Exact quasiparticle properties of a heavy polaron in BCS Fermi superfluids

TL;DR

This paper provides exact calculations of quasiparticle properties of a heavy impurity in a BCS Fermi superfluid, revealing novel features and resonances that can be experimentally observed.

Contribution

It introduces an exact functional determinant approach to analyze impurity quasiparticles in a superfluid, confirming key features and predicting new resonances.

Findings

Confirmation of dark continuum, molecule-hole continuum, and repulsive polarons.

Prediction of Yu-Shiba-Rusinov bound states related to the superfluid gap.

Existence of undamped repulsive polarons at zero temperature.

Abstract

We present the Ramsey response and radio-frequency spectroscopy of a heavy impurity immersed in an interacting Fermi superfluid, using exact functional determinant approach. We describe the Fermi superfluid through the conventional Bardeen-Cooper-Schrieffer theory and investigate the role of the pairing gap on quasiparticle properties revealed by the two spectroscopies. The energy cost for pair breaking prevents Anderson\textquoteright s orthogonality catastrophe that occurs in a non-interacting Fermi gas and allows the existence of polaron quasiparticles in the exactly solvable heavy impurity limit. Hence, we rigorously confirm the remarkable features such as dark continuum, molecule-hole continuum and repulsive polaron. For a magnetic impurity scattering at finite temperature, we predict additional resonances related to the sub-gap Yu-Shiba-Rusinov bound state, whose positions can be used to measure the superfluid pairing gap. For a non-magnetic scattering at zero temperature, we surprisingly find undamped repulsive polarons. These exact results might be readily observed in quantum gas experiments with Bose-Fermi mixtures that have a large-mass ratio.