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In this brief review, we report some new development in the functionaldeterminant approach (FDA), an exact numerical method, in the studies of aheavy quantum impurity immersed in Fermi gases and manipulated withradio-frequency pulses. FDA has been successfully applied to investigate theuniversal dynamical responses of a heavy impurity in an ultracold ideal Fermigas in both the time and frequency domain, which allows the exploration of therenowned Anderson's orthogonality catastrophe (OC). In such a system, OC isinduced by the multiple particle-hole excitations of the Fermi sea, which isbeyond a simple perturbation picture and manifests itself as the absence ofquasiparticles named polarons. More recently, two new directions for studyingheavy impurity with FDA have been developed. One is to extend FDA to a stronglycorrelated background superfluid background, a Bardeen-Cooper-Schrieffer (BCS)superfluid. In this system, Anderson's orthogonality catastrophe is prohibiteddue to the suppression of multiple particle-hole excitations by the superfluidgap, which leads to the existence of genuine polaron. The other direction is togeneralize the FDA to the case of multiple RF pulses scheme, which extends thewell-established 1D Ramsey spectroscopy in ultracold atoms intomultidimensional, in the same spirit as the well-known multidimensional nuclearmagnetic resonance and optical multidimensional coherent spectroscopy.Multidimensional Ramsey spectroscopy allows us to investigate correlationsbetween spectral peaks of an impurity-medium system that is not accessible inthe conventional one-dimensional spectrum.

Functional Determinant Approach Investigations of Heavy Impurity Physics