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.
Highlights
The interaction of a mobile impurity with a surrounding many-body quantum system is one of the most prominent and oldest problems in condensed matter physics
Using the coherent state path integral for the condensate has been shown to yield good results in 1D for the polaron and the bipolaron problem [33,46,47]. This is conceptually close to the approach originally developed by Feynman [42] and applied to the Bose polaron in [19,24] with the main difference being that we do not expand the condensate around a homogeneous density, and our focus lies on out-of-equilibrium phenomena
We used this framework to calculate the dynamics of an impurity after sudden immersion in a surrounding bath and the absorption spectrum
Summary
The interaction of a mobile impurity with a surrounding many-body quantum system is one of the most prominent and oldest problems in condensed matter physics. Using the coherent state path integral for the condensate has been shown to yield good results in 1D for the polaron and the bipolaron problem [33,46,47] This is conceptually close to the approach originally developed by Feynman [42] and applied to the Bose polaron in [19,24] with the main difference being that we do not expand the condensate around a homogeneous density, and our focus lies on out-of-equilibrium phenomena.
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