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arXiv:cond-mat/0107628 · Physical Review Letters

Low Energy Collective Modes of a Superfluid Trapped Atomic Fermi Gas

Georg M. Bruun, Ben R. Mottelson

Published Dec 11, 2001• 70 citations
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Abstract

We consider the low energy collective mode spectrum of a superfluid Fermi gas in a spherical trap in the collisionless regime. Using a self-consistent random-phase approximation, the effects of superfluidity on modes of dipole and quadrupole symmetries are systematically examined. The spectrum is calculated for varying pairing strength and temperature, and we identify several spectral features such as the emergence of Goldstone modes that can be used to detect the onset of superfluidity. Our analysis is relevant for present experiments aimed at observing a superfluid phase transition in trapped Fermi gases.

DOI
10.1103/physrevlett.87.270403

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We consider the low energy collective mode spectrum of a superfluid Fermi gas in a spherical trap in the collisionless regime. Using a self-consistent random-phase approximation, the effects of superfluidity on modes of dipole and quadrupole symmetries are systematically examined. The spectrum is calculated for varying pairing strength and temperature, and we identify several spectral features such as the emergence of Goldstone modes that can be used to detect the onset of superfluidity. Our analysis is relevant for present experiments aimed at observing a superfluid phase transition in trapped Fermi gases.
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We consider the collective mode spectrum of a normal Fermi gas in a spherical harmonic trap. Using a self-consistent random-phase approximation, we systematically examine the effects of the two-body interactions on modes of various symmetries. For weak coupling, where the spectrum is shifted very little away from the ideal gas case, a sum-rule approach is shown to work well. For stronger coupling, the interplay between the single particle and collective excitations causes effects such as mode splitting and Landau damping. A finite low-frequency response present at stronger coupling is predicted for the quadrupole mode. Finally, we briefly discuss the effect of a finite temperature on the spectrum, and the excitation of higher collective modes.
We examine a dilute two-component atomic Fermi gas trapped in a harmonic potential in the superfluid phase. For experimentally realistic parameters, the trapping potential is shown to have crucial influence on various properties of the gas. Using an effective Hamiltonian, analytical results for the critical temperature, the temperature dependence of the superfluid gap, and the energy of the lowest collective modes are derived. These results are shown to agree well with numerical calculations. We also discuss in more detail a previously proposed method to experimentally observe the superfluid transition by looking at the collective-mode spectrum. Our results are aimed at the present experimental effort to observe a superfluid phase transition in a trapped atomic Fermi gas.
At finite temperature, the hydrodynamic collective modes of superfluid trapped Fermi gases are coupled to the motion of the normal component, which in the BCS limit behaves like a collisionless normal Fermi gas. The coupling between the superfluid and the normal components is treated in the framework of a semiclassical transport theory for the quasiparticle-distribution function, combined with a hydrodynamic equation for the collective motion of the superfluid component. We develop a numerical test-particle method for solving these equations in the linear-response regime. As a first application we study the temperature dependence of the collective quadrupole mode of a Fermi gas in a spherical trap. The coupling between the superfluid collective motion and the quasiparticles leads to a rather strong damping of the hydrodynamic mode already at very low temperatures. At higher temperatures the spectrum has a two-peak structure, the second peak corresponding to the quadrupole mode in the normal phase.
We discuss collective monopole and quadrupole excitations of a collisionless gas of trapped Fermionic atoms in the superfluid BCS phase, comparing the fully microscopic Bogoliubov--de Gennes and quasiparticle random-phase approximation method with widely used semiclassical methods. In particular, the microscopic treatment allows us to address the questions of temperature dependence and nontrivial dependence on the trap parameters, which cannot be answered within the semiclassical approach. The main result concerning the temperature dependence is a strong Landau damping at intermediate temperature, which disappears in the limits of zero and critical temperature. However, even at zero temperature, considerable deviations from superfluid hydrodynamics are found if the trap frequency is of the same order of magnitude as the pairing gap.
We investigate the ``twist'' mode (rotation of the upper against the lower hemisphere) of a dilute atomic Fermi gas in a spherical trap. The normal and superfluid phases are considered. The linear response to this external perturbation is calculated within the microscopic Hartree-Fock-Bogoliubov approach. In the normal phase the excitation spectrum is concentrated in a rather narrow peak very close to the trapping frequency. In the superfluid phase the strength starts to be damped and fragmented and the collectivity of the mode is progressively lost when the temperature decreases. In the weak-pairing regime some reminiscence of the collective motion still exists, whereas in the strong-pairing regime the twist mode is completely washed out. The disappearance of the twist mode in the strong-pairing regime with decreasing temperature is interpreted in the framework of the two-fluid model.