Title: Coherence in resonance fluorescence

Abstract: Resonance fluorescence (RF) of a two-level emitter displays persistently anti-bunching irrespective of the excitation intensity, but inherits the driving laser's linewidth under weak excitation. These properties are commonly explained disjoinedly as the emitter's single photon saturation or passively scattering light, until a recent theory attributes anti-bunching to the laser-like spectrum's interference with the incoherently scattered light. However, the theory implies higher-order scattering processes, and led to an experiment purporting to validate an atom's simultaneous scattering of two photons. If true, it could complicate RF's prospects in quantum information applications. Here, we propose a unified model that treats all RF photons as spontaneous emission, one at a time, and can explain simultaneously both the RF's spectral and correlation properties. We theoretically derive the excitation power dependencies, with the strongest effects measurable at the single-photon incidence level, of the first-order coherence of the whole RF and super-bunching of the spectrally filtered, followed by experimental confirmation on a semiconductor quantum dot micro-pillar device. Furthermore, our model explains peculiar coincidence bunching observed in phase-dependent two-photon interference experiments. Our work provides novel understandings of coherent light-matter interaction and may stimulate new applications.