Signatures of the orthogonality catastrophe in a coherently driven impurity

We consider a fixed impurity immersed in a Fermi gas at arbitrary temperature. We take the impurity to have two internal spin states where the $\ensuremath{\uparrow}$ state is assumed to interact with the medium such that it exhibits the orthogonality catastrophe, whereas the $\ensuremath{\downarrow}$ state is a bare noninteracting particle. Introducing a Rabi coupling between the impurity states, therefore, allows us to investigate the coupling between a discrete spectral peak and the Fermi-edge singularity, i.e., between states with and without a quasiparticle residue. Combining an exact treatment of the uncoupled impurity Green's functions with a variational approach to treat the Rabi driven dynamics, we find that the system features Rabi oscillations whose frequency scales as a nontrivial power of the Rabi drive at low temperatures. This reflects the power law of the Fermi-edge singularity and, importantly, this behavior is qualitatively different from the case of a mobile impurity quasiparticle where the scaling is linear. We, therefore, argue that the scaling law serves as an experimentally implementable probe of the orthogonality catastrophe. We additionally simulate rf spectroscopy beyond linear response, finding a remarkable agreement with an experiment using heavy impurities [Kohstall et al., Nature 485, 615 (2012)], thus, demonstrating the power of our approach.