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

arXiv:cond-mat/0208263

Hydrodynamic modes in a trapped gas of metastable helium above the Bose-Einstein transition

Michèle Leduc, Jérémie Léonard, Franck Pereira dos Santos, Jahier, E., Sylvain Schwartz, Claude N. Cohen-Tannoudji

Published Aug 13, 2002• 1 citation
arXivHTMLPDF

Abstract

This article describes experiments performed with an ultracold gas of metastable helium above the Bose-Einstein transition. The gas is trapped in an harmonic magnetic potential and collective excitations are induced. Both the frequency and the damping rate of the lowest monopole-quadrupole m = 0 mode of excitation are studied at different temperatures and compared to theoretical predictions. Results indicate that the gas goes from a collisionless regime towards a hydrodynamic regime as the elastic collision rate increases, when one goes down along the evaporative cooling ramp. However we find a discrepancy for the collisional parameters in comparison with predictions relying on the value of the scattering length previously estimated. Possible explanations are put forward in the final discussion.

DOI
10.48550/arxiv.cond-mat/0208263

Related papers

Frequency and damping of hydrodynamic modes in a trapped Bose-condensed gas

Tetsuro Nikuni, Allan Griffin

Recently it was shown that the Landau-Khalatnikov two-fluid hydrodynamics describes the collision-dominated region of a trapped Bose condensate interacting with a thermal cloud. We use these equations to discuss the low frequency hydrodynamic collective modes in a trapped Bose gas at finite temperatures. We derive variational expressions based on these equations for both the frequency and damping of collective modes. A new feature is our use of frequency-dependent transport coefficients, which produce a natural cutoff by eliminating the collisionless low-density tail of the thermal cloud. Above the superfluid transition, our expression for the damping in trapped inhomogeneous gases is analogous to the result first obtained by Landau and Lifshitz for uniform classical fluids. We also use the moment method to discuss the crossover from the collisionless to the hydrodynamic region. Recent data for the monopole-quadrupole mode in the hydrodynamic region of a trapped gas of metastable ${}^{4}\mathrm{He}$ is discussed. We also present calculations for the damping of the analogous $m=0$ monopole-quadrupole condensate mode in the superfluid phase.

arXiv:cond-mat/0309269•Physical Review A•Feb 4, 2004•23 citations

Kinetic Theory of Collective Modes in Atomic Clouds above the Bose-Einstein Transition Temperature

Usama Al Khawaja, C. J. Pethick, H. Smith

We calculate frequencies and damping rates of the lowest collective modes of a dilute Bose gas confined in an anisotropic trapping potential above the Bose-Einstein transition temperature. From the Boltzmann equation with a simplified collision integral we derive a general dispersion relation that interpolates between the collisionless and hydrodynamic regimes. In the case of axially symmetric traps we obtain explicit expressions for the frequencies and damping rates of the lowest modes in terms of a phenomenological collision time. Our results are compared with microscopic calculations and experiments.

arXiv:cond-mat/9908043•Aug 3, 1999•0 citations

Hydrodynamic Modes in a Trapped Bose Gas above the Bose-Einstein Transition

Adam Griffin, Wen-Chin Wu, S. Stringari

We discuss the collective modes of a trapped Bose gas in the hydrodynamic regime where atomic collisions ensure local thermal equilibrium for the distribution function. Starting from the conservation laws, in the linearized limit we derive a closed equation for the velocity fluctuations in a trapped Bose gas above the Bose-Einstein transition temperature. Explicit solutions for a parabolic trap are given. We find that the surface modes above the transition have the same dispersion relation as the one recently obtained by Stringari for the oscillations of the condensate at $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ within the Thomas-Fermi approximation. Results are also given for the monopole ``breathing'' mode as well as for the $m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ excitations which result from the coupling of the monopole and quadrupole modes in an anisotropic parabolic well.

arXiv:cond-mat/9610187•Physical Review Letters•Mar 10, 1997•91 citations

Hydrodynamic versus collisionless dynamics of a one-dimensional harmonically trapped Bose gas

Giulia De Rosi, S. Stringari

By using a sum-rule approach we investigate the transition between the hydrodynamic and the collisionless regime of the collective modes in a one-dimensional (1D) harmonically trapped Bose gas. Both the weakly interacting gas and the Tonks-Girardeau limits are considered. We predict that the excitation of the dipole compression mode is characterized in the high-temperature collisionless regime by a beating signal of two different frequencies (${\ensuremath{\omega}}_{z}$ and $3{\ensuremath{\omega}}_{z}$), while in the high-temperature collisional regime, the excitation consists of a single frequency ($\sqrt{7}{\ensuremath{\omega}}_{z}$). This behavior differs from the case of the lowest breathing mode whose excitation consists of a single frequency ($2{\ensuremath{\omega}}_{z}$) in both regimes. Our predictions for the dipole compression mode open promising perspectives for the experimental investigation of collisional effects in 1D configurations.

arXiv:1608.08417•Physical Review A•Dec 7, 2016•23 citations

Dynamics of a trapped ultracold two-dimensional atomic gas

David Guéry-Odelin, Thierry Lahaye

This article is devoted to the study of two-dimensional Bose gases harmonically confined. We first summarize their equilibrium properties. For such a gas above the critical temperature, we also derive the frequencies and the damping of the collective oscillations and we investigate its expansion after releasing of the trap. The method is well suited to study the collisional effects taking place in the system and in particular to discuss the crossover between the hydrodynamic and the collisionless regimes. We establish the link between the relaxation times relevant for the damping of the collective oscillations and for the time-of-flight expansion. We also evaluate the collision rate and its relationship with the relaxation time.

