Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Decay of hydrodynamic modes in dilute Bose-Einstein condensates

Erich D. Gust, L. E. Reichl

Published Oct 15, 2014• 5 citations
Publisher

Abstract

Expressions for the speed and lifetimes of the sound modes in a dilute Bose-Einstein condensate are obtained using Bogoliubov mean field theory. The condensate has two pairs of sound modes which undergo an avoided crossing as the equilibrium temperature is varied. The two pairs of sound modes decay at very different rates, except in the neighborhood of the avoided crossing, where the identity of the longest-lived mode switches. The predicted speed and lifetime of the longest-lived sound mode are consistent with recent experimental observations on sound in an $^{87}\mathrm{Rb}$ Bose-Einstein condensate.

DOI
10.1103/physreva.90.043615

Related papers

Transport theory for a dilute Bose-Einstein condensate

L. E. Reichl, Erich D. Gust

We obtain microscopic expressions for the six hydrodynamic modes of a dilute Bose-Einstein condensate: two transverse (shear) modes and four longitudinal modes corresponding to the first sound (elastic waves) and second sound (temperature waves). Our microscopic expressions include both the speed of the two types of sound and the rate of relaxation of the sound waves. We obtain numerical values for the shear viscosity of a dilute BEC composed of bosons which interact via a contact potential. Our values for the shear viscosity are obtained using the eigenvalues and eigenvectors of the three types of collision operators that govern the relaxation of the condensate.

Physical Review A•Nov 6, 2013•15 citations

A kinetic equation for ultra-low temperature Bose–Einstein condensates

L. E. Reichl, Minh-Binh Tran

Abstract Bose–Einstein condensates (BECs) are starting to play a role in quantum information processing, and there is a need to better understand the dynamical processes at play in the condensates. In this paper, we review recent work on a kinetic model for ultra-low temperature dilute Bose–Einstein condensates that gives correct behavior for first and second sound speeds at very low temperature, and gives explicit expressions and values for decay processes. The predictions of the theory are in agreement with experiment. The method explicitly computes the hydrodynamic modes of the condensate using a method that has also been used to describe decay processes in noble gas mixtures, and thereby opens the way for future analysis of decay processes in BEC mixtures.

Journal of Physics A Mathematical and Theoretical•Dec 11, 2018•12 citations

Collisionless and Hydrodynamic Excitations of a Bose-Einstein Condensate

Dan Stamper-Kurn, H.‐J. Miesner, S. Inouye +2 more

Collective excitations of a dilute Bose gas were probed above and below the Bose-Einstein condensation temperature. The temperature dependencies of the frequency and damping rates of condensate oscillations indicate significant interactions between the condensate and the thermal cloud. Hydrodynamic oscillations of the thermal cloud analogous to first sound were observed. An out-of-phase dipolar oscillation of the thermal cloud and the condensate was also studied, analogous to second sound. The excitations were observed in situ using nondestructive imaging techniques.

Physical Review Letters•Jul 20, 1998•367 citations

First and Second Sound Modes of a Bose-Einstein Condensate in a Harmonic Trap

Vivek B. Shenoy, Tin-Lun Ho

We have calculated the first and second sound modes of a dilute interacting Bose gas in a spherical trap for temperatures $(0.6<{T/T}_{c}<1.2)$ and for systems with ${10}^{4}$ to ${10}^{8}$ particles. The second sound modes (which exist only below ${T}_{c}$) generally have a stronger temperature dependence than the first sound modes. The puzzling temperature variations of the sound modes near ${T}_{c}$ recently observed at JILA in systems with ${10}^{3}$ particles match surprisingly well with those of the first and second sound modes of much larger systems.

arXiv:cond-mat/9710274•Physical Review Letters•May 4, 1998•27 citations

Propagation of Sound in a Bose-Einstein Condensate

Michael R. Andrews, Dan Stamper-Kurn, H.‐J. Miesner +4 more

Sound propagation has been studied in a magnetically trapped dilute Bose-Einstein condensate. Localized excitations were induced by suddenly modifying the trapping potential using the optical dipole force of a focused laser beam. The resulting propagation of sound was observed using a novel technique, rapid sequencing of nondestructive phase-contrast images. The speed of sound was determined as a function of density and found to be consistent with Bogoliubov theory. This method may generally be used to observe high-lying modes and perhaps second sound.

