# Bose polaron in spherically symmetric trap potentials: Ground states with zero and lower angular momenta

## TL;DR

This paper develops a variational method to analyze the ground states of Bose polarons in spherical traps, considering angular momentum constraints, revealing how impurity-boson interactions influence spatial and quantum distributions.

## Contribution

It introduces a conditional variational approach with fixed angular momentum expectations for Bose polarons in traps, incorporating a cranking gauge transformation for bosons.

## Key findings

- Impurity-boson attraction causes overlap of boson distributions with impurity wave functions.
- The method effectively captures angular momentum sharing between impurity and bosons.
- Ground-state properties depend on the impurity-boson interaction strength.

## Abstract

Single-atomic impurities immersed in a dilute Bose gas in the spherically symmetric harmonic trap potentials are studied at zero temperature. In order to find the ground state of the polarons, we present a conditional variational method with fixed expectation values of the total angular momentum operators, $\hat{J}^2$ and $\hat{J}_z$, of the system, using a cranking gauge-transformation for bosons to move them in the frame co-rotating with the impurity. In the formulation, the expectation value $\langle \hat{J^2}\rangle$ is shown to be shared in impurity and bosons, but the value $\langle \hat{J}_z\rangle$ is carried by the impurity due to the rotational symmetry. We also analyze the ground-state properties numerically obtained in this variational method for the system of the attractive impurity-boson interaction, and find that excited boson distributions around the impurity overlap largely with impurity's wave function in their quantum-number spaces and also in the real space because of the attractive interaction employed.