Signatures of the orthogonality catastrophe in a coherently driven impurity

TL;DR

This paper investigates how a coherently driven impurity in a Fermi gas exhibits signatures of the orthogonality catastrophe through Rabi oscillations and spectral features, providing experimental probes and matching experimental data.

Contribution

It introduces a combined exact and variational approach to analyze Rabi-driven impurity dynamics, revealing non-trivial scaling laws linked to the orthogonality catastrophe.

Findings

Rabi oscillation frequency scales as a non-trivial power of the drive

Spectral features reflect the Fermi-edge singularity

Theoretical results agree with experimental rf spectroscopy data

Abstract

We consider a fixed impurity immersed in a Fermi gas at finite temperature. We take the impurity to have two internal spin states, where the $\uparrow$ state is assumed to interact with the medium such that it exhibits the orthogonality catastrophe, while the $\downarrow$ 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 non-trivial 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 $\textit{et al.}$, Nature $\textbf{485}$, 615 (2012)], thus demonstrating the power of our approach.