# Strong coupling Bose polarons in a BEC

## TL;DR

This paper employs a non-perturbative renormalization group method to analyze the Bose polaron problem in a BEC, revealing phase transitions, effective mass behavior, and quantum fluctuation effects across interaction regimes.

## Contribution

It provides a unified theoretical framework for Bose polarons, including a detailed phase diagram and insights into the polaron-to-molecule transition near Feshbach resonances.

## Key findings

- Prediction of a sharp increase in effective mass near Feshbach resonance
- Identification of a transition to states below polaron energy at weaker interactions
- Logarithmic corrections to polaron energy due to quantum fluctuations

## Abstract

We use a non-perturbative renormalization group approach to develop a unified picture of the Bose polaron problem, where a mobile impurity is strongly interacting with a surrounding Bose-Einstein condensate (BEC). A detailed theoretical analysis of the phase diagram is presented and the polaron-to-molecule transition is discussed. For attractive polarons we argue that a description in terms of an effective Fr\"ohlich Hamiltonian with renormalized parameters is possible. Its strong coupling regime is realized close to a Feshbach resonance, where we predict a sharp increase of the effective mass. Already for weaker interactions, before the polaron mass diverges, we predict a transition to a regime where states exist below the polaron energy and the attractive polaron is no longer the ground state. On the repulsive side of the Feshbach resonance we recover the repulsive polaron, which has a finite lifetime because it can decay into low-lying molecular states. We show for the entire range of couplings that the polaron energy has logarithmic corrections in comparison with predictions by the mean-field approach. We demonstrate that they are a consequence of the polaronic mass renormalization which is due to quantum fluctuations of correlated phonons in the polaron cloud.