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 that feature mechanical compression modes with ultralow damping rates and host spin qubits with excellent optical and spin properties. The degree of localization in the mechanical Wannier-Stark ladder, which is determined by the ratio of coupling rate to frequency spacing between adjacent resonators, sets the effective range of phonon-mediated coupling between spin qubits. Three nearest-neighbor coupling schemes with distinct geometric configurations and a large range of coupling rates have been developed and analyzed. Additional analysis on the effects of disorder indicates that the proposed Wannier-Stark ladder can be robust against realistic experimental imperfections. The development of 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 a solid-state system.