Bosonic Functional Determinant Approach and its Application to Polaron Spectra

Abstract:

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. We compare the results to the Fermi polaron problem, for which we provide more detailed spectra than previously available by deriving an explicit formula for the overlap operator.

M. Drescher, M. Salmhofer, T. Enss, „Bosonic Functional Determinant Approach and its Application
to Polaron Spectra“, 20. März 2024, arXiv:2403.13582 (2024).

https://arxiv.org/abs/2403.13582

Related to Project C03