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

TL;DR

This paper develops a comprehensive theoretical framework for understanding how stress and strain in diamond affect the spin states of embedded NV centers, resolving inconsistencies in previous literature and aiding future quantum sensor development.

Contribution

It introduces a complete formalism for spin-stress and spin-strain coupling in diamond NV centers, clarifying previous ambiguities and providing a practical stress-based approach for future research.

Findings

Stress-based formalism is straightforward and yields compact expressions.

Strain-based formalism is complex and requires careful frame transformations.

The formalism enables extraction of coupling constants from experimental data.

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 the stress-based approach is straightforward, yields compact expressions for stress-induced level shifts and therefore constitutes the preferred approach to be used in future advances in the field. In contrast, the strain-based formalism is much more complicated and requires extra care when transforming into the employed NV reference frames. 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..