Quench dynamics of one dimensional Bose polarons

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 at the mean-field level and further incorporates thermal and quantum effects up to one-loop accuracy. This framework enables us to obtain the real space trajectory of the impurity as well as the impurity Green's function and the absorption spectrum of the polaron. We find that quantum corrections and thermal effects play a crucial role in the impurity momentum and the impurity Green's function at weak to intermediate impurity-bath couplings. We also observe the broadening of the absorption spectrum with the increasing temperature.