Critical Velocities in Two-Component Superfluid Bose Gases

Abstract

On the ground of the Landau criterion we study the behavior of critical velocities in a superfluid two-component Bose gas. It is found that under motion of the components with different velocities the velocity of each component should not be lower than a minimum phase velocity of elementary excitations (s − ). The Landau criterion yields a relation between the critical velocities of the components (v c1 , v c2 ). The velocity of one or even both components may exceed s − . The maximum value of the critical velocity of a given component can be reached when the other component does not move. The approach is generalized for a two-component condensate confined in a cylindrical harmonic potential.

Andreev–Bashkin effect in superfluid cold gases mixtures

“…The critical velocities, reported in equations (42), carry a dependence on the superfluid drag. This result extends the previous ones [45][46][47] which analysed a system with contact interactions only.…”

“…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.…”

Counter-flow instability of a quantum mixture of two superfluids

“…Our results agree with those previously reported (see [3,4,5,6,7,8,10]) in the limit q → 0. b) Dilute Bose gas interacting with a unitary Fermi gas. In this case the sound velocity of the Fermi gas (hereafter called c 1 ) is given by c 1 = v F ξ/3, with v F the Fermi velocity and ξ the Bertsch parameter [14], while the constant ∆ takes the density-dependent form…”

Instabilities in relativistic two-component (super)fluids

“…[20][21][22]). We shall thus also compute the onset of this energetic instability and in particular ask the question whether an energetic instability is a necessary condition for the two-fluid system to become dynamically unstable.…”