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

TL;DR

This paper develops a stochastic-field approach using the Keldysh formalism to analyze the real-time dynamics and absorption spectrum of a quantum impurity in a one-dimensional Bose gas after a sudden interaction quench, highlighting the importance of quantum and thermal effects.

Contribution

It introduces a truncated Wigner-like framework that accounts for back action, quantum, and thermal effects in impurity dynamics within a 1D Bose gas, advancing beyond previous models.

Findings

Quantum corrections significantly affect impurity momentum.

Thermal effects cause broadening of the absorption spectrum.

The approach accurately captures real-space impurity trajectories.

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.