Photon statistics of resonantly driven spectrally diffusive quantum emitters

TL;DR

Spectral diffusion in solid-state single-photon emitters degrades photon indistinguishability. The paper develops a theoretical framework for photon statistics under resonant excitation, comparing continuous Ornstein-Uhlenbeck diffusion and discrete Gaussian random-jump SD models, and derives how $g^{(2)}(\tau)$ and long-time intensity fluctuations encode the diffusion type. Short-time bunching scales with the inhomogeneous-to-homogeneous linewidth ratio, while the long-time decay is non-exponential for OU but exponential with $\tau_b=\tau_{\text{SD}}$ for GRJ; intensity statistics (Mandel $Q$, skewness) further distinguish the models. The results provide practical diagnostic tools to characterize SD in solid-state emitters, with relevance to B centers in hexagonal boron nitride and broader quantum-optical platforms, and suggest extensions to filtered emission and multi-component diffusion.

Abstract

In the solid state, a large variety of single-photon emitters present high quality photophysical properties together with a potential for integration. However, in many cases, the host matrix induces fluctuations of the emission wavelength in time, limiting the potential applications based on indistinguishable photons. A deep understanding of the underlying spectral diffusion processes is therefore of high importance for improving the stability of the light emission. Here, we theoretically investigate the photon statistics of an emitter driven by a resonant laser, and subject to either of two qualitatively different stationary spectral diffusion processes - a continuous diffusion process and a process based on discrete spectral jumps, both of which being known to model the spectral diffusion of various solid-state emitters. We show that the statistics of light emission carries several experimentally accessible signatures that allow to discriminate between the two classes of models, both at short times in the intensity correlation function, and at long times in the fluctuations of the integrated intensity. These results establish that resonant excitation combined with photon statistics offers a rich access to the spectral diffusion processes, yielding information that goes beyond the bare characterization of the inhomogeneous shape and noise correlation time. Incidentally, our findings shed a new light on recent experimental results of spectral diffusion of B centers in hexagonal boron nitride, providing more insight in their spectral diffusion mechanisms.

Figures (20)

• Figure 1: (a) Sketch of an emitter coupled to a fluctuating environment modeled by an ensemble of identical two-level systems, yielding a OU diffusion process. (b) Numerically generated spectral trajectory.
• Figure 2: (a) Sketch of an emitter coupled to a fluctuating environment modeled by a charge hopping between various trap states. (b) Numerically generated spectral trajectory .
• Figure 3: (a) Intensity time trace generated with the OU model. (b) Intensity time trace generated with the GRJ model.
• Figure 4: Example of $g^{(2)}(\tau)$ generated from a time trace shown Fig. \ref{['fig3']}. The gray dashed line depicts the Poissonian limit $g^{(2)}(\tau) = 1$.
• Figure 5: (a) Zero-time bunching $B(0)$ as a function of the laser detuning. (b) $B(0)$ as a function of the laser power. In both simulations, $\Delta \omega_\mathrm{hom}/\Delta \omega_\mathrm{inhom} = 2.2 \cdot 10^{-2}$.