Non-Abelian geometrical control of a qubit in an NV center in diamond

Abstract

We propose an approach for an optical qubit rotation in the negatively charged nitrogen vacancy (NV) center in diamond. The qubit is encoded in the ground degenerate states at a relatively low-temperature limit. The basic idea of the rotation procedure is the non-Abelian geometric phase in an adiabatic passage, which is produced by the non-adiabatic transition between the two degenerate dark states. The feasibility is based on the success of modeling the NV center as an excited-doublet four-level atom. By applying two pump and two Stokes laser pulses, we found that the behavior of the adiabatic passage depends crucially on the applied intensity of each applied laser field and the detunings between the laser frequencies and their corresponding atomic transition. Particularly, a non-adiabatic transition appears when the applied pump and Stokes laser pulses are off resonance with their corresponding atomic transition.