Complete theory of decoherence and relaxation of qutrit spin-1 centers with C_3v symmetry.

Decoherence and relaxation of solid-state defect qutrits near a crystal surface, where they are commonly used as quantum sensors, originate from charge and magnetic field noise. A complete theory requires a formalism for dephasing and relaxation that includes all field-dependent Hamiltonian terms allowed by the defect’s point-group symmetry. This formalism, presented here for the C_3v symmetry of a NV-center in a diamond, relies on a Lindblad dynamical equation and clarifies the relative contributions of charge and spin noise to the different relaxation and decoherence times [1]. For instance, we show that the relaxation between the spin-defect states | ±1〉and | 0〉, usually attributed to magnetic noise, also has a significant contribution from the charge noise via the commonly ignored dipole term d'E_± [2,3]. Further, we also comment on the implication of ignoring the presence of this dipole term in terms of ODMR spectra and dephasing processes [1].

[1] DR Candido and ME Flatté et al, PRB 110, 024419 (2024).

[2] P Udvarhelyi, et al PRB 98, 075201 (2018).

[3] HY Chen, et al PRA 13, 054068 (2020).