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arXiv:1803.11494 · Physical Review A

Transition from supersonic to subsonic waves in superfluid Fermi gases

Senne Van Loon, Wout Van Alphen, Jacques Tempere, Hadrien Kurkjian

Published Dec 26, 2018• 4 citations
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Abstract

We study the propagation of dispersive waves in superfluid Fermi gases in the BEC-BCS crossover. Unlike in other superfluid systems where dispersive waves have already been studied and observed, Fermi gases can exhibit a subsonic dispersion relation for which the dispersive wave pattern appears at the tail of the wave front. We show that this property can be used to distinguish between a subsonic and a supersonic dispersion relation at unitarity.

DOI
10.1103/physreva.98.063627

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We study the propagation of dispersive waves in superfluid Fermi gases in the BEC-BCS crossover. Unlike in other superfluid systems where dispersive waves have already been studied and observed, Fermi gases can exhibit a subsonic dispersion relation for which the dispersive wave pattern appears at the tail of the wave front. We show that this property can be used to distinguish between a subsonic and a supersonic dispersion relation at unitarity.
We investigate the linear and nonlinear sound propagations in a cigar-shaped superfluid Fermi gas with a large particle number. We first solve analytically the eigenvalue problem of linear collective excitations and provide explicit expressions of all eigenvalues and eigenfunctions, which are valid for all superfluid regimes in the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation (BCS-BEC) crossover. The linear sound speed obtained agrees well with that of a recent experimental measurement. We then consider a weak nonlinear excitation and show that the time evolution of the excitation obeys a Korteweg de Vries equation. Different from the result obtained in quasi-one-dimensional case studied previously, where subsonic dark solitons are obtained via the balance between quantum pressure and nonlinear effect, we demonstrate that bright solitons with supersonic propagating velocity can be generated in the present three-dimensional system through the balance between a waveguidelike dispersion and the interparticle interaction. The supersonic bright solitons obtained display different physical properties in different superfluid regimes and hence can be used to characterize superfluid features of the BCS-BEC crossover.
We investigate shock waves in the unitary Fermi gas by using the zero-temperature equations of superfluid hydrodynamics. We obtain analytical solutions for the dynamics of a localized perturbation of the uniform gas. These supersonic bright and subsonic dark solutions produce, after a transient time, an extremely large (divergent) density gradient: the shock. We calculate the time of formation of the shock and also simulate the space-time behavior of the waves by solving generalized hydrodynamic equations, which include a reliable dispersive regularization of the shock. We find that the shock spreads into wave ripples whose properties crucially depend on the chosen initial configuration.
We perform a detailed study of the collective mode across the whole crossover from the Bose-Einstein condensate (BEC)-to the BCS regime in fermionic gases at zero temperature, covering the whole range of energy beyond the linear regime. This is done on the basis of the dynamical BCS model. We recover first the results of the linear regime in a simple form. Then specific attention is paid to the nonlinear part of the dispersion relation and its interplay with the continuum of single-fermionic excitations. In particular we consider in detail the merging of the collective mode into the continuum of single-fermionic excitations. This occurs not only on the BCS side of the crossover, but also slightly beyond unitarity on the BEC side. Another remarkable feature is the very linear behavior of the dispersion relation in the vicinity of unitarity almost up to merging with the continuum. Finally, while on the BEC side the mode is quite analogous to the Bogoliubov mode, a difference appears at high wave vectors. On the basis of our results we determine the Landau critical velocity in the BEC-BCS crossover which is found to be largest close to unitarity. Our investigation has revealed interesting qualitative features which deserve experimental exploration as well as further theoretical studies by more sophisticated means.
We consider the evolution of superfluid properties of a three-dimensional p-wave Fermi gas from a weak coupling Bardeen-Cooper-Schrieffer (BCS) to strong coupling Bose-Einstein condensation (BEC) limit as a function of scattering volume. At zero temperature, we show that a quantum phase transition occurs for p-wave systems, unlike the s-wave case where the BCS to BEC evolution is just a crossover. Near the critical temperature, we derive a time-dependent Ginzburg-Landau (GL) theory and show that the GL coherence length is generally anisotropic due to the p-wave nature of the order parameter, and becomes isotropic only in the BEC limit.