A Hybrid Jump-Diffusion Model for Coherent Optical Control of Quantum Emitters in hBN

TL;DR

The paper addresses coherence losses in mechanically decoupled hBN quantum emitters arising from temperature-dependent spectral diffusion and discrete spectral jumps. It introduces a hybrid stochastic model that combines Ornstein–Uhlenbeck diffusion with Gaussian random jumps, calibrated to the empirical cubic linewidth law $\Gamma_{exp}(T)=A+BT^3$, to reproduce linewidths, $g^{(2)}(\tau)$ damping, and the drive-dependent loss of coherence. A key finding is the identification of a crossover to overdamped dynamics at $T_{crit} \approx 25.91$ K, linked to the increasing dephasing $\gamma_{sd+j}$ that scales with drive strength, providing a quantitative bridge between spectroscopic observables and microscopic noise processes. The framework is general and enables inference of microscopic noise parameters from measured linewidths, offering a path to engineering strategies that extend coherent operation of hBN emitters and similar solid-state systems.

Abstract

Hexagonal boron nitride (hBN) has emerged as a promising two-dimensional host for stable single-photon emission owing to its wide bandgap, high photostability, and compatibility with nanophotonic integration. We present a simulation-based study of temperature-dependent spectral dynamics and optical coherence in a mechanically decoupled quantum emitter in hBN. Employing a hybrid stochastic framework that combines Ornstein--Uhlenbeck detuning fluctuations with temperature-dependent, Gaussian-distributed discrete frequency jumps, motivated by experimentally observed spectral diffusion and blinking, we reproduce the measured evolution of inhomogeneous linewidth broadening and the progressive degradation of photon coherence across the relevant cryogenic range (5-30K). The model captures phonon-related spectral diffusion with a cubic temperature dependence and the onset of jump-like spectral instabilities at higher temperatures. By calibrating the hybrid diffusion, jump parameters to the experimentally measured full width at half maximum (FWHM) of the emission line and analyzing the second-order correlation function $g^{(2)}(τ)$ under resonant driving, we establish a unified phenomenological description that links stochastic detuning dynamics to the decay of optical coherence in a resonantly driven emitter. Analysis of $g^{(2)}(τ)$ under resonant driving reveals an additional dephasing rate $γ_{\mathrm{sd+j}}$ that rises monotonically with temperature and drive strength, leading to a predicted critical crossover to overdamped dynamics at $T_{\mathrm{crit}} \approx 25.91$~K. This hybrid framework provides a quantitative connection between accessible spectroscopic observables and the dominant noise mechanisms limiting coherent optical control in mechanically decoupled quantum emitters, exemplified in hBN and generalizable to similar emitters in other materials.

Figures (6)

• Figure 1: Simulated and experimental inhomogeneous linewidth broadening as a function of temperature. The simulated FWHM values (blue) closely follow the empirical $A + BT^3$ trend (red dashed line), confirming the expected phonon-limited broadening behavior.
• Figure 2: (a--c) Simulated second-order correlation functions $g^{(2)}(\tau)$ for the hBN quantum emitter studied in Ref. Koch2024 at 5 K, 20 K, and 30 K, respectively. Increasing excitation power increases the Rabi frequency ($\Omega_R \propto \sqrt{P}$), which manifests in $g^{(2)}(\tau)$ as more pronounced oscillatory shoulders and a higher oscillation frequency at short delay times. At elevated temperatures, these oscillatory features are progressively damped due to enhanced spectral diffusion and thermally activated frequency jumps, leading to suppression of coherent Rabi dynamics (see Supplementary Information, Fig. S2 for parameter dependence).
• Figure 3: Decay rate extracted from simulated $g^{(2)}(\tau)$ traces as a function of Rabi frequency for 5 K, 20 K, and 30 K. The dashed red line marks the $\Gamma = \Omega_R$ boundary separating coherent and overdamped regimes. The increase in slope with temperature reflects the monotonic rise of $\gamma_{\mathrm{sd+j}}$, which captures spectral-diffusion- and jump-induced inhomogeneous broadening.
• Figure S1: Figure S1: Independent effects of spectral diffusion parameters in the OU model. (a) Linewidth as a function of correlation time $\tau_{\mathrm{sd}}$ for different diffusion strengths $\sigma$. The dependence on $\tau_{\mathrm{sd}}$ is weak across three decades. (b) Linewidth as a function of diffusion strength $\sigma$ for different $\tau_{\mathrm{sd}}$, showing an approximately linear increase in FWHM with noise amplitude. (c) $g^{(2)}(\tau)$ at fixed $\sigma = 1$ for varying $\tau_{\mathrm{sd}}$. Despite changes in correlation time, the Rabi oscillations remain nearly unchanged. (d) $g^{(2)}(\tau)$ at fixed $\tau_{\mathrm{sd}} = 0.01ns$ for varying $\sigma$, showing strong damping with increasing diffusion strength.
• Figure S2: Figure S2: Independent parameter study of Ornstein--Uhlenbeck spectral diffusion with Gaussian random jumps. (a) FWHM as a function of jump rate $\lambda_J$ for different fixed jump amplitudes $\sigma_J$. (b) $g^{(2)}(\tau)$ at fixed jump amplitude and varying jump rate. (c) FWHM as a function of jump amplitude $\sigma_J$ for different fixed jump rates. (d) $g^{(2)}(\tau)$ at fixed jump rate and varying jump amplitude. Jump rate predominantly governs temporal coherence, while jump amplitude controls spectral broadening and non-Gaussian tails.