Purcell-enhanced lifetime modulation of quantum emitters as a probe of local changes in refractive index

Quantum emitters embedded in photonic integrated circuit (PIC) cavities offer a powerful and scalable platform for label-free refractive-index sensing at the nanoscale. We propose and theoretically analyze a sensing mechanism based on Purcell-enhanced modulation of the emitter's spontaneous-emission lifetime, enabling detection of refractive-index changes via time-correlated single-photon counting (TCSPC). In contrast to traditional resonance-shift sensors, our approach exploits the lifetime sensitivity to variations in the local density of optical states, providing a sensing modality that is intensity independent, spectrally unresolvable, and potentially compatible with complementary metal-oxide-semiconductor technology. We derive analytical expressions linking refractive-index perturbations to relative lifetime shifts and identify an optimal off-resonance operation regime where the lifetime response becomes linear and maximally sensitive to small perturbations. As a PIC material, silicon offers seamless integration of single-photon avalanche detectors suitable for TCSPC. We therefore illustrate the applicability of the proposed mechanism for quantum emitters in silicon. Parametric evaluation of the analytical expressions shows that, for moderate-quality-factor photonic cavities ($Q={10}^{5}$--${10}^{7}$), this method enables refractive-index detection limits as low as ${10}^{\ensuremath{-}9}$ refractive index units---competitive with or even outperforming state-of-the-art plasmonic and microresonator sensors yet with significantly simpler instrumentation. Furthermore, long-lived emitters such as T centers in silicon offer a unique advantage, allowing subnanosecond lifetime shifts to be resolved with standard TCSPC systems. Although room-temperature operation of quantum emitters in silicon has yet to be demonstrated, our results lay the theoretical foundation for scalable, room-temperature, quantum-enabled refractive-index sensing---eliminating the need for spectral resolution and cryogenic infrastructure. Given the generic nature of the proposed approach, and with ongoing advances in PIC technologies such as diamond-on-silicon, hybrid silicon-silicon nitride, and silicon-silicon carbide platforms, the method can be readily extended to materials in which room-temperature operation of quantum emitters has already been experimentally demonstrated.