Broadband Spatio-Spectral Mode Conversion via Four-Wave Mixing

TL;DR

This work tackles the challenge of interfacing visible color centers with quantum networks by proposing a scalable, broadband free-space spatio-spectral conversion via four-wave mixing in a diamond ring resonator. The approach co-designs a phase-matched FFWM process with a diamond-on-insulator platform to create modular unit cells that bridge the visible and infrared, achieving a predicted idler-bandwidth of about $165\,\mathrm{nm}$ and end-to-end efficiency analysis that accounts for emitter coupling and cavity losses. Key results include a non-Hermitian Hamiltonian framework for idler efficiency, a quantified spatial-overlap efficiency of $\eta_{spatial}\approx0.21$, and an interplay between pump power, quality factors, and the $r_{ZPL}$ radiative factor that caps efficiency at realistic values (e.g., $\eta_{idler}\approx0.85$ with certain parameters). The proposed co-design, fabrication-ready pathway, and end-to-end efficiency analysis offer a pathway toward scalable spin-photon interfaces and compact, integrated building blocks for telecom-band quantum networks, with suggested directions for experimental validation and extension to other material platforms.

Abstract

We introduce a framework for scalable and broadband free-space phase-matched four-wave mixing in ring resonators. This method for four-wave mixing reduces the complexity of coupling an emitter to a quantum network by combining the spatial and spectral interfaces between them into one nonlinear optical process. The device is compliant with current heterogeneous integration capabilities and has a bandwidth of 165 nm for efficient spatio-spectral conversion. We outline a fabrication-ready diamond-on-insulator pathway towards modular unit cells that natively bridge visible color centers to the infrared spectrum for scalable quantum networks. We also present and analyze an end-to-end framework for considering single-photon coupling efficiency from a color center to a quantum network. This framework represents a step forwards in analyzing and reducing system-scale losses in a spin-photon interface.

Figures (8)

• Figure 1: (a) Light couples into a diamond resonator from a silicon nitride bus waveguide. The bus sits next to the ring, with a back reflector embedded in the oxide. The signal emits into the ring from a color center embedded in the diamond. Light converts to the infrared using the $\chi^3$ nonlinearity in diamond, and emits into free space for collection into an objective lens that connects to an optical fiber. This forms a unit cell for many copies of the same device that can be addressed by an objective lens. (b) The energy conservation condition for QFC in Bragg scattering mode. (c) The phase matching condition in the plane of the cavity. (d) The phase matching condition in the free space direction, out of the plane of the cavity.
• Figure 2: (a) The effective refractive index for discretized mode numbers of the ring resonator from mode solver data, plotted for multiple ring widths. (b) Output wavelengths that satisfy the in-plane phase matching condition in Equation \ref{['pm_cond']}. (c) Polarization in the $\hat{r}$ direction obtained from FDTD simulation. (d) The phase of the output polarization in the $\hat{r}$ direction, confirming that the FPM condition $m_{idl}=0$ is fulfilled.
• Figure 3: The ring emits the idler into the far-field through FFWM. We calculate the transverse idler electric field profile after the objective using the Debye-Wolf integral at $z_p^-$, just before the S-waveplate. The idler field after S-waveplate transformation at $z_p^+$ can be collected with efficiency $\eta_{spatial}$ into the fiber lens. See Sec. \ref{['sm:Spatial']} for detailed field profile simulations.
• Figure 4: (a) $\eta_{idler}$ and $\beta$ factor plotted as a function of pump budget and $\overline{Q_{cav}}$ for $r_{ZPL}=0.48$. (b) The maximum $\eta_{idler}$ possible at saturation and corresponding $\beta$ factor, plotted for multiple values of $r_{ZPL}$, with a maximum pump budget of 10 kW. Note that $\eta_{idler}$ must be lower than the $\beta$ factor, demonstrating the need for high quality factor devices.
• Figure 5: A potential fabrication scheme, displayed as a positive mask in diamond.