Counter-flow instability of a quantum mixture of two superfluids

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 vcr. When the interspecies coupling is small the critical value approaches the value vcr = c1 + c2, 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.

Andreev–Bashkin effect in superfluid cold gases mixtures

“…Symmetric mixture Some insight into the dynamic stability of the mixture can be gained by considering a 2  symmetric mixture, in which n n = ā¯, m m = a and m aa are the same for both species (hence also the speeds of sound coincide, c c = a ).The stability equation (40) then simplifies to a biquadratic equation whose roots can be readily calculated. Restricting to positive relative velocities, the condition that the two-fluid speed of sound be real then yields the critical relative velocities for the stability of the mixture: , confirming the results of[45][46][47]. When the relative velocity v lies within v c1 and v c2 , the mixture becomes unstable, as schematically shown infigure 4. in the language of the effective mass, m m 2 *  ).…”

“…In the following, we determine the critical relative velocity required to trigger the dynamical instability of a binary mixture of superfluids at zero temperature. To this end, we generalise equations (2) and(5) and the results of [46,47] ( ) the internal energy density. We subtracted 12 r from the diagonal kinetic terms, so that the condition (3) on the total density is automatically satisfied.…”

“…In particular, the presence of complex roots flags a dynamical instability. By setting 0 = , equation(40) reduces to the problem of the stability of a mixture interacting only via contact interactions, which was studied in depth in[46].This equation simplifies considerably when rewritten in a symmetric frame of reference in which v that the projection of the relative velocity of the two fluids along q is simply v. When n…”

Critical Velocity and Dissipation of an Ultracold Bose-Fermi Counterflow

“…This critical velocity has been measured both in superfluid helium [10] and ultracold atoms [1,[4][5][6]11]. However the recent production of a Bose-Fermi double superfluid [12] raised new questions on Bose-Fermi mixtures [13][14][15][16] and interrogations on the validity of Landau's argument in the case of superfluid counterflow [17][18][19][20][21][22].In this letter, we study the dynamics of a Bose-Fermi superfluid counterflow in the BEC-BCS crossover and at finite temperature. We show how friction arises when the relative velocity of the Bose and Fermi clouds increases and we confirm that damping occurs only above a certain critical relative velocity v c .…”

Dark–bright solitons in a superfluid Bose–Fermi mixture

“…We finally notice that the range of parameters in which we find partial mixing may be experimentally accessible using, for instance, mixtures of 6 Li-7 Li, 6 Li-87 Rb or 23 Na-87 Rb. When the mass of the two components is different, and particularly when m m 1 f b  , the situation is expected to be even more favourable.…”