Non-Markovian transient spectroscopy in cavity QED

We theoretically analyze measurements of the transient field leaving a cavity as a tool for studying non-Markovian dynamics in cavity quantum electrodynamics (QED). Combined with a dynamical decoupling pulse sequence, transient spectroscopy can be used to recover spectral features that may be obscured in the stationary cavity transmission spectrum due to inhomogeneous broadening. The formalism introduced here can be leveraged to perform in situ noise spectroscopy, revealing a robust signature of quantum noise arising from non-commuting observables, a purely quantum effect.