Quantum dynamics and quantum state transfer between separated nitrogen-vacancy centers embedded in photonic crystal cavities

We investigate dynamics of a laser-driven and dissipative system consisting of two nitrogen-vacancy (N-V) centers embedded in two spatially separated single-mode nanocavities in a planar photonic crystal (PC). Spontaneous emission from the excited states of the N-V centers can be effectively suppressed by virtue of the Raman transition in the dispersive regime. The system displays a series of damped oscillations under various experimental situations, where we solve the time-dependent Schrödinger equation analytically for arbitrary values of the hopping and PC-N-V coupling strengths. In particular, our results indicate that some special values should be taken for the hopping strength if we hope to have high-fidelity quantum state transfer between the two distant N-V centers. We have also analyzed the relevant entanglement dynamics in the presence of decoherence. The experimental feasibility and challenge are justified using currently available technology.