Fano profile in the resonance fluorescence spectrum of a solid-state quantum emitter coupled to phonons
We present a theory of resonance fluorescence (RF) of a solid-state quantum emitter in the regime of weak optical excitation. The emitter is coupled to phonon modes of the surrounding bulk semiconductor, described by a super-Ohmic spectral density. We show that the RF spectrum of this system consists of a central elastic line, a broad phonon sideband known from other linear and nonlinear spectra of such systems, as well as a narrow inelastic contribution, which is characteristic of scattering spectra and stems from noise-induced transient dynamics. At moderate phonon couplings or low temperatures, the interplay between the broad sideband and the inelastic feature leads to a Fano-like profile near the resonant energy with the Fano parameter determined by laser detuning. In the weak-coupling limit (where only single-phonon processes are included), the spectrum becomes an exact Fano shape and resonant light scattering is entirely suppressed. The amplitude of this spectral feature grows linearly with temperature, while its width depends solely on the spontaneous emission rate of the emitter. We relate the quantum character of the reservoir to the non-commutativity of noise observables and show that Fano resonance persists in the classical limit. We also discuss how the redistribution of optical coupling efficiency between the central line and the sidebands affects the total scattering rate under various excitation conditions.