Time resolved multi-photon effects in the fluorescence spectra of two-level systems at rest and in motion

We study the time-resolved fluorescence spectrum in two-level systems interacting with an incident coherent field, both in the weak and intermediate coupling regimes. For a single two-level system in the intermediate coupling case, as time flows, the spectrum develops distinct features, that are not captured by a semi-classical treatment of the incident field. Specifically, for a field on resonance with the atomic transition energy, the usual Mollow spectrum is replaced by a four peak structure, and for a frequency that is half of the atomic transition energy, the time-dependent spectrum develops a second harmonic peak with a superimposed Mollow triplet. In the long-time limit, our description recovers results previously found in the literature. After analyzing why a different behavior is observed in the quantum and classical dynamics, the reason for the occurrence of a second harmonic signal in a two-level system is explained via a symmetry analysis of the total (electron and photon) system, and in terms of a three level system operating in limiting regimes. We find an increased second harmonic signal in an array of two-level systems, suggesting a superradiance-like enhancement for multiple two-level systems in cavity setups. Finally, initial explorative results are presented for two-level model atoms entering and exiting a cavity, which hint at an interesting interplay between cavity-photon screening and atomic dynamics effects.