Fano profile in the resonance fluorescence spectrum of a solid-state quantum emitter coupled to phonons

Abstract

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 the 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 non-linear spectra of such systems, and a narrow inelastic contribution characteristic of scattering spectra, stemming 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, with the inelastic component vanishing completely at the exact laser frequency. The amplitude of this spectral feature grows linearly with temperature, while its width depends solely on the spontaneous emission rate of the emitter. Because the spectral line shape is extremely sensitive to dephasing, resonance fluorescence can serve as a direct, non-interferometric probe of coherence at dephasing rates critical for generating highly indistinguishable single photons. We relate the quantum character of the reservoir to the non-commutativity of noise observables and show that the Fano resonance persists in the classical (commutative) 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.