Fig. 1: Depiction of spin entanglement via a spin-optomechanical interface.

Each node contains an optical resonator (orange cavity/operator) coupled to a mechanical resonator (blue spring/operator), with an embedded color center (inset/green operator). A pump (red) is used to induce a two-mode squeezing in the opto-mechanical system. The leakage of an optical photon (orange waveguide) and its detection (orange detector) herald the creation of a single mechanical phonon. A beamsplitter (in gray) can be used to “erase” the knowledge of which is the original source of the photon, leading to the heralding of an entangled state\(| 10\left.\right\rangle \pm | 01\left.\right\rangle\) between two neighboring nodes. The phase depends on which of the two detectors clicked⁷⁸. The ground state splittingΔ_gs (black) can be actuated with DC strain to selectively detune ω_σ and g_sm²³ to turn on and off the spin-phonon interaction and swap the entangled phonon to the spin degree of freedom.