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Hybrid quantum systems, which combine quantum-mechanical systems withmacroscopic mechanical oscillators, have attracted increasing interest as theyare well suited as high-performance sensors or transducers in quantumcomputers. A promising candidate is based on diamond cantilevers, whose motionis coupled to embedded Nitrogen-Vacancy (NV) centers through crystaldeformation. Even though this type of coupling has been investigatedintensively in the past, several inconsistencies exist in available literature,and no complete and consistent theoretical description has been given thus far.To clarify and resolve these issues, we here develop a complete and consistentformalism to describe the coupling between the NV spin degree of freedom andcrystal deformation in terms of stress, defined in the crystal coordinatesystem XYZ, and strain, defined in the four individual NV reference frames. Wefind that the stress-based approach is straightforward, yields compactexpressions for stress-induced level shifts and therefore constitutes thepreferred approach to be used in future advances in the field. In contrast, thestrain-based formalism is much more complicated and requires extra care whentransforming into the employed NV reference frames. Furthermore, we illustratehow the developed formalism can be employed to extract values for thespin-stress and spin-strain coupling constants from data published by Teissieret al..

Spin-stress and spin-strain coupling in diamond-based hybrid spin oscillator systems