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:1309.3651 · Physical Review A

Damping of the quadrupole mode in a two-dimensional Fermi gas

Silvia Chiacchiera, D. Davesne, Tilman Enss, Mi­chael Urban

Published Nov 13, 2013• 14 citations
arXivHTMLPDF

Abstract

In a recent experiment [Vogt et al., Phys. Rev. Lett. 108, 070404 (2012)], quadrupole and breathing modes of a two-dimensional Fermi gas were studied. We model these collective modes by solving the Boltzmann equation via the method of phase-space moments up to fourth order, including in-medium effects on the scattering cross section. In our analysis, we use a realistic Gaussian potential deformed by the presence of gravity and magnetic field gradients. We conclude that the origin of the experimentally observed damping of the quadrupole mode, especially in the weakly interacting (or even noninteracting) case, cannot be explained by these mechanisms.

DOI
10.1103/physreva.88.053616

Related papers

Applicability of the Boltzmann equation for a two-dimensional Fermi gas

Lei Wu, Yonghao Zhang

We study the validity range of the semiclassical Boltzmann equation in describing the dynamics of two-dimensional Fermi gas. Here we numerically solve the Boltzmann equation based on the relaxation-time approximation. By comparing the numerically extracted damping of the quadrupole mode with the experimental data reported in Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)], we demonstrate that the Boltzmann equation is applicable at least when the temperature is larger than $0.47{T}_{F}$, up to the strong coupling regime, where ${T}_{F}$ is the Fermi temperature.

Physical Review A•Apr 12, 2012•13 citations

Collective modes of three- and two-dimensional trapped Fermi gases in the normal phase

Mi­chael Urban, Silvia Chiacchiera, D. Davesne +2 more

We study the transition from the hydrodynamic to the collisionless regime in collective modes of three- and two-dimensional Fermi gases by using the semiclassical Boltzmann equation. We use direct numerical simulations as well as the method of phase-space moments to solve the Boltzmann equation and show that the restriction to second-order moments is not accurate enough. By including higher-order moments, we can successfully describe the hydrodynamic to collisionless transition observed in the quadrupole mode in three-dimensional Fermi gases and the frequency shift and damping of the sloshing mode due to the anharmonic shape of the experimental trap potential. In the case of two-dimensional Fermi gases, however, the strong damping of the quadrupole mode observed in a recent experiment remains unexplained.

Journal of Physics Conference Series•Apr 9, 2014•3 citations

Collective modes of trapped Fermi gases with in-medium interaction

Silvia Chiacchiera, Thomas Lepers, D. Davesne +1 more

Due to Pauli blocking of intermediate states, the scattering matrix (or $T$ matrix) of two fermionic atoms in a Fermi gas becomes different from that of two atoms in free space. This effect becomes particularly important near a Feshbach resonance, where the interaction in free space is very strong but becomes effectively suppressed in the medium. We calculate the in-medium $T$ matrix in ladder approximation and study its effects on the properties of collective modes of a trapped gas in the normal-fluid phase. We introduce the in-medium interaction on both sides of the Boltzmann equation, namely, in the calculation of the mean field and in the calculation of the collision rate. This allows us to explain the observed upward shift of the frequency of the quadrupole mode in the collisionless regime. By including the mean field, we also improve considerably the agreement with the measured temperature dependence of frequency and damping rate of the scissors mode, whereas the use of the in-medium cross section deteriorates the description, in agreement with previous work.

arXiv:0812.0239•Physical Review A•Mar 12, 2009•27 citations

Shear viscosity and damping of collective modes in a two-dimensional Fermi gas

Thomas Schäfer

The shear viscosity of a two-dimensional Fermi gas interacting via a short-range potential with scattering length ${a}_{2\mathrm{d}}$ in kinetic theory is computed. It is found that classical kinetic theory predicts that the shear viscosity to entropy density ratio of a strongly interacting two-dimensional gas is comparable to that of the three-dimensional unitary gas. Results are applied to the damping of collective modes of a trapped Fermi gas, and compared to experimental data recently obtained by Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)].

arXiv:1111.7242•Physical Review A•Mar 19, 2012•36 citations

Hydrodynamics of Unitary Fermi Gases

Jasmine Brewer

In this thesis we present fully nonlinear dissipative hydrodynamics simulations using the lattice Boltzmann method which we have developed to study hydrodynamics in cold atomic gases. We motivate and derive the specifics of the lattice Boltzmann implementation for this system, and then use our simulations to study collective oscillations in two-dimensional Fermi gases. We show that all dominant frequencies and damping rates of the breathing and quadrupole oscillatory modes agree quantitatively with analytic solutions in the hydrodynamic limit for a gas with ideal equation of state in a harmonic trap. We suggest improvements to our numerical methods which we expect to improve the quantitative agreement of the quadrupole mode frequency with the expected value outside of the hydrodynamic limit. We also suggest techniques for extracting the non-dominant (non-hydrodynamic) damping rate of the quadrupole mode in the hydrodynamic regime with higher precision. Additionally, we propose that the observed non-hydrodynamic damping of the quadrupole mode would be interesting to study experimentally for applications to collective oscillations in the quark-gluon plasma.

