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

Collisions and expansion of an ultracold dilute Fermi gas

B. Jackson, P. Pedri, S. Stringari

Published Jan 1, 2004• 6 citations
OpenAlex

Abstract

Abstract. – We discuss the effects of collisions on the expansion of an ultracold normal Fermi gas, following the sudden removal of the confining trap. Using a Boltzmann equation approach, we calculate the time dependence of the aspect ratio and the temperature increase of the expanding atomic cloud. We find that for dilute gases and standard choices of the trap parameters the aspect ratio does not deviate significantly from the predictions of ballistic expansion. Conversely, if the trap is sufficiently elongated the thermal broadening of the density distribution can be quite large, revealing that even at zero temperature collisions are effective in a Fermi gas. The expansion of an atomic gas following the sudden removal of the confining trap is known to provide valuable information on the state of the system and on the role of interactions [1]. In particular in the superfluid phase, where the macroscopic dynamics of the gas are governed by the equations of hydrodynamics, one expects anisotropic expansion if the gas is released from an anisotropic trap. This peculiar feature, which should be contrasted with the isotropic ballistic expansion exhibited by a non interacting gas, was first discussed in [2,3] in the case

Related papers

Collisions and expansion of an ultracold dilute Fermi gas

B Jackson, P. Pedri, S. Stringari

We discuss the effects of collisions on the expansion of a degenerate normal Fermi gas, following the sudden removal of the confining trap. Using a Boltzmann equation approach, we calculate the time dependence of the aspect ratio and the entropy increase of the expanding atomic cloud taking into account the collisional effects due to the deformation of the distribution function in momentum space. We find that in dilute gases the aspect ratio does not deviate significantly from the predictions of ballistic expansion. Conversely, if the trap is sufficiently elongated the thermal broadening of the density distribution due to the entropy increase can be sizeable, revealing that even at zero temperature collisions are effective in a Fermi gas.

arXiv:cond-mat/0404175•Europhysics Letters (EPL)•Aug 1, 2004•7 citations

Expansion of an Interacting Fermi Gas

C. Menotti, P. Pedri, S. Stringari

We study the expansion of a dilute ultracold sample of fermions initially trapped in an anisotropic harmonic trap. The expansion of the cloud provides valuable information about the state of the system and the role of interactions. In particular, the time evolution of the deformation of the expanding cloud behaves quite differently depending on whether the system is in the normal or in the superfluid phase. For the superfluid phase, we predict an inversion of the deformation of the sample, similar to what happens with Bose-Einstein condensates. Vice versa, in the normal phase, the inversion of the aspect ratio is never achieved, if the mean field interaction is attractive and collisions are negligible.

arXiv:cond-mat/0208150•Physical Review Letters•Dec 2, 2002•201 citations

Effects of trap anisotropy on the impurity scattering regime in a Fermi gas

P. Capuzzi, Patrizia Vignolo, Monica Tosi

We evaluate the low-lying oscillation modes and the ballistic expansion properties of a harmonically trapped gas of fermionic $^{40}\mathrm{K}$ atoms containing thermal $^{87}\mathrm{Rb}$ impurities as functions of the anisotropy of the trap. Numerical results are obtained by solving the Vlasov-Landau equations for the one-body phase-space distribution functions and are used to test simple scaling Ans\"atzes. Starting from the gas in a weak impurity-scattering regime inside a spherical trap, the time scales associated to motions in the axial and azimuthal directions enter into competition as the trap is deformed to an elongated cigarlike shape. This competition gives rise to coexistence of collisionless and hydrodynamic behaviors in the low-lying surface modes of the gas as well as to a dependence of the aspect ratio of the expanding cloud on the collision time.

arXiv:cond-mat/0506496•Physical Review A•Jul 28, 2005•1 citation

Collisions in Zero Temperature Fermi Gases

Subhadeep Gupta, Zoran Hadzibabic, J. R. Anglin +1 more

We examine the collisional behavior of two-component Fermi gases released at zero temperature from a harmonic trap. Using a phase-space formalism to calculate the collision rate during expansion, we find that Pauli blocking plays only a minor role for momentum changing collisions. As a result, for a large scattering cross section, Pauli blocking will not prevent the gas from entering the collisionally hydrodynamic regime. In contrast to the bosonic case, hydrodynamic expansion at very low temperatures is therefore not evidence for fermionic superfluidity.

arXiv:cond-mat/0307088•Physical Review Letters•Mar 12, 2004•26 citations

Model-independent determination of the shear viscosity of the unitary Fermi gas at high temperature

Marcus Bluhm, Thomas Schäfer

Determinations of the shear viscosity of trapped ultracold gases suffer from systematic, uncontrolled uncertainties related to the treatment of the dilute part of the gas cloud. In this work we present an analysis of expansion experiments based on a new method, anisotropic fluid dynamics, that interpolates between Navier-Stokes fluid dynamics at the center of the cloud and ballistic behavior in the dilute corona. We validate the method using a comparison between anisotropic fluid dynamics and numerical solutions of the Boltzmann equation. We then apply anisotropic fluid dynamics to the expansion data reported by Cao et al. In the high temperature limit we find $\eta=0.282(mT)^{3/2}$, which agrees within about 5\% with the theoretical prediction $\eta=0.269(mT)^{3/2}$.

