Quantum dynamics of a Bose polaron in a d -dimensional Bose-Einstein condensate

Abstract

We study the quantum motion of an impurity atom immersed in a Bose-Einstein condensate in arbitrary dimensions. It was shown, for all dimensions, that the Bogoliubov excitations of the Bose-Einstein condensate act as a bosonic bath for the impurity, where linear coupling is possible for a certain regime of validity, which was assessed only in one dimension. Here we present the detailed derivation of the d-dimensional Langevin equations that describe the quantum dynamics of the system, and of the associated generalized tensor that describes the spectral density in the full generality, and assesses the linear assumption in all dimensions. As results, we obtain, when the impurity is not trapped, the mean square displacement in all dimensions, showing that the motion is superdiffusive. We obtain also explicit expressions for the superdiffusive coefficient in the small and large temperature limits. We find that, in the latter case, the maximal value of this coefficient is the same in all dimensions, but is only reachable in one dimension, within the validity of the assumptions. We study also the behavior of the average energy and compare the results for various dimensions. In the trapped case, we study squeezing and find that the stronger position squeezing can be obtained in lower dimensions. We quantify the non-Markovianity of the particle's motion and find that it increases with dimensionality.

Bose polaron in a quantum fluid of light

“…As indicated by our analysis of the coupling with the electromagnetic vacuum bath outside the cavity, corrections beyond the Markov approximation (see [80] for an approximate treatment) could lead to experimentally relevant non-trivial corrections of the dynamics, that would be interesting to examine. Another open direction is to go beyond the semiclassical description of the impurity trajectories, and beyond the weak impurity-fluid interaction regime.…”

Bose Polaron in a quantum fluid of light

“…This work shows that the impurity dynamics can be used as a test particle to probe the different regimes of nonequilibrium quantum flow, including superfluidity, in quantum fluids of light. As indicated by our analysis of the coupling with the electromagnetic vacuum bath outside the cavity, corrections beyond the Markov approximation (see [67] for an approximate treatment) could lead to experimentally relevant non-trivial corrections of the dynamics, that would be interesting to examine. Another open direction is to go beyond the semiclassical description of the impurity trajectories, and beyond the weak impurity-fluid interaction regime.…”

Static Impurities in a Weakly Interacting Bose Gas

“…The arbitrary D one-polaron case was considered in Ref. [46]. As far as we know, the problem of two Bose polarons in 2D Bose gas has never been discussed; therefore, the objective of this study was to make the first step toward the revealing of peculiarities of the bipolaron physics and the boson-induced effective interaction between impurities by considering the static limit.…”