Purcell-enhanced lifetime modulation of quantum emitters as a probe of local changes in refractive index
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2025-10-21 |
| Journal | Physical Review Applied |
| Authors | Yevhenii M. Morozov, Anatoliy Lapchuk |
| Institutions | Austrian Institute of Technology, Institute for Information Recording |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”This analysis outlines a theoretical framework for a novel, highly sensitive refractive index (RI) sensing modality utilizing Purcell-enhanced lifetime modulation of quantum emitters (QEs) in silicon photonic integrated circuits (PICs).
- Novel Sensing Mechanism: The approach relies on measuring changes in the spontaneous emission lifetime (T1) via Time-Correlated Single-Photon Counting (TCSPC), rather than traditional resonance wavelength shifts. This makes the sensor robust against thermal broadening and spectral noise.
- Ultra-High Sensitivity: Theoretical analysis predicts a minimum detectable RI change (Δnopt) as low as 3.75 x 10-9 RIU when using high-quality (Q = 107) photonic cavities. This performance is competitive with or superior to state-of-the-art plasmonic and microresonator sensors.
- Off-Resonance Optimization: The system is designed to operate off-resonance (at the maximum slope of the Purcell factor curve, Δω = κ/2). This strategy ensures a linear response to small RI perturbations and maximizes sensitivity, relaxing the requirements for ultra-high spectral resolution.
- CMOS Compatibility: The platform leverages T-centers (carbon-hydrogen complexes) embedded in silicon, offering emission in the telecom band (~1326 nm) and seamless integration with CMOS fabrication and on-chip Single-Photon Avalanche Detectors (SPADs).
- Relaxed Instrumentation Demands: Long-lived QEs, such as T-centers (intrinsic lifetime Tint ~1 µs), maintain effective lifetimes in the nanosecond to hundreds of nanoseconds range even under high Purcell enhancement. This allows sub-nanosecond lifetime shifts to be resolved using standard, cost-effective TCSPC systems.
- Scalability and Versatility: The generic nature of the approach allows extension to other PIC materials (e.g., diamond-on-silicon, silicon carbide, silicon nitride) where room-temperature QE operation is already demonstrated.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Minimum RI Detection Limit (Δnopt) | 3.75 x 10-9 | RIU | Achievable with Q = 107 cavity |
| Linear Dynamic Range (LDR) Width | 1.12 x 10-7 | RIU | For Q = 107 cavity |
| RI Detection Limit (Q=105) | 3.75 x 10-7 | RIU | Comparable to typical SPR limit (~10-6 RIU) |
| Target Cavity Q Factors | 105 to 107 | Dimensionless | Required for competitive sensing |
| Effective Refractive Index (neff) | 2.5 | Dimensionless | Assumed for silicon PIC |
| T-Center Intrinsic Lifetime (Tint) | ~1 | µs | Uncoupled spontaneous emission lifetime |
| T-Center ZPL Emission Wavelength | ~1326 | nm | Telecom band |
| Required TCSPC Resolution (Q=105) | ~2 to 5 | ns | Standard system, using T-centers |
| Relative Lifetime Change (Δτ/τ) | 3 | % | Target change for practical detection |
| Sensitivity Slope (Q=107) | 8 x 106 | RIU-1 | Relative lifetime change per unit Δn |
| Estimated Direct Binding Δn | 1.2 x 10-7 | RIU | Single molecule binding (no aptagel amplification) |
Key Methodologies
Section titled “Key Methodologies”The proposed sensing scheme is based on a theoretical model linking local refractive index changes (Δn) to the spontaneous emission lifetime (τ) via the Purcell factor (FP).
- Purcell Factor Modeling: The spontaneous emission lifetime (τ) is calculated using the Purcell factor (FP), which is a function of the cavity quality factor (Q), effective mode volume (V), and the spatial/orientational alignment of the quantum emitter (QE) dipole moment relative to the cavity electric field.
- Refractive Index Perturbation: A local change in RI (Δn) is modeled as a permittivity perturbation (Δε), which induces a shift (Δω) in the cavity resonance frequency (ωcav). This shift is calculated using first-order perturbation theory.
- Off-Resonance Operation Regime: The system is intentionally detuned from the cavity resonance (Δω = 0) to the point of maximum slope of the Lorentzian Purcell factor curve (Δω = ±κ/2, where κ is the cavity decay rate). This operating point (n0) ensures the lifetime response (Δτ/τ) is linear and maximally sensitive to small Δn changes.
- Sensitivity Calculation: Analytical expressions are derived to link the relative lifetime change (Δτ/τ) linearly to the RI change (Δn) at the optimal off-resonance point (n0). The minimum detectable Δnopt is then calculated based on the cavity Q and the temporal resolution (Δτ/τ0) of the TCSPC system.
- Ensemble Averaging (Realistic Model): To account for practical challenges (imperfect alignment, spatial distribution), an effective coupling efficiency factor (ηeff) is introduced. The normalized fluorescence decay curve f(t) for an ensemble of QEs is numerically modeled by averaging the position- and orientation-dependent lifetime τ(θ,x) over the cavity volume.
- Signal Amplification Modeling: The effect of a signal transduction amplifier (e.g., aptagel hydrogel) is modeled by calculating the amplified effective RI perturbation (Δnaptagel) based on the polymer volume fraction increase (Δφ) and the field-weighted overlap (foverlap).
Commercial Applications
Section titled “Commercial Applications”The proposed Purcell-enhanced lifetime sensing platform is designed for high-sensitivity, integrated detection, making it suitable for several advanced applications:
- Integrated Biosensing and Diagnostics:
- Label-Free Detection: Monitoring molecular binding events (e.g., antibody-antigen, aptamer-target) in real-time without fluorescent labels.
- Single-Molecule Interaction Studies: Achieving the sensitivity required (10-7 to 10-9 RIU) for detecting individual molecular binding events in compact, scalable devices.
- Personalized Medicine: Integration into CMOS PICs with on-chip SPADs for real-time monitoring of drug efficacy (e.g., optimizing immunosuppressive drug dosing in transplant patients).
- Quantum-Enabled Photonic Sensing:
- Scalable PIC Platforms: Leveraging mature silicon photonics and CMOS fabrication for mass-producible, multiplexed sensor arrays (Fig. 1).
- Robust Environmental Monitoring: Utilizing the T1 lifetime measurement, which is inherently less susceptible to temperature fluctuations and spectral noise compared to resonance tracking methods.
- Material Science and Process Control:
- Local Density of Optical States (LDOS) Probing: High-precision measurement of subtle environmental changes that modulate the electromagnetic environment at the nanoscale.
- Alternative QE Hosts: The generic methodology is adaptable to emerging PIC materials like diamond, silicon carbide, and silicon nitride, facilitating the development of room-temperature quantum sensors.
View Original 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.