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arXiv:0704.3366 · Physical Review A

Dynamics of a strongly interacting Fermi gas: The radial quadrupole mode

A. Altmeyer, S. Riedl, Matthew J. Wright, Christoph Kohstall, Johannes Hecker Denschlag, Rudolf Grimm

Published Sep 18, 2007• 65 citations
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Abstract

We report on measurements of an elementary surface mode in an ultracold, strongly interacting Fermi gas of $^{6}\mathrm{Li}$ atoms. The radial quadrupole mode allows us to probe hydrodynamic behavior in the crossover from Bose-Einstein condensation (BEC) to the Bardeen-Cooper-Schrieffer (BCS) regime without being influenced by changes in the equation of state. We examine the frequency and damping of this mode, along with its expansion dynamics. In the unitarity limit and on the BEC side of the resonance, the observed frequencies agree with standard hydrodynamic theory. However, on the BCS side of the crossover, a striking downshift of the oscillation frequency is observed in the hydrodynamic regime as a precursor to an abrupt transition to collisionless behavior; this indicates coupling of the oscillation to fermionic pairs.

DOI
10.1103/physreva.76.033610

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We report on measurements of an elementary surface mode in an ultracold, strongly interacting Fermi gas of 6Li^{6}\mathrm{Li}6Li atoms. The radial quadrupole mode allows us to probe hydrodynamic behavior in the crossover from Bose-Einstein condensation (BEC) to the Bardeen-Cooper-Schrieffer (BCS) regime without being influenced by changes in the equation of state. We examine the frequency and damping of this mode, along with its expansion dynamics. In the unitarity limit and on the BEC side of the resonance, the observed frequencies agree with standard hydrodynamic theory. However, on the BCS side of the crossover, a striking downshift of the oscillation frequency is observed in the hydrodynamic regime as a precursor to an abrupt transition to collisionless behavior; this indicates coupling of the oscillation to fermionic pairs.
Abstract In this work, we present a theoretical study for the collective oscillation modes, i.e. quadrupole, radial and axial mode, of a mixture of Bose and Fermi superfluids in the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a molecular Bose–Einstein condensate (BEC) in harmonic trapping potentials with cylindrical symmetry of experimental interest. To this end, we start from the coupled superfluid hydrodynamic equations for the dynamics of Bose–Fermi superfluid mixtures and use the scaling theory that has been developed for a coupled system. The collective oscillation modes of Bose–Fermi superfluid mixtures are found to crucially depend on the overlap integrals of the spatial derivations of density profiles of the Bose and Fermi superfluids at equilibrium. We not only present the explicit expressions for the overlap density integrals, as well as the frequencies of the collective modes provided that the effective Bose–Fermi coupling is weak, but also test the valid regimes of the analytical approximations by numerical calculations in realistic experimental conditions. In the presence of a repulsive Bose–Fermi interaction, we find that the frequencies of the three collective modes of the Bose and Fermi superfluids are all upshifted, and the change speeds of the frequency shifts in the BCS–BEC crossover can characterize the different groundstate phases of the Bose–Fermi superfluid mixtures for different trap geometries.
We present a comprehensive study of the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover in fermionic 6Li using Bragg spectroscopy. A smooth transition from molecular to atomic spectra is observed with a clear signature of pairing at and above unitarity. These spectra probe the dynamic and static structure factors of the gas and provide a direct link to two-body correlations. We have characterized these correlations and measured their density dependence across the broad Feshbach resonance at 834 G.
We study collective excitation modes of a fermionic gas of (6)Li atoms in the BEC-BCS crossover regime. While measurements of the axial compression mode in the cigar-shaped trap close to a Feshbach resonance confirm theoretical expectations, the radial compression mode shows surprising features. In the strongly interacting molecular BEC regime, we observe a negative frequency shift with increasing coupling strength. In the regime of a strongly interacting Fermi gas, an abrupt change in the collective excitation frequency occurs, which may be a signature for a transition from a superfluid to a collisionless phase.
Abstract We report on the measurement of shear viscosity in an ultracold Fermi gas with variable temperatures and tunable interactions. A quadrupole mode excitation in an isotropic harmonic trap is used to quantify the shear viscosity of the quantum gas within the hydrodynamic regime. The shear viscosity of the system as a function of temperature has been investigated, and the results closely align with calculations in the high-temperature limit utilizing a new definition of the cutoff radius. Through an adiabatic sweep across the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensate (BEC) crossover, we find that the minimum value of the shear viscosity, as a function of interaction strength, is significantly shifted toward the BEC side. Furthermore, the behavior of the shear viscosity is asymmetric on both sides of the location of the minimum.
We investigate the dynamical behavior of large-amplitude collective modes in a superfluid Fermi gas in the crossover from Bardeen--Cooper--Schrieffer (BCS) superfluid to Bose--Einstein condensate (BEC) based on a hydrodynamic approach. We first solve the superfluid hydrodynamic equations that describe the time evolution of fermionic condensates in the BCS-BEC crossover and calculate explicitly the frequency shifts of the collective modes induced by nonlinear effects using the Lindstedt--Poincar\'e method. The result shows that the frequency shifts display different features in different superfluid regimes. We then study the second-harmonic generation of the collective modes under a phase-matching condition, which can be fulfilled by choosing appropriate parameters of the system. The analytical results obtained are checked by numerical simulations and good agreement is found.
The excitation spectra of the radial quadrupole and scissors modes of ultracold Fermi gases in elongated traps are studied across the BCS superfluid-normal phase transition in the framework of a transport theory for quasiparticles. In the limit of zero temperature, this theory reproduces the results of superfluid hydrodynamics, while in the opposite limit, above the critical temperature, it reduces to the collisionless Vlasov equation. In the intermediate temperature range, the excitation spectra have two or three broad peaks, respectively, which are roughly situated at hydrodynamic and collisionless frequencies, and whose strength is shifted from the hydrodynamic to the collisionless modes with increasing temperature. By fitting the time-dependent quadrupole deformation with a damped oscillation of a single frequency, we can understand the ``jump'' of the frequency of the radial quadrupole mode as a function of interaction strength which has recently been reported by the Innsbruck group.