  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.
