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arXiv:cond-mat/0105441 · Physical Review Letters

Transition from Collisionless to Hydrodynamic Behavior in an Ultracold Fermi Gas

S. D. Gensemer, D. S. Jin

Published Oct 4, 2001• 67 citations
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Abstract

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.

DOI
10.1103/physrevlett.87.173201

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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.
We develop a numerical method to study the dynamics of a two-component atomic Fermi gas trapped inside a harmonic potential at temperature T well below the Fermi temperature TF.{T}_{F}.TF​. We examine the transition from the collisionless to the collisional regime down to T=0.2TFT=0.2{T}_{F}T=0.2TF​ and find a good qualitative agreement with the experiments of B. DeMarco and D.S. Jin [Phys. Rev. Lett. 88, 040405 (2002)]. We demonstrate a twofold role of temperature on the collision rate and on the efficiency of collisions. In particular, we observe a hitherto unreported effect, namely, the transition to hydrodynamic behavior is shifted towards lower collision rates as temperature decreases.
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.
We derive analytical expressions for the frequency and damping of the lowest collective modes of a two-dimensional Fermi gas using kinetic theory. For strong coupling, we furthermore show that pairing correlations overcompensate the effects of Pauli blocking on the collision rate for a large range of temperatures, resulting in a rate which is larger than that of a classical gas. Our results agree well with experimental data, and they recover the observed crossover from collisionless to hydrodynamic behavior with increasing coupling for the quadruple mode. Finally, we show that a trap anisotropy within the experimental bounds results in a damping of the breathing mode which is comparable to what is observed, even for a scale-invariant system.
We calculate the effects of two-body interactions on the low-frequency oscillations of a normal Fermi gas confined in a harmonic trap. The mean-field contribution to the collective frequencies is evaluated in the collisionless regime using a sum-rule approach. We also discuss the transition between the collisionless and hydrodynamic regimes with special emphasis on the spin dipole mode in which two atomic clouds occupying different spin states oscillate in the opposite phase. The spin dipole mode is predicted to be overdamped in the hydrodynamic regime. The relaxation time is calculated as a function of temperature and the effects of Fermi statistics are explicitly pointed out.
Ultracold quantum-gas mixtures of fermionic atoms with resonant control of interactions offer a unique test-bed to explore few- and many-body quantum states with unconventional properties. The emergence of such strongly correlated systems, for instance, symmetry-broken superfluids, is usually accompanied by hydrodynamic collective behavior. Thus experimental progress in this field naturally requires a deep understanding of hydrodynamic regimes. Here, we report on experiments employing a tunable Fermi-Fermi mixture of Dy 161 and K 40 near quantum degeneracy. We investigate the full spectrum of dipole modes across a Feshbach resonance and characterize the crossover from collisionless to deep hydrodynamic behavior in measurements of frequencies and damping rates. We compare our results with a theoretical model that considers the motion of the mass centers of the two species, and we identify the contributions of friction and mean-field interaction. We show that one oscillating mode exists over the whole range of interactions, exhibiting striking changes of frequency and damping in the deep hydrodynamic regime. We observe the second oscillating mode to split into two purely exponential damping modes. One of these exponential modes shows very fast damping, faster than any other relevant timescale, and is largely insensitive to experimental imperfections. It provides an accurate measure for the interspecies drag effect, which generalizes the concept of spin drag explored in other experiments. We finally characterize the interspecies drag in terms of a microscopic friction coefficient, and we discuss its unitarity-limited universal behavior on top of the resonance.
We study the transition from the collisionless to the hydrodynamic regime in a two-component spin-polarized mixture of 40 K atoms by exciting its dipolar oscillation modes inside harmonic traps. The time evolution of the mixture is described by the Vlasov-Landau equations and numerically solved with a fully three-dimensional concurrent code. We observe a master/slave behaviour of the oscillation frequencies depending on the dipolar mode that is excited. Regardless of the initial conditions, the transition to hydrodynamics is found to shift to lower values of the collision rate as the temperature decreases.