Stochastic-field approach to the quench dynamics of the one-dimensional Bose polaron

Abstract

We consider the dynamics of a quantum impurity after a sudden interaction quench into a one-dimensional degenerate Bose gas. We use the Keldysh path-integral formalism to derive a truncated Wigner-like approach that takes the back action of the impurity onto the condensate into account already on the mean-field level and further incorporates thermal and quantum effects up to one-loop accuracy. This framework enables us not only to calculate the real-space trajectory of the impurity but also the absorption spectrum. We find that quantum corrections and thermal effects play a crucial role for the impurity momentum at weak to intermediate impurity-bath couplings. Furthermore, we see the broadening of the absorption spectrum with increasing temperature.