Abstract
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 Schr\"odinger 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.
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