Nonlinear phenomena represent one of the central topics in the study of wave-matter interactions and constitute the key blocks for various applications in optical communication, computing, sensing, and imaging. In this work, we show that by employing the interactions between microwave photons and electron spins of nitrogen-vacancy (NV) centers, one can realize a variety of nonlinear effects, ranging from the resonance at the sum or difference frequency of two or more waves to electromagnetically induced transparency from the interference between spin transitions. We further verify the phase coherence through two-photon Rabi-oscillation measurements. The highly sensitive, optically detected NV-center dynamics not only provides a platform for studying magnetically induced nonlinearities but also promises novel functionalities in quantum control and quantum sensing.

15 pages and 10 figures