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

Abstract

Hybrid quantum systems, which combine quantum-mechanical systems with macroscopic mechanical oscillators, have attracted increasing interest as they are well suited as high-performance sensors or transducers in quantum computers. A promising candidate is based on diamond cantilevers, whose motion is coupled to embedded nitrogen-vacancy (NV) centers through crystal deformation. Even though this type of coupling has been investigated intensively 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 consistent formalism to describe the coupling between the NV spin degree of freedom and crystal deformation in terms of stress, defined in the crystal coordinate system $XYZ$, and strain, defined in the four individual NV reference frames. We find that describing crystal deformation in $XYZ$ significantly simplifies the formalism and therefore constitutes the preferred approach for future advances in the field. Furthermore, we illustrate how the developed formalism can be employed to extract values for the spin-stress and spin-strain coupling constants from data published by Teissier et al. [Phys. Rev. Lett. 113, 020503 (2014)].