Breathing oscillations of a trapped impurity in a Bose gas

TL;DR

This paper investigates the breathing oscillations of an impurity in a Bose gas, revealing how interactions, phonons, and temperature influence the impurity's dynamics through a variational approach and simulations.

Contribution

It introduces a theoretical framework for impurity breathing oscillations, incorporating phonon effects and temperature, aligning with experimental observations and predicting new phenomena.

Findings

Breathing oscillations are suppressed by self-trapping due to interactions.

Phonons cause damping and non-Markovian effects in impurity dynamics.

Predicted novel effects at lower temperatures include self-trapping and inhomogeneity impacts.

Abstract

Motivated by a recent experiment [J. Catani et al., arXiv:1106.0828v1 preprint, 2011], we study breathing oscillations in the width of a harmonically trapped impurity interacting with a separately trapped Bose gas. We provide an intuitive physical picture of such dynamics at zero temperature, using a time-dependent variational approach. In the Gross-Pitaevskii regime we obtain breathing oscillations whose amplitudes are suppressed by self trapping, due to interactions with the Bose gas. Introducing phonons in the Bose gas leads to the damping of breathing oscillations and non-Markovian dynamics of the width of the impurity, the degree of which can be engineered through controllable parameters. Our results reproduce the main features of the impurity dynamics observed by Catani et al. despite experimental thermal effects, and are supported by simulations of the system in the Gross-Pitaevskii regime. Moreover, we predict novel effects at lower temperatures due to self-trapping and the inhomogeneity of the trapped Bose gas.