Creation of an entangled state between two NV centers in a single-photon interferometric scheme

We study a method for creating an entangled state between two NV centers in diamond that do not directly interact with each other. The method is based on excitation of centers with a single photon via a half divider with subsequent coherent inversion of the spin of the excited center by a microwave pulse and on the detection of a photon that was emitted by the excited center and that passed through the divider. We consider the general case in which the transition frequencies of the centers are shifted with respect to each other and the control pulses are detuned with respect to these transitions. We find the probability of creating an entangled state and its fidelity in relation to the parameters of the method and transition frequencies of the centers. Optimal values of these parameters are determined.