Diamond Lamb wave spin-mechanical resonators with optically coherent nitrogen vacancy centers.

We report the design and fabrication of diamond Lamb wave spin-mechanical resonators embedded in a two-dimensional (2D) phononic crystal square lattice. The rectangular resonator features gigahertz in-plane compression modes protected by the phononic bandgap of the square lattice. A membrane-in-bulk approach is developed for the fabrication of the suspended 2D structure. This approach overcomes the limitations of fabrication approaches, which are either incompatible with the necessary high-temperature thermal annealing or unsuitable for 2D structures with the required feature size. Graded soft oxygen etching, with the etching rate decreased gradually to below 1 nm/min, is used to remove defective surface layers damaged by reactive ion etching. Combining the graded etching with other established surface treatment techniques reduces the optical linewidth of nitrogen vacancy centers in resonators with a thickness below 1 μm to as narrow as 330 MHz. [ABSTRACT FROM AUTHOR]