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

Quantum emitters embedded in photonic integrated circuit (PIC) cavities offer a 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). Unlike traditional resonance-shift sensors, our approach uses lifetime sensitivity to variations in the local density of optical states (LDOS), providing an intensity-independent, spectrally unresolvable, CMOS-compatible modality. We derive analytical expressions linking refractive index perturbations to relative lifetime shifts and identify an optimal off-resonance regime with linear, high sensitivity to small perturbations. Using silicon PICs as an example, we show detection limits down to 10^{-9} RIU for Q = 10^5-10^7 cavities, matching or exceeding plasmonic and microresonator sensors with simpler instrumentation. Long-lived emitters such as T-centers in silicon allow sub-nanosecond shifts to be resolved with standard TCSPC systems. Although room-temperature operation of silicon-based quantum emitters remains unproven, the concept is generic and applicable to other PIC platforms, including diamond-, silicon nitride-, and silicon carbide-based systems where such operation is established.