Dynamical formation of polarons in a Bose-Einstein condensate: A variational approach

TL;DR

This paper studies the real-time formation and dynamics of polarons in a Bose-Einstein condensate using a variational approach, aligning with recent experiments and highlighting the transition from weak to strong coupling regimes.

Contribution

It introduces a time-dependent variational method to analyze impurity dynamics in a BEC, providing analytical results and insights into polaron formation.

Findings

Analytical expressions for impurity overlap at weak coupling

Good agreement with master equation results at weak coupling

Quantitative description of polaron dynamics and transition at strong coupling

Abstract

We investigate the non-equilibrium dynamics of an impurity coupled to a Bose-Einstein condensate, systematically compared with recent experimental results [M. G. Skou et al., Nat. Phys. (2021)]. The dynamics of the impurity is tracked down by using a time-dependent variational coherent ansatz. For weak coupling between the impurity and the bath, analytical expressions for the time-dependent overlap (or contrast) are derived, matching quite well with previous findings obtained within a master equation approach. For strong coupling instead, the variational ansatz provides a good quantitative description of the polaron dynamics, in particular, in signaling the transition from the few to the many-body correlated regime where polarons are expected to form.