Indistinguishable Single-Photon Sources with Dissipative Emitter Coupled to Cascaded Cavities

Abstract: Recently, Grange et al. [Phys. Rev. Lett. 114, 193601 (2015)] showed the possibility of single photon generation with high indistinguishability from a quantum emitter, despite strong pure dephasing, by `funneling' emission into a photonic cavity. Here, we show that cascaded two-cavity system can further improve the photon characteristics and greatly reduce the Q-factor requirement to levels achievable with present-day technology. Our approach leverages recent advances in nanocavities with ultrasmall mode volume and does not require ultrafast excitation of the emitter. These results were obtained by numerical and closed-form analytical models with strong emitter dephasing, representing room-temperature quantum emitters.

• The paper demonstrates a cascaded cavity QED framework that reduces ultrahigh Q-factor requirements while achieving high photon indistinguishability and efficiency.
• The methodology leverages strong emitter-cavity couplings and controlled dephasing to navigate between regimes of optimal indistinguishability and collection efficiency.
• Numerical and analytical models confirm that the setup robustly suppresses spectral diffusion, offering a scalable platform for on-chip quantum photonics.

Indistinguishable Single-Photon Sources via Dissipative Emitter Coupling to Cascaded Cavities

Introduction

The realization of single-photon sources that exhibit high indistinguishability $I$ and collection efficiency $\eta$ is a critical requirement for quantum information processing, linear-optics quantum computing, and photonic quantum networks. The generation of such photons at room temperature is fundamentally limited by strong dephasing and spectral diffusion in realistic solid-state emitters, necessitating advanced photonic engineering for effective emission control. The paper "Indistinguishable Single-Photon Sources with Dissipative Emitter Coupled to Cascaded Cavities" (1809.01645) introduces and analyzes a cascaded-cavity quantum electrodynamics (CQED) framework that overcomes the $Q$-factor and $V_\text{eff}$ bottlenecks present in conventional single-cavity approaches, thereby enabling the generation of high-quality single photons with feasible nanofabrication requirements.

Physical Model and Device Architecture

The emission properties of a quantum emitter are severely degraded at room temperature due to multiple linewidth broadening mechanisms, including natural radiative linewidth ($\gamma$), Markovian pure dephasing ($\gamma^*$), and slow spectral diffusion (Gaussian width $\Delta\delta$), yielding total emitter linewidth $\Gamma = \gamma + \gamma^* + \Delta \delta$. For color centers in diamond, pure dephasing dominates at room temperature, rendering $I \sim 10^{-4}$ for bare emission.

To address this, the paper investigates a room-temperature photonic quantum emitter coupled sequentially to two distinct cavities, $C_1$ and $C_2$ (cascaded-cavity system). The emitter couples strongly to $C_1$ (low $Q$, ultrasmall $V_\text{eff}$ for efficient emission) and $C_1$ is then coupled to $C_2$ (potentially higher $Q$ but not ultrahigh), which acts as a spectral and temporal funnel for emission. The physical realization leverages dielectric photonic crystal nanocavities with concentrator tips to maximize $g_1$, and inter-cavity coupling $g_2$ is tuned by spatial separation.

Figure 1: Cascaded-cavity architecture for high-efficiency, indistinguishable photon emission at room temperature, with photonic crystal implementation of the emitter-cavity system.

Analytical and Numerical Framework

The formalism treats the emitter-$C_1$ ($g_1$) and $C_1$-$C_2$ ($g_2$) couplings under strong dephasing ($\gamma^* \gg \gamma$). Population transfer rates are analytically derived as

$$R_1 = \frac{4g_1^2}{\Gamma + \kappa_1}, \qquad R_2 = \frac{4g_2^2}{R_1 + \kappa_1 + \kappa_2}$$

The photon indistinguishability and efficiency at the output of $C_2$ are calculated using master equation simulations and confirmed by closed-form analytical solutions, demonstrating high fidelity with numerical results. Two operational regimes emerge: Reg. 1 (high $I$, moderate $\eta$) where $R_2, \kappa_2 \ll \kappa_1$, and Reg. 2 (large $\eta$, moderate $I$) where $R_2, \kappa_2 \gg \kappa_1$.

