Dynamics of an impurity in a one-dimensional lattice

TL;DR

This paper investigates the non-equilibrium behavior of an impurity in a one-dimensional lattice, revealing various states from bound molecules to free particles depending on interaction strength, with potential applications in cold atom experiments.

Contribution

It provides a comprehensive analysis of impurity dynamics in 1D lattices beyond linear response, combining numerical and analytical methods to characterize different impurity states.

Findings

Identification of impurity states across interaction regimes

Quantitative characterization of impurity dynamics

Potential realization in cold atom systems

Abstract

We study the non-equilibrium dynamics of an impurity in an harmonic trap that is kicked with a well-defined quasi-momentum, and interacts with a bath of free fermions or interacting bosons in a 1D lattice configuration. Using numerical and analytical techniques we investigate the full dynamics beyond linear response, which allows us to quantitatively characterise states of the impurity in the bath for different parameter regimes. These vary from a tightly bound molecular state in a strongly interacting limit to a polaron (dressed impurity) and a free particle for weak interactions, with composite behaviour in the intermediate regime. These dynamics and different parameter regimes should be readily realizable in systems of cold atoms in optical lattices.