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arXiv:1208.1653 · Condensed Matter Physics

Mechanism of collisionless sound damping in dilute Bose gas with condensate

Yu. V. Slyusarenko, Alexander Kruchkov

Published Jan 1, 2013• 2 citations

Abstract

We develop a microscopic theory of sound damping due to Landau mechanism in dilute gas with Bose condensate.It is based on the coupled evolution equations of the parameters describing the system.These equations have been derived in earlier works within a microscopic approach which employs the Peletminskii-Yatsenko reduced description method for quantum many-particle systems and Bogoliubov model for a weakly nonideal Bose gas with a separated condensate.The dispersion equations for sound oscillations were obtained by linearization of the mentioned evolution equations in the collisionless approximation.They were analyzed both analytically and numerically.The expressions for sound speed and decrement rate were obtained in high and low temperature limiting cases.We have shown that at low temperature the dependence of the obtained quantities on temperature significantly differs from those obtained by other authors in the semi-phenomenological approaches.Possible effects connected with non-analytic temperature dependence of dispersion characteristics of the system were also indicated.

DOI: 10.5488/cmp.16.23004

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We develop a microscopic theory of sound damping due to Landau mechanism in dilute gas with Bose condensate.It is based on the coupled evolution equations of the parameters describing the system.These equations have been derived in earlier works within a microscopic approach which employs the Peletminskii-Yatsenko reduced description method for quantum many-particle systems and Bogoliubov model for a weakly nonideal Bose gas with a separated condensate.The dispersion equations for sound oscillations were obtained by linearization of the mentioned evolution equations in the collisionless approximation.They were analyzed both analytically and numerically.The expressions for sound speed and decrement rate were obtained in high and low temperature limiting cases.We have shown that at low temperature the dependence of the obtained quantities on temperature significantly differs from those obtained by other authors in the semi-phenomenological approaches.Possible effects connected with non-analytic temperature dependence of dispersion characteristics of the system were also indicated.

We study the low-energy collective oscillations of a dilute Bose gas at finite temperature in the collisionless regime. By using a time-dependent mean-field scheme we derive for the dynamics of the condensate and noncondensate components a set of coupled equations, which we solve perturbatively to second order in the interaction coupling constant. This approach is equivalent to the finite-temperature extension of the Beliaev approximation and includes corrections to the Gross-Pitaevskii theory due to both quantum and thermal fluctuations. For a homogeneous system we explicitly calculate the temperature dependence of the velocity of propagation and damping rate of zero sound. In the case of harmonically trapped systems in the thermodynamic limit, we calculate, as a function of temperature, the frequency shift of the low-energy compressional and surface modes.

We study the dynamics of dilute and ultracold bosonic gases in a quasi-two-dimensional (quasi-2D) configuration and in the collisionless regime. We adopt the 2D Landau-Vlasov equation to describe a three-dimensional gas under very strong harmonic confinement along one direction. We use this effective equation to investigate the speed of sound in quasi-2D bosonic gases, i.e., the sound propagation around a Bose-Einstein distribution in collisionless 2D gases. We derive coupled algebraic equations for the real and imaginary parts of the sound velocity, which are then solved also taking into account the equation of state of the 2D bosonic system. Above the Berezinskii-Kosterlitz-Thouless critical temperature we find that there is rapid growth of the imaginary component of the sound velocity, which implies a strong Landau damping. Quite remarkably, our theoretical results are in good agreement with very recent experimental data obtained with a uniform 2D Bose gas of

^{87}\mathrm{Rb}

atoms.

By using a mean-field approximation which describes the coupled oscillations of condensate and noncondensate atoms in the collisionless regime, Landau damping in a dilute dipolar Bose–Fermi mixture in the BEC limit where Fermi superfluid is treated as tightly bounded molecules, is investigated. In the case of a uniform quasi-two-dimensional (2D) case, the results for the Landau damping due to the Bose–Fermi interaction are obtained at low and high temperatures. It is shown that at low temperatures, the Landau damping rate is exponentially suppressed. By increasing the strength of dipolar interaction, and the energy of boson quasiparticles, Landau damping is suppressed over a broader temperature range.

Using linear response theory within the random phase approximation, we investigate the propagation of sound in a uniform two dimensional (2D) Bose gas in the collisionless regime. We show that the sudden removal of a static density perturbation produces a damped oscillatory behavior revealing that sound can propagate also in the absence of collisions, due to mean-field interaction effects. We provide explicit results for the sound velocity and damping as a function of temperature, pointing out the crucial role played by Landau damping. We support our predictions by performing numerical simulations with the stochastic (projected) Gross-Pitaevskii equation. The results are consistent with the recent experimental observation of sound in a weakly interacting 2D Bose gas both below and above the superfluid Berezinskii-Kosterlitz-Thouless transition.

The superfluidity of low-temperature bosons is well established in the collisional regime. In the collisionless regime, however, the presence of superfluidity is not yet fully clarified, in particular in lower spatial dimensions. Here, we compare the Vlasov-Landau equation, which does not take into account the superfluid nature of the bosonic system, with the Andreev-Khalatnikov equations, which instead explicitly contain a superfluid velocity. We show that recent experimental data of the sound mode in a two-dimensional collisionless Bose gas of

^{87}\mathrm{Rb}

atoms are in good agreement with both theories, but the sound damping is better reproduced by the Andreev-Khalatnikov equations below the Berezinskii-Kosterlitz-Thouless critical temperature

^{87}\mathrm{Rb}

, while above

{T}_{c}

the Vlasov-Landau results are closer to the experimental ones. For one-dimensional bosonic fluids, where experimental data are not yet available, we find larger differences between the sound velocities predicted by the two transport theories and, also in this case, the existence of a superfluid velocity reduces the sound damping.