Counter-flow instability of a quantum mixture of two superfluids

TL;DR

This paper investigates the dynamical instability in a mixture of two counter-flowing superfluids, identifying the critical relative velocity at which the system becomes unstable, and explores how interspecies coupling influences this threshold.

Contribution

It provides a detailed analysis of the critical velocity for instability in two-component superfluid mixtures, including the effects of interspecies coupling and applicability to Bose-Bose and Bose-Fermi systems.

Findings

Critical velocity approaches sum of sound velocities for weak coupling.

Interspecies coupling significantly affects the instability threshold.

Results extend to trapped superfluid mixtures.

Abstract

We study the instability of a mixture of two interacting counter-flowing superfluids. For a homogeneous system, we show that superfluid hydrodynamics leads to the existence of a dynamical instability at a critical value of the relative velocity $v_{cr}$. When the interspecies coupling is small the critical value approaches the value $v_{cr}=c_1+c_2$, given by the sum of the sound velocities of the two uncoupled superfluids, in agreement with the recent prediction of [1] based on Landau's argument. The crucial dependence of the critical velocity on the interspecies coupling is explicitly discussed. Our results agree with previous predictions for weakly interacting Bose-Bose mixtures and applies to Bose-Fermi superfluid mixtures as well. Results for the stability of transversally trapped mixtures are also presented.