Semiclassical polaron dynamics of impurities in ultracold gases

TL;DR

This paper develops a semiclassical model for impurity dynamics in ultracold gases, revealing different behaviors in sub- and supersonic regimes and providing new insights into polaron properties and drag forces.

Contribution

It introduces a semiclassical approach to impurity dynamics in BECs, capturing non-Markovian effects and estimating the polaron radius as a function of coupling strength.

Findings

No impurity deceleration in subsonic regime

Non-Markovian dissipation causes slowing in supersonic regime

Drag force scales as 1/v^2, not v^4 as perturbative theory suggests

Abstract

We present a semiclassical treatment of a fermionic impurity coupled to Bogolyubov modes of a 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 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 expansion around the classical path. This allows for estimation of the all-important polaron radius as a function of fermion-boson coupling strength. 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 $\sim v^4$, it turns out to be proportional to $1/v^2$ in the semiclassical regime.