Even-order harmonics in the nitrogen vacancy center in diamond from intertwined intraband and interband transitions

Different from odd-order harmonics, even-order harmonics are a result of broken inversion symmetry, where the second harmonic generation has long been used in the study of surface magnetism. Their underlying mechanisms are always intriguing. Here we reveal an unreported mechanism of even harmonics from the diamond with a nitrogen-vacancy (NV) center from the viewpoint of group theory. Two different types of interband transition channels are identified. One is the direct transitions between a valence band and a conduction band, called type-I interband transition. Type II is defined as the indirect interband transitions between two conduction bands or two valence bands. Once type-II transitions are involved only through the inversion symmetry breaking, even-order harmonics occur in the NV center in diamond. The physical origin of this new type of interband transitions is rooted in group theory, where the inversion symmetry forbids type-II transitions between two valence or conduction bands with the same irreducible representation. By contrast, the broken inversion symmetry in the NV center lifts this restriction, giving rise to even-order harmonics. Our study represents a paradigm shift in high harmonic generation.