Spin-phonon entanglement in SiC optomechanical quantum oscillators

Scaling up quantum systems, especially solid-state spins, presents a significant challenge in the field of quantum information science. While spin-based quantum processors and networks show promise for remote entanglement and long-coherence quantum memory, the development of scalable schemes for large-scale spin entanglement remains elusive. In this study, we propose a hybrid spin-phonon architecture based on spin-embedded optomechanical crystal (OMC) cavities. This architecture combines integrated photonic and phononic accesses, allowing for the simultaneous entanglement of multiple spins. Remarkably, we proposed the hybrid spin-optomechanical system in a Raman-facilitated scheme which offers a coupling of spins to the vibration mode of simulated Silicon Carbide OMC cavities approaching MHz, enabling a fast and efficient spin-phonon entanglement with fidelity of 98%. By incorporating the Stimulated Raman Adiabatic Passage (STIRAP) protocol into the coupled tripod-phonon system, a two-qubit Controlled-Z gate with 97% fidelity is implemented by engineering the non-vanishing geometry phase in a strongly coupled spin-phonon state basis, which is optically dark and robust against the dominated loss from the spin excited-state decoherence, spectral diffusion and the additional two- level system decoherence of phononic cavity. Our work establishes a crucial platform for exploring the spin entanglement with potential scalability in addition to the optical link, which opens the path to investigate cavity quantum-acousto dynamics in the hybrid solid-state system.