  In this brief review, we report some new development in the functional
determinant approach (FDA), an exact numerical method, in the studies of a
heavy quantum impurity immersed in Fermi gases and manipulated with
radio-frequency pulses. FDA has been successfully applied to investigate the
universal dynamical responses of a heavy impurity in an ultracold ideal Fermi
gas in both the time and frequency domain, which allows the exploration of the
renowned Anderson's orthogonality catastrophe (OC). In such a system, OC is
induced by the multiple particle-hole excitations of the Fermi sea, which is
beyond a simple perturbation picture and manifests itself as the absence of
quasiparticles named polarons. More recently, two new directions for studying
heavy impurity with FDA have been developed. One is to extend FDA to a strongly
correlated background superfluid background, a Bardeen-Cooper-Schrieffer (BCS)
superfluid. In this system, Anderson's orthogonality catastrophe is prohibited
due to the suppression of multiple particle-hole excitations by the superfluid
gap, which leads to the existence of genuine polaron. The other direction is to
generalize the FDA to the case of multiple RF pulses scheme, which extends the
well-established 1D Ramsey spectroscopy in ultracold atoms into
multidimensional, in the same spirit as the well-known multidimensional nuclear
magnetic resonance and optical multidimensional coherent spectroscopy.
Multidimensional Ramsey spectroscopy allows us to investigate correlations
between spectral peaks of an impurity-medium system that is not accessible in
the conventional one-dimensional spectrum.
