Stationary Waves in a Supersonic Flow of a Two-Component Bose Gas

Abstract

A stationary wave pattern occurring in a flow of a two-component Bose-Einstein condensate past an obstacle is studied. We consider the general case of unequal velocities of two superfluid components. The Landau criterium applied to the two-component system determines a certain region in the velocity space in which superfluidity may take place. Stationary waves arise out of this region, but under the additional condition that the relative velocity of the components does not exceed some critical value. Under increase of the relative velocity the spectrum of the excitations becomes complex valued and the stationary wave pattern is broken. In case of equal velocities two sets of stationary waves that correspond to the lower and the upper Bogolyubov mode can arise. If one component flows and the other is at rest only one set of waves may emerge. Two or even three interfere sets of waves may arise if the velocities approximately of equal value and the angle between the velocities is close to π/2. In two latter cases the stationary waves correspond to the lower mode and the densities of the components oscillate out-of-phase. The ratio of amplitudes of the components in the stationary waves is computed. This quantity depends on the relative velocity, is different for different sets of waves, and varies along the crests of the waves. For the cases where two or three waves interfere the density images are obtained.

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…”

Persistent currents in two-component condensates in a toroidal trap

“…For real frequencies, both modes are gapless and sound-like at low k, and are characterized by the density and the spin speeds of sound. The full spectrum of (8) has been solved in several references [21][22][23][24], with different scopes, and the general expression is cumbersome.…”

Superfluid state of magnetoexcitons in double layer graphene structures

“…The counterflow superfluidity is a special kind of the two-component superfluidity. In similarity with the spectrum (19), the spectrum of elementary excitations of two-component superfluid system demonstrates a complicate dependence on the superfluid velocities (see, for instance, [21]).…”