The dynamics of a hybrid system based on the NV center in spin bath

Hybrid system based on nuclear spins coupled to defect electron spin in solid has been proposed as an appealing strategy to manipulate qubits for quantum information processing. While universal quantum control and the time optimal control have been arrived, the influence of environment on the system has been ignored. We studied the dynamics of the hybrid system under the surrounding environment using the quantum master equation approach. The quantum master equation and the mean-value equations of the dynamical variables have been derived. Here we focus on a special platform based on the Nitrogen-Vacancy center electronic spin in diamond and nearby carbon-13 nuclear spins.