Heavy polarons in ultracold atomic Fermi superfluids at the BEC-BCS crossover: formalism and applications

TL;DR

This paper extends an exact numerical approach to study a heavy impurity in a superfluid Fermi gas across the BEC-BCS crossover, revealing how pairing gaps influence polaron formation and enabling spectroscopic measurements of superfluid properties.

Contribution

The authors develop an extended functional determinant approach for superfluid backgrounds, allowing exact analysis of polarons and impurity-induced bound states in BEC-BCS crossover systems.

Findings

Pairing gap prevents Anderson's orthogonality catastrophe in superfluids.

Polaron spectrum can measure the superfluid pairing gap.

Magnetic impurities reveal Yu-Shiba-Rusinov bound states.

Abstract

We investigate the system of a heavy impurity embedded in a paired two-component Fermi gas at the crossover from a Bose-Einstein condensate (BEC) to a Bardeen--Cooper--Schrieffer (BCS) superfluid via an extension of the functional determinant approach (FDA). FDA is an exact numerical approach applied to study manifestations of Anderson\textquoteright s orthogonality catastrophe (OC) in the system of a static impurity immersed in an ideal Fermi gas. Here, we extend the FDA to a strongly correlated superfluid background described by a BCS mean-field wavefunction. In contrast to the ideal Fermi gas case, the pairing gap in the BCS superfluid prevents the OC and leads to genuine polaron signals in the spectrum. Thus, our exactly solvable model can provide a deeper understanding of polaron physics. In addition, we find that the polaron spectrum can be used to measure the superfluid pairing gap, and in the case of a magnetic impurity, the energy of the sub-gap Yu-Shiba-Rusinov (YSR) bound state. Our theoretical predictions can be examined with state-of-art cold-atom experiments.