Title: Coherence in resonance fluorescence

Abstract: Resonance fluorescence (RF) serves as a fundamental path for matter to coherently interact with light. Accompanying this coherent process, recent studies suggested parallel existence of an incoherent scattering channel in order to explain the long-standing paradox of joint observation of a laser-like spectrum and anti-bunching in the RF of a weakly driven two-level emitter. If truly present, this incoherent process would cast doubt over RF's prospects in quantum information applications. Here, we exploit the concept of single-photon time-energy entanglement and have thus revolved the paradox without reliance on any incoherent scattering process. We derive a dimensionless dependence of the first-order coherence of the RF on the driving strength, followed by experimental verification on a cavity-enhanced quantum dot device with near-perfect light coupling. Furthermore, we perform the first phase-dependent two-photon interference experiment and observe peculiar coincidence bunching that is explained by single-photon time-energy entanglement. Our work reveals a new dimension in the understanding of photonic quantum superposition and may stimulate new applications.