•Jan 1, 2015•0 citations

Damping of collective modes in ultracold trapped Fermi gases with in-medium cross section

Mi­chael Urban, Silvia Chiacchiera, D. Davesne +1 more

We study the damping of the quadrupole and scissors modes of ultracold trapped Fermi gases with large negative scattering length at temperatures above the superfluid critical temperature T c within the framework of the Boltzmann equation. The in-medium scattering cross-section is strongly enhanced at temperatures slightly above T c . This has strong effects on the collisional damping of the collective modes and the transition from hydrodynamic to collisionless behaviour as a function of temperature. Within the method of phase-space moments of second order, it was found that the resulting damping rates are in strong disagreement with experimental data from the Innsbruck group, which seemed to favour the free cross section. However, the comparison with numerical solutions of the Boltzmann equation revealed that the method of second-order phase-space moments is insufficient. Here we show that the agreement between the calculation using the in-medium cross-section and the data can be clearly improved by including also fourth-order moments.

Journal of Physics Conference Series•Sep 16, 2011•0 citations
In a recent experiment [Vogt et al., Phys. Rev. Lett. 108, 070404 (2012)], quadrupole and breathing modes of a two-dimensional Fermi gas were studied. We model these collective modes by solving the Boltzmann equation via the method of phase-space moments up to fourth order, including in-medium effects on the scattering cross section. In our analysis, we use a realistic Gaussian potential deformed by the presence of gravity and magnetic field gradients. We conclude that the origin of the experimentally observed damping of the quadrupole mode, especially in the weakly interacting (or even noninteracting) case, cannot be explained by these mechanisms.
We study the validity range of the semiclassical Boltzmann equation in describing the dynamics of two-dimensional Fermi gas. Here we numerically solve the Boltzmann equation based on the relaxation-time approximation. By comparing the numerically extracted damping of the quadrupole mode with the experimental data reported in Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)], we demonstrate that the Boltzmann equation is applicable at least when the temperature is larger than 0.47TF0.47{T}_{F}0.47TF​, up to the strong coupling regime, where TF{T}_{F}TF​ is the Fermi temperature.
We study the transition from the hydrodynamic to the collisionless regime in collective modes of three- and two-dimensional Fermi gases by using the semiclassical Boltzmann equation. We use direct numerical simulations as well as the method of phase-space moments to solve the Boltzmann equation and show that the restriction to second-order moments is not accurate enough. By including higher-order moments, we can successfully describe the hydrodynamic to collisionless transition observed in the quadrupole mode in three-dimensional Fermi gases and the frequency shift and damping of the sloshing mode due to the anharmonic shape of the experimental trap potential. In the case of two-dimensional Fermi gases, however, the strong damping of the quadrupole mode observed in a recent experiment remains unexplained.
Due to Pauli blocking of intermediate states, the scattering matrix (or TTT matrix) of two fermionic atoms in a Fermi gas becomes different from that of two atoms in free space. This effect becomes particularly important near a Feshbach resonance, where the interaction in free space is very strong but becomes effectively suppressed in the medium. We calculate the in-medium TTT matrix in ladder approximation and study its effects on the properties of collective modes of a trapped gas in the normal-fluid phase. We introduce the in-medium interaction on both sides of the Boltzmann equation, namely, in the calculation of the mean field and in the calculation of the collision rate. This allows us to explain the observed upward shift of the frequency of the quadrupole mode in the collisionless regime. By including the mean field, we also improve considerably the agreement with the measured temperature dependence of frequency and damping rate of the scissors mode, whereas the use of the in-medium cross section deteriorates the description, in agreement with previous work.
The shear viscosity of a two-dimensional Fermi gas interacting via a short-range potential with scattering length a2d{a}_{2\mathrm{d}}a2d​ in kinetic theory is computed. It is found that classical kinetic theory predicts that the shear viscosity to entropy density ratio of a strongly interacting two-dimensional gas is comparable to that of the three-dimensional unitary gas. Results are applied to the damping of collective modes of a trapped Fermi gas, and compared to experimental data recently obtained by Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)].
In this thesis we present fully nonlinear dissipative hydrodynamics simulations using the lattice Boltzmann method which we have developed to study hydrodynamics in cold atomic gases. We motivate and derive the specifics of the lattice Boltzmann implementation for this system, and then use our simulations to study collective oscillations in two-dimensional Fermi gases. We show that all dominant frequencies and damping rates of the breathing and quadrupole oscillatory modes agree quantitatively with analytic solutions in the hydrodynamic limit for a gas with ideal equation of state in a harmonic trap. We suggest improvements to our numerical methods which we expect to improve the quantitative agreement of the quadrupole mode frequency with the expected value outside of the hydrodynamic limit. We also suggest techniques for extracting the non-dominant (non-hydrodynamic) damping rate of the quadrupole mode in the hydrodynamic regime with higher precision. Additionally, we propose that the observed non-hydrodynamic damping of the quadrupole mode would be interesting to study experimentally for applications to collective oscillations in the quark-gluon plasma.
We study the damping of the quadrupole and scissors modes of ultracold trapped Fermi gases with large negative scattering length at temperatures above the superfluid critical temperature T c within the framework of the Boltzmann equation. The in-medium scattering cross-section is strongly enhanced at temperatures slightly above T c . This has strong effects on the collisional damping of the collective modes and the transition from hydrodynamic to collisionless behaviour as a function of temperature. Within the method of phase-space moments of second order, it was found that the resulting damping rates are in strong disagreement with experimental data from the Innsbruck group, which seemed to favour the free cross section. However, the comparison with numerical solutions of the Boltzmann equation revealed that the method of second-order phase-space moments is insufficient. Here we show that the agreement between the calculation using the in-medium cross-section and the data can be clearly improved by including also fourth-order moments.