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

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 $⟨\widehat{J^2}⟩$ is shown to be shared in impurity and bosons, but the value $⟨{\hat{J}}_z⟩$ 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.

Comments: 31 pages, 6 figures. Some comments, references, and new figures in Fig.3 have been added