Semiclassical polaron dynamics of impurities in ultracold gases

Abstract

We present a semiclassical treatment of a fermionic impurity coupled to Bogolyubov modes of a Bose-Einstein condensate (BEC). In the lowest-order approximation we find a full solution of an initial value problem, which turns out to behave differently in the sub- and supersonic regimes. While in the former case no impurity deceleration is observed, in the latter case non-Markovian dissipation effects kick in, resulting in a slowing down of the fermion. Although this scenario is compatible with the one offered by an elementary field-theoretical picture at weak coupling, the details of the dynamics turn out to be completely different. Fluctuation effects can be taken into account by expanding around the classical path, which leads to a natural cutoff scale for the momentum integrals of the order of the inverse polaron radius. As an application we calculate the drag force which is exerted by the BEC on the impurity moving with constant velocity $v$. Contrary to the perturbative result, according to which the drag force is $\ensuremath{\sim}{v}^{4}$, it turns out to be proportional to $1/{v}^{2}$ in the semiclassical regime.