Real-Time Dynamics of an Impurity in an Ideal Bose Gas in a Trap

TL;DR

This paper studies the real-time behavior of an impurity in a trapped ideal Bose gas using a field theory approach, revealing oscillatory dynamics and control via periodic interaction switching.

Contribution

It introduces a T-matrix based theoretical framework for analyzing impurity dynamics in a trapped Bose gas, including novel numerical insights into oscillations and interaction control.

Findings

Impurity density oscillates after interaction is switched on.

Oscillation amplitude can be controlled by periodic interaction modulation.

Theoretical framework applicable to one-dimensional systems.

Abstract

We investigate the behavior of a harmonically trapped system consisting of an impurity in a dilute ideal Bose gas after the boson-impurity interaction is suddenly switched on. As theoretical framework, we use a field theory approach in the space-time domain within the T-matrix approximation. We establish the form of the corresponding T-matrix and address the dynamical properties of the system. As a numerical application, we consider a simple system of a weakly interacting impurity in one dimension where the interaction leads to oscillations of the impurity density. Moreover, we show that the amplitude of the oscillations can be driven by periodically switching the interaction on and off.