Indistinguishablity from dephased emitters using combined plasmonic-dielectric cavities

Abstract: The concept of cavity funneling has emerged recently as a promising route towards creating indistinguishable photons from highly dephased emitters. So far, all suggested solutions are solely based on dielectric cavities that require extremely high quality factors that are difficult to reach at visible wavelengths. Here we suggest a hybrid funneling architecture where a dephased emitter is coupled to a plasmonic nanoresonator that is enclosed by an outer dielectric cavity. The estimated lower limit of the outer cavity quality factor is found to be $\sim2$ orders of magnitude lower compared to a cascaded cavity system. Furthermore, the surrounding topology of our approach allows for a partial direct coupling between the emitter and the outer cavity which in turn can increase the overall system extraction efficiency $\left(β\right)$ by a factor of 12, boosting the probability of photon collection.

• The paper develops a hybrid plasmonic-dielectric cavity architecture that lowers Q-factor requirements by over 40-fold while achieving >90% photon indistinguishability.
• It employs a nested system combining a plasmonic bowtie resonator with a Fabry–Perot cavity to enhance effective decay rates and photon extraction efficiency.
• The design, validated through numerical and FDTD simulations, offers a scalable route for robust single-photon sources in quantum photonic networks.

Combined Plasmonic-Dielectric Cavities for Indistinguishable Photon Generation from Highly Dephased Emitters

Motivation and Background

Photon indistinguishability is central to optical quantum information applications, including photonic quantum computing, quantum simulation, and QKD. In solid-state emitters, high pure dephasing rates at room temperature substantially broaden the emission linewidth, undermining photon-based quantum information protocols. Conventional cavity funneling schemes, which mitigate dephasing by coupling the emitter to high-$Q$ dielectric cavities, face prohibitive requirements; typical room-temperature implementations necessitate $Q$ factors in excess of $10^7$, well beyond fabrication feasibility for visible wavelengths. Even cascaded dielectric cavities only reduce this requirement to $Q \sim 10^5$ [PhysRevLett.122.183602], still unattainable for most practical platforms.

This work develops a hybrid cavity architecture comprising a plasmonic nanoresonator (e.g., a bowtie antenna) nested within a Fabry-Perot (F-P) dielectric cavity. The concept leverages the large decay rate and small mode volume intrinsic to plasmonic structures to form a composite "effective emitter" with drastically increased total decay rate, thereby relaxing the outer cavity's $Q$ requirement by orders of magnitude.

Figure 1: Schematic of the hybrid system, showing a single quantum emitter within a bowtie plasmonic structure encased by an outer dielectric Fabry-Perot cavity.

Theoretical Framework

The system consists of an emitter (decay rate $\Gamma_1$), plasmonic nanoresonator (decay rate $\kappa_1$, coupling rate $g_1$), and outer dielectric cavity (decay rate $\kappa_2$, coupling rate $g_2$ to the plasmonic device). The geometry permits a direct emitter-to-cavity coupling channel ($Q$0), bypassing the plasmonic nanoresonator and significantly enhancing photon extraction efficiency ($Q$1).

The indistinguishability parameter $Q$2 is quantified in the single-mode regime via the two-time correlator:

$Q$3

where $Q$4 represents the bosonic operator for the outer cavity.

Photon extraction efficiency is defined as:

$Q$5

The funneling ratio $Q$6, central to evaluating performance against linear filtering, is:

$Q$7

Numerical Results and Performance Analysis

Numerical solutions of the master and Dyson equations, under highly dissipative conditions ($Q$8, $Q$9, $10^7$0), demonstrate the hybrid system's superiority. High indistinguishability ($10^7$1) is attainable for outer dielectric cavities with $10^7$2 values as high as $10^7$3. Specifically, for $10^7$4 and $10^7$5, $10^7$6 and $10^7$7, yielding a funneling ratio $10^7$8—a $10^7$9-fold improvement in photon collection over simple filtering.

Figure 2: Photon indistinguishability $Q \sim 10^5$0 and funneling ratio $Q \sim 10^5$1 as functions of outer cavity decay rate $Q \sim 10^5$2 and coupling rate $Q \sim 10^5$3, highlighting high $Q \sim 10^5$4 and broad favorable regions.

