Linear response study of collisionless spin drag

In this work we are concerned with the understanding of the collisionless drag or entrainment between two superfluids, also called Andreev-Bashkin effect, in terms of current response functions. The drag density is shown to be proportional to the cross transverse current-current response function, playing the role of a normal component for the single-species superfluid density. We can in this way link the existence of finite entrainment with the exhaustion of the energy-weighted sum rule in the spin channel. The formalism is then used to reproduce some known results for a weakly interacting Bose-Bose mixture. We include the drag effect to determine the beyond mean-field correction on the speed of sound and on the spin dipole excitations for a homogeneous and a trapped weakly interacting gas, respectively. Finally, we show that the response to a quick dipole perturbation on one of the species induces a dipole moment on the other species which is proportional to the drag at short times.

Figure 1

Beyond mean-field correction to the spin speed of sound (full line) as a function of the interspecies interactions $\eta =|g_{AB}|/g$. We limited the analysis to values of $\eta$ smaller than 1 to avoid the regimes of phase separation and collapse. The correction coming from the drag (dashed) is at least one order of magnitude smaller than that coming from Lee-Huang-Yang terms in the susceptibility (dotted).

Figure 2

Beyond mean-field correction to the spin dipole frequency (full line) as a function of the interspecies interactions $\eta =|g_{AB}|/g$. We limited the analysis to values of $\eta$ smaller than 1 to avoid the regimes of phase separation and collapse. Although the overall correction is smaller than in the case of the spin speed of sound, here the effect of the drag (dashed) is comparable with that of the susceptibility (dotted).