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arXiv:0812.3643 · Physical Review Letters

Large Amplitude Dynamics of the Pairing Correlations in a Unitary Fermi Gas

Aurel Bulgac, Sukjin Yoon

Published Feb 25, 2009• 55 citations
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Abstract

A unitary Fermi gas has a surprisingly rich spectrum of large amplitude modes of the pairing field alone, which defies a description within a formalism involving only a reduced set of degrees of freedom, such as quantum hydrodynamics or a Landau-Ginzburg-like description. These modes are very slow, with oscillation frequencies well below the pairing gap, which makes their damping through quasiparticle excitations quite ineffective. In atomic traps these modes couple naturally with the density oscillations, and the corresponding oscillations of the atomic cloud are an example of a new type of collective mode in superfluid Fermi systems. They have lower frequencies than the compressional collective hydrodynamic oscillations, have a nonspherical momentum distribution, and could be excited by a quick time variation of the scattering length.

DOI
10.1103/physrevlett.102.085302

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A unitary Fermi gas has a surprisingly rich spectrum of large amplitude modes of the pairing field alone, which defies a description within a formalism involving only a reduced set of degrees of freedom, such as quantum hydrodynamics or a Landau-Ginzburg-like description. These modes are very slow, with oscillation frequencies well below the pairing gap, which makes their damping through quasiparticle excitations quite ineffective. In atomic traps these modes couple naturally with the density oscillations, and the corresponding oscillations of the atomic cloud are an example of a new type of collective mode in superfluid Fermi systems. They have lower frequencies than the compressional collective hydrodynamic oscillations, have a nonspherical momentum distribution, and could be excited by a quick time variation of the scattering length.
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.
There are several situations in which the collective motion of a superfluid Fermi gas is coupled to quasiparticle excitations. Quasiparticle excitations are, for example, present at finite temperature, but also at zero temperature in the case of a rotating trap. In this paper, I present a semiclassical description of such systems, where the superfluid component is described by hydrodynamics while the normal component, formed by the quasiparticles, is described by a transport equation similar to the Vlasov equation. The coupling between the two components generates a strong damping of the collective modes. As applications of the semiclassical theory, the case of a rotating trap and several collective modes (quadrupole and scissors modes) of the trapped gas are discussed.
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 have investigated collective breathing modes of a unitary Fermi gas in deformed harmonic traps. The ground state is studied by the superfluid local density approximation (SLDA) and small-amplitude collective modes are studied by the iterative quasiparticle random phase approximation (QRPA). The results illustrate the evolutions of collective modes of a small system in traps from spherical to elongated or pancake-shaped deformations. For small spherical systems, the influences of different SLDA parameters are significant, and, in particular, a large pairing strength can shift up the oscillation frequency of collective modes. The transition currents from QRPA show that the compressional flow patterns are nontrivial and dependent on the deformation. Finally, the finite-size effects are demonstrated to be reasonable when progressing towards larger systems. The hydrodynamical results of collective frequencies can be reproduced by SLDA-QRPA with reduced pairing strengths. Our studies indicate that experiments on small and medium systems are valuable for understanding effective interactions in systems with varying sizes and trap deformations.
The key feature of time-dependent dynamics in a paired Fermi superfluid is the presence of a large number of independent degrees of freedom---the pairing amplitudes of fermions with different momenta. We argue that useful prototypes of this dynamics come from D-brane constructions of string theory. Using a specific example of that kind, we identify the mechanism by which a strongly coupled Fermi superfluid relaxes to equilibrium; it involves a wave of excitation in the momentum space, propagating from the Fermi surface towards the ultraviolet. For a sudden quench induced by a change in the fermion coupling, we find that the relaxation occurs rapidly, over only a few oscillations of the quasiparticle gap.
We study low-energy collective excitations in a trapped superfluid Fermi gas. These excitations originate from slow variations of the phase of the superfluid order parameter and, in this sense, are similar to the Bogolyubov sound in a homogeneous superfluid Fermi gas. Well below the critical temperature the eigenfrequencies of the lowest collective excitations are of the order of the trap frequency, and these modes manifest themselves in the density oscillations under periodic modulations of the trap frequencies. This gives a clear signature of the presence of a superfluid phase.