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/0409660 · Physical Review A

Viscous relaxation and collective oscillations in a trapped Fermi gas near the unitarity limit

Pietro Massignan, Georg M. Bruun, H. Smith

Published Mar 4, 2005• 113 citations
arXivHTMLPDF

Abstract

The viscous relaxation time of a trapped two-component gas of fermions in its normal phase is calculated as a function of temperature and scattering length, with the collision probability being determined by an energy-dependent $s$-wave cross section. The result is used for calculating the temperature dependence of the frequency and damping of collective modes studied in recent experiments, starting from the kinetic equation for the fermion distribution function with mean-field effects included in the streaming terms.

DOI
10.1103/physreva.71.033607

Related papers

Transition and Damping of Collective Modes in a Trapped Fermi Gas between BCS and Unitary Limits near the Phase Transition

Hang Dong, Wenyuan Zhang, Zhou Li +1 more

We investigate the transition and damping of low-energy collective modes in a trapped unitary Fermi gas by solving the Boltzmann-Vlasov kinetic equation in a scaled form, which is combined with both the T-matrix fluctuation theory in normal phase and the mean-field theory in order phase. In order to connect the microscopic and kinetic descriptions of many-body Feshbach scattering, we adopt a phenomenological two-fluid physical approach, and derive the coupling constants in the order phase. By solving the Boltzmann-Vlasov steady-state equation in a variational form, we calculate two viscous relaxation rates with the collision probabilities of fermion's scattering including fermions in the normal fluid and fermion pairs in the superfluid. Additionally, by considering the pairing and depairing of fermions, we get results of the frequency and damping of collective modes versus temperature and s-wave scattering length. Our theoretical results are in a remarkable agreement with the experimental data, particularly for the sharp transition between collisionless and hydrodynamic behaviour and strong damping between BCS and unitary limits near the phase transition. The sharp transition originates from the maximum of viscous relaxation rate caused by fermion-fermion pair collision at the phase transition point when the fermion depair, while the strong damping due to the fast varying of the frequency of collective modes from BCS limit to unitary limit.

Scientific Reports•Nov 2, 2015•8 citations

Shear viscosity and damping for a Fermi gas in the unitarity limit

Georg M. Bruun, H. Smith

The shear viscosity of a two-component Fermi gas in the normal phase is calculated as a function of temperature in the unitarity limit, taking into account strong-coupling effects that give rise to a pseudogap in the spectral density for single-particle excitations. The results indicate that recent measurements of the damping of collective modes in trapped atomic clouds can be understood in terms of hydrodynamics, with a decay rate given by the viscosity integrated over an effective volume of the cloud.

arXiv:cond-mat/0612460•Physical Review A•Apr 17, 2007•103 citations

Viscosity and thermal relaxation for a resonantly interacting Fermi gas

Georg M. Bruun, H. Smith

The viscous and thermal relaxation rates of an interacting fermion gas are calculated as functions of temperature and scattering length, using a many-body scattering matrix which incorporates medium effects due to Fermi blocking of intermediate states. These effects are demonstrated to be large close to the transition temperature ${T}_{c}$ to the superfluid state. For a homogeneous gas in the unitarity limit, the relaxation rates are increased by nearly an order of magnitude compared to their value obtained in the absence of medium effects due to the Cooper instability at ${T}_{c}$. For trapped gases the corresponding ratio is found to be about three due to the averaging over the inhomogeneous density distribution. The effect of superfluidity below ${T}_{c}$ is considered to leading order in the ratio between the energy gap and the transition temperature.

arXiv:cond-mat/0504734•Physical Review A•Oct 13, 2005•87 citations

Collective oscillations of a Fermi gas in the unitarity limit: Temperature effects and the role of pair correlations

S. Riedl, Edmundo R. Sánchez Guajardo, Christoph Kohstall +6 more

We present detailed measurements of the frequency and damping of three different collective modes in an ultracold trapped Fermi gas of $^{6}\mathrm{Li}$ atoms with resonantly tuned interactions. The measurements are carried out over a wide range of temperatures. We focus on the unitarity limit, where the scattering length is much greater than all other relevant length scales. The results are compared to theoretical calculations that take into account Pauli blocking and pair correlations in the normal state above the critical temperature for superfluidity. We show that these two effects nearly compensate each other and the behavior of the gas is close to that of a classical gas.

