# Interaction-induced Bloch Oscillation in a Harmonically Trapped and Fermionized Quantum Gas in One Dimension

## TL;DR

This paper investigates how an impurity in a harmonically trapped one-dimensional Bose gas exhibits Bloch oscillations induced by interaction effects, revealing complex dynamics influenced by coupling strength and trap inhomogeneity.

## Contribution

It demonstrates that impurity-boson interactions create an effective quasi-periodic potential causing Bloch oscillations without a real lattice, influenced by trap inhomogeneity and coupling sign.

## Key findings

- Impurity exhibits Bloch oscillations due to interaction-induced quasi-lattice.
- Oscillation periods and amplitudes depend on trap inhomogeneity.
- Impurity-boson coupling sign and strength significantly affect dynamics.

## Abstract

Motivated by a recent experiment by F. Meinert et al, arxiv:1608.08200, we study the dynamics of an impurity moving in the background of a harmonically trapped one-dimensional Bose gas in the hard-core limit. We show that due to the hidden "lattice" structure of background bosons, the impurity effectively feels a quasi-periodic potential via impurity-boson interactions that can drive the Bloch oscillation under an external force, even in the absence of real lattice potentials. Meanwhile, the inhomogeneous density of trapped bosons imposes an additional harmonic potential to the impurity, resulting in a similar oscillation dynamics but with different periods and amplitudes. We show that the sign and the strength of impurity-boson coupling can significantly affect above two potentials so as to determine the impurity dynamics.