arXiv:cond-mat/0407522•Comptes Rendus Physique•Jan 1, 2004•2 citations

Transition from Collisionless to Hydrodynamic Behavior in an Ultracold Fermi Gas

S. D. Gensemer, D. S. Jin

Relative motion in a two-component, trapped atomic gas provides a sensitive probe of interactions. By studying the lowest frequency excitations of a two-spin-state gas confined in a magnetic trap, we have explored the transition from the collisionless to the hydrodynamic regime. As a function of collision rate, we observe frequency shifts as large as 6% as well as a dramatic, nonmonotonic dependence of the damping rate. The measurements agree qualitatively with expectations for behavior in the collisionless and hydrodynamic limits and are quantitatively compared to a classical kinetic model.

arXiv:cond-mat/0105441•Physical Review Letters•Oct 4, 2001•67 citations
This article describes experiments performed with an ultracold gas of metastable helium above the Bose-Einstein transition. The gas is trapped in an harmonic magnetic potential and collective excitations are induced. Both the frequency and the damping rate of the lowest monopole-quadrupole m = 0 mode of excitation are studied at different temperatures and compared to theoretical predictions. Results indicate that the gas goes from a collisionless regime towards a hydrodynamic regime as the elastic collision rate increases, when one goes down along the evaporative cooling ramp. However we find a discrepancy for the collisional parameters in comparison with predictions relying on the value of the scattering length previously estimated. Possible explanations are put forward in the final discussion.
Recently it was shown that the Landau-Khalatnikov two-fluid hydrodynamics describes the collision-dominated region of a trapped Bose condensate interacting with a thermal cloud. We use these equations to discuss the low frequency hydrodynamic collective modes in a trapped Bose gas at finite temperatures. We derive variational expressions based on these equations for both the frequency and damping of collective modes. A new feature is our use of frequency-dependent transport coefficients, which produce a natural cutoff by eliminating the collisionless low-density tail of the thermal cloud. Above the superfluid transition, our expression for the damping in trapped inhomogeneous gases is analogous to the result first obtained by Landau and Lifshitz for uniform classical fluids. We also use the moment method to discuss the crossover from the collisionless to the hydrodynamic region. Recent data for the monopole-quadrupole mode in the hydrodynamic region of a trapped gas of metastable 4He{}^{4}\mathrm{He}4He is discussed. We also present calculations for the damping of the analogous m=0m=0m=0 monopole-quadrupole condensate mode in the superfluid phase.
We calculate frequencies and damping rates of the lowest collective modes of a dilute Bose gas confined in an anisotropic trapping potential above the Bose-Einstein transition temperature. From the Boltzmann equation with a simplified collision integral we derive a general dispersion relation that interpolates between the collisionless and hydrodynamic regimes. In the case of axially symmetric traps we obtain explicit expressions for the frequencies and damping rates of the lowest modes in terms of a phenomenological collision time. Our results are compared with microscopic calculations and experiments.
We discuss the collective modes of a trapped Bose gas in the hydrodynamic regime where atomic collisions ensure local thermal equilibrium for the distribution function. Starting from the conservation laws, in the linearized limit we derive a closed equation for the velocity fluctuations in a trapped Bose gas above the Bose-Einstein transition temperature. Explicit solutions for a parabolic trap are given. We find that the surface modes above the transition have the same dispersion relation as the one recently obtained by Stringari for the oscillations of the condensate at T=0T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0T=0 within the Thomas-Fermi approximation. Results are also given for the monopole ``breathing'' mode as well as for the m=0m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0m=0 excitations which result from the coupling of the monopole and quadrupole modes in an anisotropic parabolic well.
By using a sum-rule approach we investigate the transition between the hydrodynamic and the collisionless regime of the collective modes in a one-dimensional (1D) harmonically trapped Bose gas. Both the weakly interacting gas and the Tonks-Girardeau limits are considered. We predict that the excitation of the dipole compression mode is characterized in the high-temperature collisionless regime by a beating signal of two different frequencies (${\ensuremath{\omega}}_{z}$ and $3{\ensuremath{\omega}}_{z}$), while in the high-temperature collisional regime, the excitation consists of a single frequency ($\sqrt{7}{\ensuremath{\omega}}_{z}$). This behavior differs from the case of the lowest breathing mode whose excitation consists of a single frequency ($2{\ensuremath{\omega}}_{z}$) in both regimes. Our predictions for the dipole compression mode open promising perspectives for the experimental investigation of collisional effects in 1D configurations.
This article is devoted to the study of two-dimensional Bose gases harmonically confined. We first summarize their equilibrium properties. For such a gas above the critical temperature, we also derive the frequencies and the damping of the collective oscillations and we investigate its expansion after releasing of the trap. The method is well suited to study the collisional effects taking place in the system and in particular to discuss the crossover between the hydrodynamic and the collisionless regimes. We establish the link between the relaxation times relevant for the damping of the collective oscillations and for the time-of-flight expansion. We also evaluate the collision rate and its relationship with the relaxation time.
Relative motion in a two-component, trapped atomic gas provides a sensitive probe of interactions. By studying the lowest frequency excitations of a two-spin-state gas confined in a magnetic trap, we have explored the transition from the collisionless to the hydrodynamic regime. As a function of collision rate, we observe frequency shifts as large as 6% as well as a dramatic, nonmonotonic dependence of the damping rate. The measurements agree qualitatively with expectations for behavior in the collisionless and hydrodynamic limits and are quantitatively compared to a classical kinetic model.