  We study the non-Markovian quantum dynamics of an emitter inside an open
multimode cavity, focusing on the case where the emitter is resonant with
high-frequency cavity modes. Based on a Green's function technique suited for
open photonic structures, we study the crossovers between three distinct
regimes as the coupling strength is gradually increased: (i) overdamped decay
with a time scale given by the Purcell modified decay rate, (ii) underdamped
oscillations with a time scale given by the effective vacuum Rabi frequency,
and (iii) pulsed revivals. The final multimode strong coupling regime (iii)
gives rise to quantum revivals of the atomic inversion on a time scale
associated with the cavity round-trip time. We show that the crucial parameter
to capture the crossovers between these regimes is the nonlinear Lamb shift,
accounted for exactly in our formalism.
