Strong Coupling between a Superconducting Circuit, Phonon, and Electron Spin via a Piezomechanical Nanocavity*

A central goal in quantum information science is to exchange quantum information between different physical modalities, a process known as quantum transduction. This goal is urgently pursued in the context of microwave-to-optical transduction, which has applications in quantum networking. Recent work has considered highly efficient acoustic coupling via a phononic bus from microwave superconducting circuits (SCs) to a diamond color center, which is a near-unity spin-photon interface. However, transduction via traveling acoustic waves requires engineering a complex single mode-to-multimode-to-single mode interaction. Here, we theoretically show that it is possible to achieve strong coupling of a single acoustic mode of a Lamb wave-like resonator to both a SC mode and a single diamond electron spin. Based on this ability, we introduce a superconductor-phonon-spin transducer (SPST) that simultaneously achieves > 10 MHz coupling rates to both modes, allowing it to act as a mediary in deterministic microwave-to-spin transduction. Finally, we discuss the applications of an SPST in high-density, optically addressable quantum memory registers and superconducting-spin interconnects to a quantum network.