Polaron Interactions and Bipolarons in One-Dimensional Bose Gases in the Strong Coupling Regime

TL;DR

This paper develops a non-perturbative mean-field theory for heavy polarons in one-dimensional Bose gases, accurately describing polaron interactions and bipolaron binding energies in the strong coupling regime, validated by quantum Monte Carlo simulations.

Contribution

It introduces an analytic mean-field approach for strong impurity-boson coupling in 1D Bose gases, extending understanding of polaron interactions beyond weak coupling.

Findings

Analytic expression for heavy polaron interaction potential.

Bipolaron binding energies match quantum Monte Carlo results.

Potential shape transitions from exponential to linear at strong coupling.

Abstract

Bose polarons, quasi-particles composed of mobile impurities surrounded by cold Bose gas, can experience strong interactions mediated by the many-body environment and form bipolaron bound states. Here we present a detailed study of heavy polarons in a one-dimensional Bose gas by formulating a non-perturbative theory and complementing it with exact numerical simulations. We develop an analytic approach for weak boson-boson interactions and arbitrarily strong impurity-boson couplings. Our approach is based on a mean-field theory that accounts for deformations of the superfluid by the impurities and in this way minimizes quantum fluctuations. The mean-field equations are solved exactly in Born-Oppenheimer (BO) approximation leading to an analytic expression for the interaction potential of heavy polarons which is found to be in excellent agreement with quantum Monte-Carlo (QMC) results. In the strong-coupling limit the potential substantially deviates from the exponential form valid for weak coupling and has a linear shape at short distances. Taking into account the leading-order Born-Huang corrections we calculate bipolaron binding energies for impurity-boson mass ratios as low as 3 and find excellent agreement with QMC results.