Asymptotic Freedom of Two Heavy Impurities in a Bose-Einstein Condensate

TL;DR

This paper investigates the interaction and asymptotic behavior of two heavy impurities in a Bose-Einstein condensate, revealing conditions for their effective independence and the nature of their polaron states.

Contribution

It introduces a detailed analysis of two-impurity polarons using Wilsonian renormalization, highlighting the asymptotic freedom and crossover phenomena in their interactions.

Findings

Impurities become asymptotically free at large separation in the repulsive regime.

Effective potentials and crossover behaviors are characterized across Feshbach resonances.

Repulsive-dominant polarons can exist even with attractive impurity-boson interactions.

Abstract

We consider two heavy impurities immersed in a Bose-Einstein condensate, and calculate the self-energy using the Wilsonian renormalization. The polaron energy, quasiparticle residue and damping rate are extracted from the self-energy. We demonstrate that various effective potentials emerge from the polaron energy under the specific conditions. In the limit of large separation between the impurities, the polaron spectrum converges to the results for a single impurity, exhibiting an attractive-repulsive crossover across the Feshbach resonance. The boundary of this crossover is identified through the analysis of the damping rate. We highlight that repulsive-dominant polarons can exist as long as the impurities are sufficiently close, even when the impurity-boson interactions are attractive. Additionally, we observe that the two impurities become asymptotically free in the repulsive polaron regime. These results are verifiable and offer a fresh perspective on the interaction dynamics between two polarons.