For an emitter at $Q \sim 10^5$5 with $Q \sim 10^5$6, $Q \sim 10^5$7 is achieved with an outer cavity having $Q \sim 10^5$8; for $Q \sim 10^5$9, $Q$0 drops to $Q$1. These $Q$2 values are within reach of current experimental platforms, a stark contrast to prior approaches.

Effective Emitter Model and Analytical Insights

The plasmonic nanoresonator with high $Q$3 and $Q$4 forms an effective emitter with enhanced decay rate, $Q$5, coupled to the outer cavity with effective decay rate $Q$6 and photon exchange rate $Q$7. The ratio $Q$8 is central; for $Q$9, $\Gamma_1$0 is achieved with $\Gamma_1$1 as large as $\Gamma_1$2, validating high $\Gamma_1$3.

Figure 3: Evolution of effective system parameter ratios and comparison of analytical and numerical $\Gamma_1$4 estimations, showing strong agreement and regime boundaries.

Direct Emitter-Cavity Coupling and Extraction Efficiency Enhancement

The nested architecture enables a direct photon exchange channel ($\Gamma_1$5), not present in cascaded cavities. Increasing $\Gamma_1$6 yields significant gains in $\Gamma_1$7 with marginal degradation in $\Gamma_1$8. At $\Gamma_1$9, $\kappa_1$0 increases 25-fold ($\kappa_1$1), and at $\kappa_1$2, the gain reaches $\kappa_1$3-fold ($\kappa_1$4), with $\kappa_1$5 remaining above $\kappa_1$6.

Figure 4: Indistinguishability $\kappa_1$7 and funneling ratio $\kappa_1$8 as functions of $\kappa_1$9 and $g_1$0, illustrating efficiency gains from direct coupling.

Extending $g_1$1 to practical values ($g_1$2) enables $g_1$3 and boosts $g_1$4 by a factor of 12 ($g_1$5).

Figure 5: $g_1$6 and $g_1$7 as functions of $g_1$8 and $g_1$9 for fixed $\kappa_2$0, showing broader regions of enhanced extraction and indistinguishability.

Plasmonic Bowtie Resonator Design and Realistic Implementation

Finite-difference time-domain simulations optimize bowtie geometry for hBN emitters at $\kappa_2$1. Aluminum is chosen for compatibility with visible wavelengths.

Figure 6: Optimized bowtie geometry and spatial electric field profile at resonance.

The bowtie mode exhibits a full-width at half maximum of $\kappa_2$2, yielding $\kappa_2$3 for $\kappa_2$4. Purcell factors exceed $\kappa_2$5 for optimal alignment and $\kappa_2$6 for a $\kappa_2$7 offset. *Figure 7: Bowtie spectral profile and Purcell factor dependence on emitter alignment. *

Numerical estimates with moderate $\kappa_2$8 and $\kappa_2$9 values confirm robustness: high $g_2$0 and $g_2$1 are sustained over wide $g_2$2 and $g_2$3 ranges.

Figure 8: Photon indistinguishability and funneling ratio contours for conservative bowtie parameters.

Practical and Theoretical Implications

This hybrid plasmonic-dielectric cavity scheme radically reduces the quality factor required for indistinguishable photon generation from highly dephased emitters, bringing the regime within existing experimental capabilities. Compared to cascaded or single dielectric cavities, $g_2$4 requirements are lowered by two to three orders of magnitude. The nested geometry's direct emitter-cavity coupling channel enables an additional pathway for photon extraction, enhancing funneling ratio and efficiency beyond what is achievable with linear filtering or traditional funnelling configurations.

The relaxation of mode volume dependence not only tolerates larger outer cavities but opens the possibility for higher-order modes and increased device lengths, further facilitating practical photonic device integration. The theoretical framework, including the effective emitter model, provides a robust tool for analyzing complex hybrid photonic architectures.

Conclusion

The composite plasmonic-dielectric cavity architecture establishes a highly practical method for generating indistinguishable photons from solid-state emitters with substantial dephasing, without the need for prohibitively high-$g_2$5 cavities. High indistinguishability ($g_2$6) and extraction efficiency are achievable under conditions that are compatible with modern fabrication methods. The framework's flexibility, enabling efficient photon funneling via both indirect (plasmonic) and direct emitter-cavity pathways, paves the way for scalable, robust single-photon sources appropriate for quantum photonic networks, simulation, and secure communication. Theoretical results presented here highlight the potential for further advancements in photonic device engineering, including integration of hybrid nanostructures and complex cavity field topologies (2604.19666).