Physical Review Letters•Jul 28, 1997•444 citations

Collective excitations of a Bose-condensed gas: Fate of second sound in the crossover regime between hydrodynamic and collisionless regimes

Hoshu Hiyane, Shohei Watabe, Tetsuro Nikuni

We develop the moment method for Bose-Einstein condensates at finite temperatures that enable us to study collective sound modes from the hydrodynamic to the collisionless regime. In particular, we investigate collective excitations in a weakly interacting dilute Bose gas by applying the moment method to the Zaremba-Nikuni-Griffin equation, which is the coupled equation of the Boltzmann equation with the generalized Gross-Pitaevskii equation. Utilizing the moment method, collective excitations in the crossover regime between the hydrodynamic and collisionless regimes are investigated in detail. In the crossover regime, the second sound mode loses the weight of the density response function because of the significant coupling with incoherent modes, whereas the first sound shows a distinct but broad peak structure. We compare the result obtained by the moment method with that of the Landau two-fluid equations and show that the collective mode predicted by the Landau two-fluid equations well coincides with the result from the moment method even far from the hydrodynamic regime, whereas clear distinction also emerges in the relatively higher momentum regime.

arXiv:2310.01988•Physical Review A•Mar 4, 2024•2 citations
Expressions for the speed and lifetimes of the sound modes in a dilute Bose-Einstein condensate are obtained using Bogoliubov mean field theory. The condensate has two pairs of sound modes which undergo an avoided crossing as the equilibrium temperature is varied. The two pairs of sound modes decay at very different rates, except in the neighborhood of the avoided crossing, where the identity of the longest-lived mode switches. The predicted speed and lifetime of the longest-lived sound mode are consistent with recent experimental observations on sound in an 87Rb^{87}\mathrm{Rb}87Rb Bose-Einstein condensate.
We obtain microscopic expressions for the six hydrodynamic modes of a dilute Bose-Einstein condensate: two transverse (shear) modes and four longitudinal modes corresponding to the first sound (elastic waves) and second sound (temperature waves). Our microscopic expressions include both the speed of the two types of sound and the rate of relaxation of the sound waves. We obtain numerical values for the shear viscosity of a dilute BEC composed of bosons which interact via a contact potential. Our values for the shear viscosity are obtained using the eigenvalues and eigenvectors of the three types of collision operators that govern the relaxation of the condensate.
Abstract Bose–Einstein condensates (BECs) are starting to play a role in quantum information processing, and there is a need to better understand the dynamical processes at play in the condensates. In this paper, we review recent work on a kinetic model for ultra-low temperature dilute Bose–Einstein condensates that gives correct behavior for first and second sound speeds at very low temperature, and gives explicit expressions and values for decay processes. The predictions of the theory are in agreement with experiment. The method explicitly computes the hydrodynamic modes of the condensate using a method that has also been used to describe decay processes in noble gas mixtures, and thereby opens the way for future analysis of decay processes in BEC mixtures.
Collective excitations of a dilute Bose gas were probed above and below the Bose-Einstein condensation temperature. The temperature dependencies of the frequency and damping rates of condensate oscillations indicate significant interactions between the condensate and the thermal cloud. Hydrodynamic oscillations of the thermal cloud analogous to first sound were observed. An out-of-phase dipolar oscillation of the thermal cloud and the condensate was also studied, analogous to second sound. The excitations were observed in situ using nondestructive imaging techniques.
We have calculated the first and second sound modes of a dilute interacting Bose gas in a spherical trap for temperatures (0.6<T/Tc<1.2)(0.6<{T/T}_{c}<1.2)(0.6<T/Tc​<1.2) and for systems with 104{10}^{4}104 to 108{10}^{8}108 particles. The second sound modes (which exist only below Tc{T}_{c}Tc​) generally have a stronger temperature dependence than the first sound modes. The puzzling temperature variations of the sound modes near Tc{T}_{c}Tc​ recently observed at JILA in systems with 103{10}^{3}103 particles match surprisingly well with those of the first and second sound modes of much larger systems.
Sound propagation has been studied in a magnetically trapped dilute Bose-Einstein condensate. Localized excitations were induced by suddenly modifying the trapping potential using the optical dipole force of a focused laser beam. The resulting propagation of sound was observed using a novel technique, rapid sequencing of nondestructive phase-contrast images. The speed of sound was determined as a function of density and found to be consistent with Bogoliubov theory. This method may generally be used to observe high-lying modes and perhaps second sound.
We develop the moment method for Bose-Einstein condensates at finite temperatures that enable us to study collective sound modes from the hydrodynamic to the collisionless regime. In particular, we investigate collective excitations in a weakly interacting dilute Bose gas by applying the moment method to the Zaremba-Nikuni-Griffin equation, which is the coupled equation of the Boltzmann equation with the generalized Gross-Pitaevskii equation. Utilizing the moment method, collective excitations in the crossover regime between the hydrodynamic and collisionless regimes are investigated in detail. In the crossover regime, the second sound mode loses the weight of the density response function because of the significant coupling with incoherent modes, whereas the first sound shows a distinct but broad peak structure. We compare the result obtained by the moment method with that of the Landau two-fluid equations and show that the collective mode predicted by the Landau two-fluid equations well coincides with the result from the moment method even far from the hydrodynamic regime, whereas clear distinction also emerges in the relatively higher momentum regime.