Device Parameter Optimization

The cascaded-cavity configuration provides increased degrees of freedom for simultaneous optimization of $I$ and $\eta$, as visualized in the parameter space of $g_2$ and $\kappa_2$.

Figure 2: Efficiency $(\eta)$ and indistinguishability $(I)$ of the cascaded-cavity system shown as functions of $g_2$ and $\kappa_2$, illustrating two operational regimes.

In Reg. 1, the emitter and $C_1$ act as a composite high-dephasing quasi-emitter feeding $C_2$, so $I$ can reach $\sim 0.95$ with a first-cavity $Q_1$ of only $7 \times 10^3$ and a second-cavity $Q_2$ of $5 \times 10^5$, representing a two-orders-of-magnitude reduction in required $Q$-factor for fixed indistinguishability compared to single-cavity CQED. In regimes targeted for high $\eta$, the system still demonstrates a $17\%$ improvement in the $\eta I$ product over single-cavity designs.

Figure 3: Numerical and analytical comparison of $I$ and $\eta$ versus $\kappa_2$ in the regime optimized for indistinguishability; non-trivial agreement is shown except in limits where cavity-cavity coherence is non-negligible.

By tuning $\kappa_2$ and $g_2$, the device transitions from acting as a “photon filter” with maximal indistinguishability to a “photon router” with maximum collection efficiency, always outperforming analogous single-cavity designs at equivalent total photonic quality factors.

Figure 4: Regime with maximal $\eta I$ product; cascaded-cavity architecture outperforms the best single-cavity system throughout the parameter sweep of $\kappa_2$.

Robustness to Spectral Diffusion

The influence of spectral diffusion on emission statistics is analyzed by statistical averaging over Gaussian detuning distributions. Both $I$ and $\eta$ are found to be notably insensitive to moderate $\Delta\delta$ as long as $\Delta\delta \ll \gamma^*$, a regime naturally realized at room temperature for solid-state color centers.

Figure 5: $I$ and $\eta$ versus $\Delta\delta$ for the two main regimes, demonstrating stability of system performance despite inhomogeneous broadening.

This robustness arises as pure dephasing acts as a resource, enforcing population transfer via the cavity funnel and suppressing spectral wandering effects, a result not paralleled by single-cavity or bare-emitter scenarios.

Comparison to Other Multi-Mode and Hybrid CQED Architectures

The paper distinguishes the cascaded system from photonic molecule and hybrid-cavity approaches. In the present protocol, weak $C_1$-$C_2$ coupling maintains spectrally isolated cavity modes, and photon emission only passes through $C_1$ to $C_2$ without forming delocalized supermodes. The resulting emission statistics and tunability offer significant practical benefits for scalable on-chip quantum photonic devices.

Implications and Future Directions

The cascaded-cavity architecture removes the major technological barrier—the ultrahigh $Q$-factor requirement—for room-temperature indistinguishable single-photon emission from solid-state centers. The framework generalizes to other dissipative quantum emitters and may be implemented with existing photonic crystal and nanofabrication techniques. Extension to low-temperature operation or integration with deterministic photon sources and photonic quantum gates is direct.

Potential future developments include:

• Monolithic integration of cascaded-CQED with heralded photon sources for fault-tolerant quantum communication.
• Dynamical control of cavity parameters for real-time adjusting of emission statistics.
• Extension to multi-cavity and waveguide-coupled superstructures for multiplexed quantum networks.
• Application of similar funneling models for microwave or mid-infrared quantum photonics.

Conclusion

This work establishes a comprehensive theoretical and numerical foundation for high-indistinguishability, high-efficiency single-photon generation using cascaded cavity QED systems with dissipative solid-state emitters. By leveraging enhanced emitter-cavity coupling and funneling through an auxiliary cavity, the system achieves strong performance improvements—particularly a dramatic reduction in $Q$-factor requirements and robust suppression of spectral diffusion effects. The proposed architecture constitutes a scalable, fabrication-compatible platform for room-temperature quantum light sources and provides valuable insight into dissipative quantum optics in nanostructures (1809.01645).