Quantum impurities in finite-temperature Bose gases: Detecting vortex proliferation across the BKT and BEC transitions

Detecting vortices in neutral superfluids represents an outstanding experimental challenge. Using stochastic classical-field methods, we theoretically show that a quantum impurity repulsively coupled to a weakly-interacting Bose gas at finite temperature carries direct spectroscopic signatures of vortex proliferation. In two dimensions, we find that a low-energy (attractive) branch in the excitation spectrum becomes prominent when the temperature is tuned across the Berezinskii-Kosterlitz-Thouless (BKT) transition. We explain this red-shifted resonance as originating from the binding of the impurity to vortices, where the bosons density (and hence, the repulsive Hartree energy) is reduced. This mechanism could be exploited to spectroscopically estimate the BKT transition in excitonic insulators. In contrast, in three dimensions, the impurity spectra reflect the presence of vortex rings well below the condensation temperature, and herald the presence of a thermal gas above the Bose-Einstein condensation transition. Importantly, we expect our results to have impact on the understanding of Bose-polaron formation at finite temperatures.