We report a study of the magnetic field dependence of the photo-luminescence of NV$^-$ centers (negatively charged nitrogen-vacancy centers) in diamond single crystals. In such a magnetic field dependence characteristic lines are observed, which are coming from Level Anti-Crossings (LACs) in the coupled electron-nuclear spin system. For enhancing the sensitivity, we used lock-in detection to measure the photo-luminescence intensity and observed a remarkably strong dependence of the LAC-derived lines on the modulation frequency. Upon decreasing of the modulation frequency from 12 kHz to 17 Hz the amplitude of the lines increases by approximately two orders of magnitude. To take a quantitative account for such effects, we developed a theoretical model, which describes the spin dynamics in the coupled electron-nuclear spin system under the action of an oscillating external magnetic field. Good agreement between experiments and theory allows us to conclude that the observed effects are originating from coherent spin polarization exchange in the NV$^-$ center. Our results are of great practical importance allowing one to optimize the experimental conditions for probing LAC-derived lines in diamond defect centers.
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