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

TL;DR

This paper investigates the quantum dynamics of an impurity in a Bose-Einstein condensate across various dimensions, deriving Langevin equations, analyzing superdiffusive motion, and exploring squeezing and non-Markovian effects.

Contribution

It provides a comprehensive derivation of $d$-dimensional Langevin equations and analyzes impurity dynamics, including superdiffusion and squeezing, in arbitrary dimensions.

Findings

Impurity motion is super diffusive in untrapped condensates.

Maximal super diffusive coefficient is dimension-independent at high temperatures.

Stronger position squeezing occurs in lower dimensions.

Abstract

We study the quantum motion of an impurity atom immersed in a Bose Einstein condensate in arbitrary dimension. The Bogoliubov excitations of the Bose Einstein condensate act as a bosonic bath for the impurity. We present a 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. When the impurity is not trapped, we calculate the mean square displacement, showing that the motion is super diffusive. We obtain also explicit expressions for the super diffusive 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. We study also the behaviour 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.