  We report a study of the magnetic field dependence of photoluminescence of
NV$^-$ centers (negatively charged nitrogen-vacancy centers) in diamond single
crystals. In such a magnetic field dependence characteristic sharp features are
observed, which are coming from Level Anti-Crossings (LACs) in a coupled
electron-nuclear spin system. For sensitive detection of such LAC-lines we use
lock-in detection to measure the photoluminescence intensity. This experimental
technique allows us to obtain new LAC lines. Additionally, a remarkably strong
dependence of the LAC-lines on the modulation frequency is found. Specifically,
upon decrease of the modulation frequency from 12 kHz to 17 Hz the amplitude of
the LAC-lines increases by approximately two orders of magnitude. To take a
quantitative account for such effects, we present a theoretical model, which
describes the spin dynamics in a 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 a coupled spin system
comprising the spin-polarized NV$^-$ center. Our results are of great practical
importance allowing one to optimize the experimental conditions for probing
LAC-derived lines in diamond crystals comprising NV$^-$ centers and for
indirect detection and identification of other paramagnetic defect centers.
