Riemann Rarefaction Waves in a Strongly Interacting Fermi Gas

Abstract

We investigate the expansion of a homogeneous, strongly interacting Fermi gas released into vacuum in a ``shock tube'' geometry. At unitarity, where the gas is scale invariant and nearly inviscid, we find that the resulting rarefaction wave dynamics are self-similar and in excellent agreement with Riemann's solution of the Euler equation for all temperatures probed. Probing interactions away from unitarity within the BEC-BCS crossover, we observe increasing deviations from the Riemann solution as viscosity increases. However, even on the BCS side, where the sound diffusivity is increased twenty-fold, self-similarity is still approximately preserved. This may reflect how 1D Navier-Stokes rarefaction flows approach Euler self-similar solutions at long times. Our work demonstrates the utility of strongly interacting Fermi gases for the study of nonlinear hydrodynamics in a highly controllable setting.