Polarons in Binary Bose-Einstein Condensates

TL;DR

This paper derives an effective Hamiltonian for Bose polarons in binary condensates, analyzing impurity interactions and their effects on properties like energy, mass, and phonon number, revealing behavior near phase boundaries.

Contribution

It introduces a generalized Fröhlich Hamiltonian for binary Bose-Einstein condensates and investigates impurity properties using a variational approach, highlighting effects of impurity-spin coupling.

Findings

IS coupling contribution to ground energy diminishes near phase boundary

Increased IS coupling raises virtual phonons and effective mass

Impurity movement is impeded by stronger IS coupling

Abstract

Bose polarons are quasiparticles formed through the interaction between impurities and Bose-Einstein condensates. In this paper, we derive an effective Fr\"{o}hlich Hamiltonian using the generalized Bogoliubov transformation. The effective Fr\"{o}hlich Hamiltonian encompasses two types of effective interactions: impurity-density (ID) coupling and impurity-spin (IS) coupling. Furthermore, we employ the Lee-Low-Pines variational approach to investigate the relevant properties of Bose polarons induced by the ID and IS coupling. These properties include the ground state energy, effective mass, and average number of virtual phonons. Our findings reveal that the contribution resulting from IS couplings to the ground energy decreases to zero near the miscible-immiscible boundary. Additionally, the increase of the IS coupling induces a greater number of virtual phonons, impeding the movement of impurities and leading to a significant increase in the effective mass of Bose polarons.