Quantum impurities: from mobile Josephson junctions to depletons

TL;DR

This paper reviews the behavior of mobile impurities in one-dimensional superfluids, modeling them as Josephson junctions, and introduces a depleton model that bridges weak and strong interaction regimes, with relevance to cold atom experiments.

Contribution

It develops a depleton model for impurities that provides exact results across different interaction regimes, enhancing understanding of impurity dynamics in superfluids.

Findings

Impurities exhibit periodic dispersion due to Josephson junction modeling.

Dissipation arises from interactions with phonons, leading to radiative friction.

The depleton model interpolates between weak and strong interaction regimes.

Abstract

We overview the main features of mobile impurities moving in one-dimensional superfluid backgrounds by modeling it as a mobile Josephson junction, which leads naturally to the periodic dispersion of the impurity. The dissipation processes, such as radiative friction and quantum viscosity, are shown to result from the interaction of the collective phase difference with the background phonons. We develop a more realistic depleton model of an impurity-hole bound state that provides a number of exact results interpolating between the semiclassical weakly-interacting picture and the strongly interacting Tonks-Girardeau regime. We also discuss the physics of a trapped impurity, relevant to current experiments with ultra cold atoms.