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We present the Ramsey response and radio-frequency spectroscopy of a heavyimpurity immersed in an interacting Fermi superfluid, using exact functionaldeterminant approach. We describe the Fermi superfluid through the conventionalBardeen-Cooper-Schrieffer theory and investigate the role of the pairing gap onquasiparticle properties revealed by the two spectroscopies. The energy costfor pair breaking prevents Anderson\textquoteright s orthogonality catastrophethat occurs in a non-interacting Fermi gas and allows the existence of polaronquasiparticles in the exactly solvable heavy impurity limit. Hence, werigorously confirm the remarkable features such as dark continuum,molecule-hole continuum and repulsive polaron. For a magnetic impurityscattering at finite temperature, we predict additional resonances related tothe sub-gap Yu-Shiba-Rusinov bound state, whose positions can be used tomeasure the superfluid pairing gap. For a non-magnetic scattering at zerotemperature, we surprisingly find undamped repulsive polarons. These exactresults might be readily observed in quantum gas experiments with Bose-Fermimixtures that have a large-mass ratio.

Exact quasiparticle properties of a heavy polaron in BCS Fermi superfluids