Bosonic Functional Determinant Approach and its Application to Polaron Spectra

The functional determinant approach (FDA) is a simple method to compute exactly certain observables for ideal quantum systems and has been successfully applied to the Fermi polaron problem to obtain the dynamical overlap and spectral function. Unfortunately, its application to Bosonic ultracold gases is prohibited by the failure of the grand canonical ensemble for these systems. In this paper, we show how to circumvent this problem and develop a Bosonic FDA. This yields exact injection and ejection spectra for ideal Bose polarons at arbitrary temperatures. While coherent features visible at absolute zero quickly smear out with rising temperature as expected, the line width of the main peak is, counterintuitively, found to decrease near unitarity. Furthermore, we provide explicit formulas for the overlap operator, which allow to compute the necessary determinants for both Bose and Fermi polarons more efficiently than previously possible.