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arXiv:1204.1659 · Few-Body Systems

Dynamical Properties of the Unitary Fermi Gas: Collective Modes and Shock Waves

Luca Salasnich

Published Apr 21, 2012• 9 citations
arXivHTMLPDF
DOI
10.1007/s00601-012-0442-y

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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.
The study of finite-temperature dynamics of one-dimensional Fermi gases is a challenging problem. These systems can present different phenomena, including the formation and propagation of shock waves and collective oscillations. Here we calculate the dynamics of collective oscillations and shock waves in a noninteracting one-dimensional ultracold Fermi gas, at both zero and finite temperature. These results are obtained using the Majorana P-function method, which is a positive phase-space representation on a space of antisymmetric matrices. At zero temperature, the results are in agreement with previous results, where the shock wave is observed as a discontinuity of the density of atoms. At finite temperature, the formation of shock waves is observed but with the shock fronts smoothed out. This places constraints on the experimental observation of shock-wave propagation in a noninteracting Fermi gas or strongly interacting Bose gas.
We show that in the collision of two superfluid fermionic atomic clouds one observes the formation of quantum shock waves as discontinuities in the number density and collective flow velocity. Domain walls, which are topological excitations of the superfluid order parameter, are also generated and exhibit abrupt phase changes by π and slower motion than the shock waves. The domain walls are distinct from the gray soliton train or number density ripples formed in the wake of the shock waves and observed in the collisions of superfluid bosonic atomic clouds. Domain walls with opposite phase jumps appear to collide elastically.