arXiv:0809.1814•Physical Review A•Nov 5, 2008•92 citations

Collective oscillations of a trapped superfluid Fermi gas near a Feshbach resonance

S. Stringari

The frequencies of the collective oscillations of a harmonically trapped Fermi gas interacting with large scattering lengths are calculated at zero temperature using hydrodynamic theory. Different regimes are considered, including the molecular Bose-Einstein condensate and the unitarity limit for collisions. We show that the frequency of the radial compressional mode in an elongated trap exhibits a pronounced non-monotonous dependence on the scattering length, reflecting the role of the interactions in the equation of state.

arXiv:cond-mat/0312614•Europhysics Letters (EPL)•Mar 1, 2004•116 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
The viscous relaxation time of a trapped two-component gas of fermions in its normal phase is calculated as a function of temperature and scattering length, with the collision probability being determined by an energy-dependent sss-wave cross section. The result is used for calculating the temperature dependence of the frequency and damping of collective modes studied in recent experiments, starting from the kinetic equation for the fermion distribution function with mean-field effects included in the streaming terms.
We investigate the transition and damping of low-energy collective modes in a trapped unitary Fermi gas by solving the Boltzmann-Vlasov kinetic equation in a scaled form, which is combined with both the T-matrix fluctuation theory in normal phase and the mean-field theory in order phase. In order to connect the microscopic and kinetic descriptions of many-body Feshbach scattering, we adopt a phenomenological two-fluid physical approach, and derive the coupling constants in the order phase. By solving the Boltzmann-Vlasov steady-state equation in a variational form, we calculate two viscous relaxation rates with the collision probabilities of fermion's scattering including fermions in the normal fluid and fermion pairs in the superfluid. Additionally, by considering the pairing and depairing of fermions, we get results of the frequency and damping of collective modes versus temperature and s-wave scattering length. Our theoretical results are in a remarkable agreement with the experimental data, particularly for the sharp transition between collisionless and hydrodynamic behaviour and strong damping between BCS and unitary limits near the phase transition. The sharp transition originates from the maximum of viscous relaxation rate caused by fermion-fermion pair collision at the phase transition point when the fermion depair, while the strong damping due to the fast varying of the frequency of collective modes from BCS limit to unitary limit.
The shear viscosity of a two-component Fermi gas in the normal phase is calculated as a function of temperature in the unitarity limit, taking into account strong-coupling effects that give rise to a pseudogap in the spectral density for single-particle excitations. The results indicate that recent measurements of the damping of collective modes in trapped atomic clouds can be understood in terms of hydrodynamics, with a decay rate given by the viscosity integrated over an effective volume of the cloud.
The viscous and thermal relaxation rates of an interacting fermion gas are calculated as functions of temperature and scattering length, using a many-body scattering matrix which incorporates medium effects due to Fermi blocking of intermediate states. These effects are demonstrated to be large close to the transition temperature Tc{T}_{c}Tc​ to the superfluid state. For a homogeneous gas in the unitarity limit, the relaxation rates are increased by nearly an order of magnitude compared to their value obtained in the absence of medium effects due to the Cooper instability at Tc{T}_{c}Tc​. For trapped gases the corresponding ratio is found to be about three due to the averaging over the inhomogeneous density distribution. The effect of superfluidity below Tc{T}_{c}Tc​ is considered to leading order in the ratio between the energy gap and the transition temperature.
We present detailed measurements of the frequency and damping of three different collective modes in an ultracold trapped Fermi gas of 6Li^{6}\mathrm{Li}6Li atoms with resonantly tuned interactions. The measurements are carried out over a wide range of temperatures. We focus on the unitarity limit, where the scattering length is much greater than all other relevant length scales. The results are compared to theoretical calculations that take into account Pauli blocking and pair correlations in the normal state above the critical temperature for superfluidity. We show that these two effects nearly compensate each other and the behavior of the gas is close to that of a classical gas.
The frequencies of the collective oscillations of a harmonically trapped Fermi gas interacting with large scattering lengths are calculated at zero temperature using hydrodynamic theory. Different regimes are considered, including the molecular Bose-Einstein condensate and the unitarity limit for collisions. We show that the frequency of the radial compressional mode in an elongated trap exhibits a pronounced non-monotonous dependence on the scattering length, reflecting the role of the interactions in the equation of state.
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.