Path-integral ground state and optical response of the charged Bose polaron

The system of a charged impurity in an interacting Bose gas has gained significant attention due to the long-range ion-atom interactions and the study of transport properties. Here, the ground-state energy of a charged Bose polaron is calculated within the Bogoliubov approximation using a generalized Feynman variational path-integral approach, which obtained accurate results for other polaron problems. We find that compared to other existing approaches, our approach gives similar and improved results while being numerically less intensive. Optical absorption, which is a standard tool to study the solid-state polaron, is introduced here as a probing method for the Bose polaron. It is calculated within the Bogoliubov approximation for weak ion-atom interactions, and the effect of finite temperature is studied. We show that the coupling of the ion to an oscillating external electric field offers a straightforward experimental probe for the charged polaron in a Bose gas, different from but complementary to existing spectroscopic techniques.