Mechanical Wannier-Stark Ladder of Diamond Spin-Mechanical Lamb Wave Resonators

We report the design and theoretical analysis of Wannier-Stark ladders of diamond Lamb wave resonators (LWRs) that can feature compression modes with ultralow damping rates and host spin qubits with excellent optical and spin properties. Three nearest-neighbor coupling schemes with distinct geometric configurations and a large range of coupling rates have been explored for the realization of Wannier-Stark ladders of LWRs, potentially enabling long-range connectivity between spin qubits through their interactions with mechanical vibrations. Additional analysis on the effects of disorder indicates that the proposed Wannier-Stark ladder can be robust against realistic experimental imperfections. The development of mechanical quantum networks of spin qubits with long-range connectivity can open the door to the implementation of newly developed quantum low-density parity-check codes in solid-state systems.