•Dec 2, 2015•0 citations

Expansion of a free Fermi gas released from an isotropic trapping potential

J. M. Luck, P. L. Krapivsky

We consider a system of non-interacting fermions prepared in the many-body ground state of an isotropic trapping potential in any dimension, and investigate the ballistic expansion of the fermionic cloud after the potential is suddenly released. Using semi-classical techniques, we derive the full late-time profile of the expanding cloud in the regime when the fermion number is large. We thus obtain explicit expressions for power-law potentials with arbitrary exponent $a$ and in all dimensions $d$. The momentum distribution and the spatial profile of the cloud exhibit a universal edge exponent $d/a$, thus generalizing the Wigner semi-circle law and the Thomas-Fermi distribution.

arXiv:2607.18007•Jul 20, 2026•0 citations
Abstract. – We discuss the effects of collisions on the expansion of an ultracold normal Fermi gas, following the sudden removal of the confining trap. Using a Boltzmann equation approach, we calculate the time dependence of the aspect ratio and the temperature increase of the expanding atomic cloud. We find that for dilute gases and standard choices of the trap parameters the aspect ratio does not deviate significantly from the predictions of ballistic expansion. Conversely, if the trap is sufficiently elongated the thermal broadening of the density distribution can be quite large, revealing that even at zero temperature collisions are effective in a Fermi gas. The expansion of an atomic gas following the sudden removal of the confining trap is known to provide valuable information on the state of the system and on the role of interactions [1]. In particular in the superfluid phase, where the macroscopic dynamics of the gas are governed by the equations of hydrodynamics, one expects anisotropic expansion if the gas is released from an anisotropic trap. This peculiar feature, which should be contrasted with the isotropic ballistic expansion exhibited by a non interacting gas, was first discussed in [2,3] in the case
We discuss the effects of collisions on the expansion of a degenerate normal Fermi gas, following the sudden removal of the confining trap. Using a Boltzmann equation approach, we calculate the time dependence of the aspect ratio and the entropy increase of the expanding atomic cloud taking into account the collisional effects due to the deformation of the distribution function in momentum space. We find that in dilute gases the aspect ratio does not deviate significantly from the predictions of ballistic expansion. Conversely, if the trap is sufficiently elongated the thermal broadening of the density distribution due to the entropy increase can be sizeable, revealing that even at zero temperature collisions are effective in a Fermi gas.
We study the expansion of a dilute ultracold sample of fermions initially trapped in an anisotropic harmonic trap. The expansion of the cloud provides valuable information about the state of the system and the role of interactions. In particular, the time evolution of the deformation of the expanding cloud behaves quite differently depending on whether the system is in the normal or in the superfluid phase. For the superfluid phase, we predict an inversion of the deformation of the sample, similar to what happens with Bose-Einstein condensates. Vice versa, in the normal phase, the inversion of the aspect ratio is never achieved, if the mean field interaction is attractive and collisions are negligible.
We evaluate the low-lying oscillation modes and the ballistic expansion properties of a harmonically trapped gas of fermionic 40K^{40}\mathrm{K}40K atoms containing thermal 87Rb^{87}\mathrm{Rb}87Rb impurities as functions of the anisotropy of the trap. Numerical results are obtained by solving the Vlasov-Landau equations for the one-body phase-space distribution functions and are used to test simple scaling Ans\"atzes. Starting from the gas in a weak impurity-scattering regime inside a spherical trap, the time scales associated to motions in the axial and azimuthal directions enter into competition as the trap is deformed to an elongated cigarlike shape. This competition gives rise to coexistence of collisionless and hydrodynamic behaviors in the low-lying surface modes of the gas as well as to a dependence of the aspect ratio of the expanding cloud on the collision time.
We examine the collisional behavior of two-component Fermi gases released at zero temperature from a harmonic trap. Using a phase-space formalism to calculate the collision rate during expansion, we find that Pauli blocking plays only a minor role for momentum changing collisions. As a result, for a large scattering cross section, Pauli blocking will not prevent the gas from entering the collisionally hydrodynamic regime. In contrast to the bosonic case, hydrodynamic expansion at very low temperatures is therefore not evidence for fermionic superfluidity.
Determinations of the shear viscosity of trapped ultracold gases suffer from systematic, uncontrolled uncertainties related to the treatment of the dilute part of the gas cloud. In this work we present an analysis of expansion experiments based on a new method, anisotropic fluid dynamics, that interpolates between Navier-Stokes fluid dynamics at the center of the cloud and ballistic behavior in the dilute corona. We validate the method using a comparison between anisotropic fluid dynamics and numerical solutions of the Boltzmann equation. We then apply anisotropic fluid dynamics to the expansion data reported by Cao et al. In the high temperature limit we find η=0.282(mT)3/2\eta=0.282(mT)^{3/2}η=0.282(mT)3/2, which agrees within about 5\% with the theoretical prediction η=0.269(mT)3/2\eta=0.269(mT)^{3/2}η=0.269(mT)3/2.
We consider a system of non-interacting fermions prepared in the many-body ground state of an isotropic trapping potential in any dimension, and investigate the ballistic expansion of the fermionic cloud after the potential is suddenly released. Using semi-classical techniques, we derive the full late-time profile of the expanding cloud in the regime when the fermion number is large. We thus obtain explicit expressions for power-law potentials with arbitrary exponent aaa and in all dimensions ddd. The momentum distribution and the spatial profile of the cloud exhibit a universal edge exponent d/ad/ad/a, thus generalizing the Wigner semi-circle law and the Thomas-Fermi distribution.