The Bose-Hubbard polaron from weak to strong coupling

TL;DR

This paper studies the properties of a mobile impurity in a bosonic lattice bath across different interaction regimes using quantum Monte Carlo simulations, revealing how the impurity can probe phase transitions and binding phenomena.

Contribution

It provides the first large-scale quantum Monte Carlo analysis of the Bose-Hubbard polaron across weak to strong coupling, including the effects of the Mott insulator to superfluid transition.

Findings

Polaron mass ratio decreases near the MI-SF transition at weak coupling.

In the strong coupling MI regime, the impurity binds to a bath particle or hole, altering the bath density.

The impurity can serve as a probe for binding phenomena in the lattice Bose system.

Abstract

We investigate the zero-temperature properties of a mobile impurity immersed in a bath of bosonic particles confined to a square lattice. We analyze the regimes of attractive and repulsive coupling between the impurity and the bath particles for different strengths of boson-boson interactions in the bath, using exact large-scale quantum Monte-Carlo simulations in the grand canonical ensemble. For weak coupling, the polaron mass ratio is found to decrease around the Mott insulator (MI) to superfluid (SF) transition of the bath, as predicted by recent theory, confirming the possible use of the impurity as a probe for the transition. For strong coupling in the MI regime, instead, the impurity is found to modify the bath density by binding to an extra bath particle or a hole, depending on the sign of the polaron-bath interactions. While the binding prevent the aforementioned use of the polaron mass ratio as an MI-SF transition probe, we show that it can be used instead as a probe of the binding itself. Our exact numerical results provide a benchmark for comparing lattice Bose polaron theories and are relevant for experiments with cold atoms trapped in optical lattices, where the presence of a confining harmonic potential can be modeled by a slowly varying local chemical potential.