recently in experiments. We find a finite normal fluid density ${\ensuremath{\rho}}_{n}$ at zero temperature which turns out to be a function of the Raman coupling. In particular, the entire fluid becomes normal at the transition point from the zero momentum to the plane wave phase, even though the condensate fraction remains finite. We emphasize the crucial role played by the breaking of Galilean invariance and by the gapped branch of the elementary excitations whose contribution to various sum rules is discussed explicitly. Our predictions for the superfluid density are successfully compared with the available experimental results based on the measurement of the sound velocities.
In a dilute Bose gas the interaction between the normal gas and the condensate can be studied both at equilibrium and for its relevance to superfluid mechanics. In this article, one reviews first the thermodynamics of the interacting Bose gas in the low density limit and in the low temperature–finite density case. This is extended to thermodynamics with a velocity difference between the two components, normal and superfluid. It is argued that, if the initial value of the momentum related to this velocity difference is larger than the one given by thermodynamic stability, a new condensate should form in a finite time with a velocity close to the that of the normal gas. In the dilute case this occurrence of a new condensate is reminiscent of the condensation in the isotropic case at high enough density.
The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated in the frame of a self-consistent stochastic mean-field approximation. General considerations are presented, which are valid for finite temperatures, arbitrary strengths of the interaction potential, and for arbitrarily strong disorder potentials. The special case of a spatially uncorrelated random field is then treated in more detail. It is shown that the system consists of three components, condensed particles, uncondensed particles, and a glassy density fraction, but that the pure Bose glass phase with only a glassy density does not appear. The theory predicts a first-order phase transition for increasing disorder parameter, where the condensate fraction and the superfluid fraction simultaneously jump to zero. The influence of disorder on the ground-state energy, the stability conditions, the compressibility, the structure factor, and the sound velocity are analyzed. The uniform ideal condensed gas is shown to be always stochastically unstable, in the sense that an infinitesimally weak disorder destroys the Bose-Einstein condensate, returning the system to the normal state; but the uniform Bose-condensed system with finite repulsive interactions becomes stochastically stable and exists in a finite interval of the disorder parameter.
We use the classical fields approximation to study a translational flow of the condensate with respect to the thermal cloud in a weakly interacting Bose gas confined in a three-dimensional box. We study both subcritical and supercritical relative velocity cases and analyze in detail a state of stationary flow which is reached in the dynamics. This state corresponds to the thermal equilibrium, which is characterized by the relative velocity of the condensate and the thermal cloud. We observe two processes---re-thermalization and drag, both of which lead to a reduction of a relative velocity of the superflow. Yet only the drag process, which is observed above the critical velocity vcr{v}_{cr}vcr​, results in transferring a Bose-Einstein condensate to a slower moving mode. In this case the relative velocity of the flow suddenly drops to a value close to zero. Finally, we report the critical velocity to be for our parameters vcr=0.21c{v}_{cr}=0.21cvcr​=0.21c for the initial condition and vcreq=0.12c{v}_{cr}^{eq}=0.12cvcreq​=0.12c for re-thermalized superflow (ccc being the Landau speed of sound), which is strikingly lower than Landau critical velocity, yet consistent with experiments.
We consider the thermodynamics of a homogeneous superfluid dilute Bose gas in the presence of weak quenched disorder. Following the zero-temperature approach of Huang and Meng, we diagonalize the Hamiltonian of a dilute Bose gas in an external random $\ensuremath{\delta}$-correlated potential by means of a Bogoliubov transformation. We extend this approach to finite temperature by combining the Popov and the many-body TTT-matrix approximations. This approach permits us to include the quasiparticle interactions within this temperature range. We derive the disorder-induced shifts of the Bose-Einstein critical temperature and of the temperature for the onset of superfluidity by approaching the transition points from below, i.e., from the superfluid phase. Our results lead to a phase diagram consistent with that of the finite-temperature theory of Lopatin and Vinokur which was based on the replica method, and in which the transition points were approached from above.