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

TL;DR

This work introduces a lifetime-based refractive-index sensing paradigm that leverages Purcell-enhanced LDOS for quantum emitters embedded in high-Q photonic cavities. By operating off-resonance at the point of maximum slope in the Purcell response, small Δn perturbations yield linear, large changes in emitter lifetime that are detectable with standard TCSPC, without requiring spectral-resolution measurements. Analytical expressions connect Δn to lifetime shifts, incorporating realistic ensemble averaging through an effective coupling factor η_eff ≈ 1/6 and showing detection limits down to ~10^−9 RIU for Q factors between 10^5 and 10^7; the approach is further strengthened by proposing aptagel-based amplification to boost Δn. With long-lived emitters like T-centers, the method relaxes TCSPC timing requirements and is compatible with CMOS PICs, offering a scalable path to single-molecule refractive-index sensing across materials such as diamond, SiC, and SiN. Overall, the concept provides a robust, spectrally agnostic, room-temperature sensing modality that can surpass plasmonic and traditional microresonator sensors in certain regimes while benefiting from mature silicon photonics fabrication.

Abstract

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.

Figures (7)

• Figure 1: Schematic illustration of a possible multiplexed PIC implementation of the proposed sensing approach, enabling simultaneous detection across multiple channels.
• Figure 2: Simulated lifetime change ($\Delta \tau / \tau$) versus refractive index change ($\Delta n$) (i.e., sensitivity): (a) linear scale for $\Delta \tau / \tau$ from 0 to 10% and logarithmic scale for $\Delta n$; (b) logarithmic scale for $\Delta \tau / \tau$ from $10^{-1}$ to $10^{5}$ and logarithmic scale for $\Delta n$.
• Figure 3: Simulated normalized Purcell factor versus refractive index change $\Delta n$: (a) linear scale for $\Delta n$ from $-10^{-4}$ to $+10^{-4}$; (b) log scale for $\Delta n$ from $10^{-9}$ to $10^{-3}$.
• Figure 4: Normalized fluorescence decay $f(t)$ (log scale) versus time $t / \tau_{int}$: $F_P^{\text{max}}=5$, $\tau_{int}=1\mu$s.
• Figure 5: Comparison of effective lifetimes $\tau_{\mathrm{eff}}$ of a typical fluorophore ($\sim$3.5 ns intrinsic) and a T-center with an uncoupled lifetime of 1 $\mu$s, as a function of Purcell factor.