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Adiabaticity of spin dynamics in diamond nitrogen vacancy centers in time-dependent magnetic fields

We study the spin dynamics of diamond nitrogen vacancy (NV) centers in an oscillating magnetic field along the symmetry axis of the NV in the presence of transverse magnetic fields. It is well-known that the coupling between the otherwise degenerate Zeeman levels $|M_S=\pm1\rangle$ due to strain and electric fields is responsible for a Landau-Zener process near the pseudo-crossing of the adiabatic energy levels when the axial component of the oscillating magnetic field changes sign. We derive an effective two-level Hamiltonian for the NV system that includes coupling between the two levels via virtual transitions into the third far-detuned level $|M_S=0\rangle$ induced by transverse magnetic fields. This coupling adds to the coupling due to strain and electric fields, with a phase that depends on the direction of the transverse field in the plane perpendicular to the NV axis. Hence, the {\em total coupling} of the Zeeman levels can be tuned to control the adiabaticity of spin dynamics by fully or partially compensating the effect of the strain and electric fields, or by enhancing it. Moreover, by varying the strength and direction of the transverse magnetic fields, one can determine the strength and direction of the local strain and electric fields at the position of the NV center, and even the {\em external} stress and electric field. The nuclear spin hyperfine interaction is shown to introduce a nuclear spin dependent offset of the axial magnetic field for which the pseudo-crossing occurs, while the adiabaticity remains unaffected by the nuclear spin. If the NV center is coupled to the environment, modeled by a bath with a Gaussian white noise spectrum, as appropriate for NVs near the diamond surface, then the spin dynamics is accompanied by relaxation of the Zeeman level populations and decoherence with a non-monotonic decrease of the purity of the system.