Dynamics of dissipative cavity solitons in a lattice trap

Dichromatic coherent pumping of optical microresonators possessing broadband Kerr nonlinearity reveals a rich variety of nonlinear and critical phenomena, including time-translation symmetry breaking, multistability, and chaos. This pumping scheme has garnered significant interest owing to its practical applications arising from optical-to-microwave frequency stability transfer and frequency-division phase noise reduction. In this work, we develop a generalized analytical model to elucidate the dynamics of dissipative Kerr cavity solitons as particles in dual-frequency pumped Kerr-nonlinear cavities. The model offers quantitative and intuitive insights into the behavior of the system both within and beyond the locking range wherein solitons synchronize to the two driving lasers. It also predicts new phenomena and expounds hitherto unexplained experimental observations covering bistability, hysteresis, and Arnold tongues. The unified framework simultaneously delineates the parameter space for the existence of dissipative discrete time crystals recently reported in dually pumped solitons. Bridging a fundamental study with practical applications, this work offers valuable understanding of two-point injection-locked microcombs for realizing chip-scale optical clocks and superior microwave photonic oscillators.