High-efficiency vertical emission spin-photon interface for scalable quantum memories

We present an efficient spin-photon interface for free-space vertical emission coupling. Using a \rev{dipole model}, we show that our design achieves a far-field collection efficiency of 96% at the numerical aperture of 0.7 with a 95% overlap to a Gaussian mode. Our approach is based on a dual perturbation layer design. The first perturbation layer extracts and redirects the resonant mode of a diamond microdisk resonator around the optical axis. The second perturbation layer suppresses side lobes and concentrates most of the light intensity near the center. This dual-layer design enhances control over the farfield pattern and also reduces alignment sensitivity. Additionally, the implemented \rev{dipole model} performs calculations ( 3.2 \times 10^6 ) times faster than full-wave FDTD simulations. These features make the design promising for quantum information applications.

💡 Research Summary

The paper addresses a central challenge in solid‑state quantum networks: efficiently converting spin excitations in color‑center qubits into free‑space photons that can be collected by conventional optics. While nitrogen‑vacancy (NV), silicon‑vacancy (SiV), and tin‑vacancy (SnV) centers in diamond provide long‑lived spin states, their zero‑phonon‑line (ZPL) emission fractions are modest (NV ≈ 3 %, SiV ≈ 70 %, SnV ≈ 80 %). Embedding these emitters in optical cavities can boost the ZPL fraction via the Purcell effect, but high‑Q, low‑mode‑volume cavities typically confine light so strongly that out‑coupling becomes inefficient. Existing out‑couplers (ring resonators, fiber‑based Fabry–Pérot cavities, circular gratings) either sacrifice Q, require precise emitter positioning, or produce far‑field patterns that do not match the Gaussian mode of standard single‑mode fibers.

The authors propose a vertically emitting spin‑photon interface that simultaneously achieves high spectral and spatial efficiencies. The core of the device is a diamond microdisk resonator supporting a whisper‑gallery mode (WGM) that couples to an SnV center. Above the disk, two hexagonal perturbation layers made of silicon nitride (n = 1.8) are deposited, separated by a silicon dioxide spacer (n = 1.4). The first perturbation layer sits in the near‑field region, directly above the disk, and acts as a “near‑field reshaper”: it extracts the WGM energy and redirects it toward the optical axis, creating a radially symmetric field distribution at low numerical aperture (NA). The second layer resides in the intermediate‑field region and functions as a spatial filter or “lens”: it concentrates most of the power near the axis while destructively interfering with side‑lobes at higher NA, thereby sculpting a far‑field pattern that closely resembles a fundamental Gaussian beam.

To design and optimize this structure, the authors extend a previously published quantum dipole model. Each perturbation hole is treated as an electric dipole with moment p = αE, where α encodes the geometry‑dependent polarizability and E is the local field at the hole. The total radiated field is obtained by superposing the contributions from all dipoles, using analytical expressions for the near‑field (kR ≪ 1), intermediate‑field (kR ≈ 1), and far‑field (kR ≫ 1) regimes. By exploiting the hexagonal lattice symmetry, the sum over N = 6ℓ dipoles on a given hexagonal trace is approximated by an integral, dramatically reducing computational cost. The model is calibrated against a single full‑wave finite‑difference time‑domain (FDTD) simulation, after which it can predict collection efficiency and far‑field overlap orders of magnitude faster—specifically, 3.2 × 10⁶ times faster than a conventional FDTD sweep.

Optimization is performed using Bayesian methods over nine geometric parameters: disk radius and thickness, lattice constants of the two perturbation layers (a₁, a₂), hole heights (d₁, d₂), and hole radii (rₕ₁, rₕ₂). The objective function is the product of collection efficiency (η_col) and Gaussian overlap (η_Gauss). The resulting design achieves η_col = 96 % for NA = 0.7 and η_Gauss = 95 %, yielding an overall figure of merit η_tot ≈ 0.91 when combined with the intrinsic SnV ZPL fraction. Importantly, the performance remains robust to misalignments between the disk and the perturbation holes; simulations show that lateral displacements of up to ~30 nm cause less than a 2 % drop in η_col, thanks to the dual‑layer approach that provides additional degrees of freedom for field shaping.

The paper also discusses practical fabrication considerations. Adding perturbation layers above the diamond surface avoids direct etching of the diamond, simplifying processing and improving yield. Silicon nitride and silicon dioxide can be deposited and patterned with standard lithography, and the spacer thickness can be tuned to control the phase relationship between the two layers. The authors note that while the dipole model captures the dominant physics for sub‑wavelength holes, higher‑order multipole contributions become relevant for larger features; incorporating these into future models is identified as a key next step.

In summary, the work delivers a scalable, high‑efficiency spin‑photon interface that combines a high‑Q whisper‑gallery microdisk with a dual‑layer perturbation grating to achieve near‑perfect vertical out‑coupling into a Gaussian mode. The analytical dipole framework enables rapid design iterations, making it attractive for large‑scale quantum network deployment where many identical nodes must be fabricated and aligned with modest tolerances. The approach promises to bridge the gap between high‑purity solid‑state qubits and low‑loss free‑space or fiber‑based photonic channels, a critical requirement for future quantum repeaters, distributed quantum computing, and long‑distance entanglement distribution.