Variational study of polarons and bipolarons in a 1D Bose lattice gas in both superfluid and Mott regimes

TL;DR

This paper investigates polarons and bipolarons in a 1D Bose lattice gas across superfluid and Mott regimes using variational methods, aligning with recent experiments and exploring impurity stability.

Contribution

It introduces a variational approach to analyze impurity binding and bipolaron formation in 1D Bose gases, providing new insights into their dispersion and stability.

Findings

Polaron binds with a hole in both regimes.

Consistent dispersion results with recent experiments.

Stable bipolarons form at strong interactions.

Abstract

We use variational methods to study a spin impurity in a 1D Bose lattice gas. Both in the strongly interacting superfluid regime and the Mott regime we find that the impurity binds with a hole, forming a polaron. Our calculations for the dispersion of the polaron are consistent with recent experiments by Fukuhara et. al. [Nature Phys. 9, 235 (2013)] and give a better understanding of their numerical simulations. We find that for sufficiently weak interactions there are ranges of momentum for which the polaron is unstable. We propose experimentally studying the stability of the polaron by measuring the correlation between the impurity and holes. We also study two interacting impurities, finding stable bipolarons for sufficiently strong interactions.