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Longitudinal spin relaxation model applied to point defect qubit systems

Controllable, partially isolated few level systems in semiconductors have recently gained multidisciplinary attention due to their widespread nanoscale sensing and quantum technology applications. Quantitative simulation of the dynamics and related applications of such systems is a challenging theoretical task that requires faithful description not only the few level systems but also their local environments. Here, we develop a method that can describe relevant relaxation processes induced by a dilute bath of nuclear and electron spins. The method utilizes an extended Lindblad equation in the framework of cluster approximation of a central spin system. We demonstrate that the proposed method can accurately describe T$_1$ time of an exemplary solid-state point defect qubit system, in particular NV center in diamond, at various magnetic fields and strain.