Abstract
Defect centres in diamond are promising building blocks for quantum networks thanks to a long-lived spin state and bright spin-photon interface. However, their low fraction of emission into a desired optical mode limits the entangling success probability. The key to overcoming this is through Purcell enhancement of the emission. Open Fabry–Perot cavities with an embedded diamond membrane allow for such enhancement while retaining good emitter properties. To guide the focus for design improvements it is essential to understand the influence of different types of losses and geometry choices. In particular, in the design of these cavities a high Purcell factor has to be weighed against cavity stability and efficient outcoupling. To be able to make these trade-offs we develop analytic descriptions of such hybrid diamond-and-air cavities as an extension to previous numeric methods. The insights provided by this analysis yield an effective tool to find the optimal design parameters for a diamond-air cavity.
Highlights
Quantum networks rely on entanglement distributed among distant nodes [1]
We have developed analytical descriptions giving the influence of key parameters on the performance of a Fabry–Perot cavity containing a diamond membrane
We find that the effective losses in the cavity are strongly dependent on the precise diamond thickness
Summary
Quantum networks rely on entanglement distributed among distant nodes [1]. Nitrogen-vacancy (NV) defect centers in diamond can be used as building blocks for such networks, with a coherent spin-photon interface that enables the generation of heralded distant entanglement [2, 3]. Entanglement protocols depend on coherent photons emitted into the zerophonon line (ZPL), which is only around 3% of the total emission [9], and collection efficiencies are finite due to limited outcoupling efficiency out of the high-refractive index diamond These can both be improved by embedding the NV centre in an optical microcavity at cryogenic temperatures, benefiting from Purcell enhancement [10,11,12,13,14,15,16,17]. In the simulations in this manuscript we assume that vibrations lead to passively stabilised cavity length deviations of 0.1 nm RMS [20] While these boundary conditions influence the simulated maximally achievable probability to detect a ZPL photon, the analytic descriptions in this manuscript are not limited to these parameter regimes.
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