  The use of atomically sized quantum systems as highly sensitive measuring
devices represents an exciting and quickly growing research field. Here, we
explore the properties of a quasiparticle formed by a mobile impurity
interacting with a two-dimensional fermionic superfluid. The energy of the
quasiparticle is shown to be lowered by superfluid pairing as this increases
the compressibility of the Fermi gas, thereby making it easier for the impurity
to perturb its surroundings. We demonstrate that the fundamentally
discontinuous nature of the superfluid to normal phase transition of a
two-dimensional system, leads to a rapid increase in the quasiparticle energy
around the critical temperature. The magnitude of this increase exhibits a
nonmonotonic behavior as a function of the pairing strength with a sizable
maximum in the cross-over region, where the spatial extend of the Cooper pairs
is comparable to the interparticle spacing.
  Since the quasiparticle energy is measurable with present experimental
techniques, our results illustrate how impurities entangled with their
environment can serve as useful probes for non-trivial thermal and quantum
correlations.
