Non-Markovian polaron dynamics in a trapped Bose-Einstein condensate

TL;DR

This paper investigates how a trapped Bose-Einstein condensate influences impurity dynamics, revealing increased memory effects, super-diffusion, and position squeezing, with potential control via trap frequency tuning.

Contribution

It introduces a modified quantum Brownian motion model for trapped gases, highlighting the impact of trapping on bath-impurity coupling and memory effects, and explores measurable impurity behaviors.

Findings

Memory effects are stronger in trapped gases.

Impurity exhibits super-diffusion and position squeezing.

Trap frequency tuning can enhance or inhibit these effects.

Abstract

We study the dynamics of an impurity embedded in a trapped Bose-Einstein condensate (Bose polaron), by recalling the quantum Brownian motion model. It is crucial that the model considers a parabolic trapping potential to resemble the experimental conditions. Thus, we detail here how the formal derivation changes due to the gas trap, in comparison to the homogeneous gas. We first find that the presence of a gas trap leads to a new form of the bath-impurity coupling constant and a larger degree in the super-ohmicity of the spectral density. This is manifested as a different dependence of the system dynamics on the past history. To quantify this, we introduce several techniques to compare the different amount of memory effects arising in the homogeneous and inhomogeneous gas. We find that it is higher in the second case. Moreover, we calculate the position variance of the impurity, represenitng a measurable quantity. We show that the impurity experiences super-diffusion and genuine position squeezing. Wdetail how both effects can be enhanced or inhibited by tuning the Bose-Einstein condensate trap frequency.