Riemann Rarefaction Waves in the Strongly-Interacting Fermi Gas

The equations of hydrodynamics emerge from fundamental conservation laws. They are therefore ubiquitous in nature and applicable to a wide variety of many-body systems, both quantum and classical. Due to their nonlinearity, these equations exhibit highly nontrivial phenomena - for example turbulence - which are of both practical and fundamental interest. The equations are, likewise, challenging to solve analytically in their full generality, such that analog simulation can be valuable to build insight.

Among analog hydrodynamic simulators, ultracold degenerate gases are an attractive platform: they combine well-understood, highly tunable microscopic interactions, pristine experimental conditions, and access to superfluid phases which further constrain the dynamics. In our work, we prepare a strongly-interacting, degenerate spin mixture of fermionic 6Li, confined in a homogeneous box trap. We expand this uniform gas into vacuum by impulsively releasing a confining wall, with the resulting dynamics quasi-1D. Thanks to the ultra-low, quantum limited dissipation in the unitary gas, these dynamics can for unitary interactions be modeled by the classical 1D Euler equations. In particular, we observe self-similar expansion dynamics which collapse, without fitting, to a prediction from analytic theory originally due to Riemann. Away from unitarity, we continue to observe self-similarity, a surprise given that dissipation increases roughly fifteen-fold at the weakest scattering lengths measured. Taken together, our results provide a useful anchor for future studies of nonlinear hydrodynamics in this system.