Eur. Phys. J. D (2015) 69: 126
https://doi.org/10.1140/epjd/e2015-50851-y

Regular Article

Counter-flow instability of a quantum mixture of two superfluids

¹ INO-CNR BEC Center Dipartimento di Fisica, Università di Trento, 38123 Povo, Italy
² Technische Universität München, James-Franck-Strasse 1, 85748 Garching, Germany
³ Laboratoire Kastler-Brossel, École Normale Supérieure, CNRS, UPMC, 24 rue Lhomond, 75005 Paris, France

^a e-mail: marta.abadgarcia@oist.jp

Received: 27 November 2014
Received in final form: 16 March 2015
Published online: 13 May 2015

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 = c₁ + c₂, given by the sum of the sound velocities of the two uncoupled superfluids, in agreement with the recent prediction of [Y. Castin, I. Ferrier-Barbut, C. Salomon, arXiv:1408.1326 (2014)] 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.