Dynamical Phase Transitions Across Slow and Fast Regimes in a Two-Tone Driven Duffing Resonator

Nonlinear driven-dissipative systems are foundational in optomechanics, photonic physics, and circuit QED. While single-tone driving is well-understood, multifrequency driving is ubiquitous and essential for Floquet engineering in ultra-cold atoms, precision sensing in nanomechanics, and qubit control. However, the complex dynamics arising from incommensurate drives are not captured by traditional approaches. In this talk, we present our study of a canonical Duffing resonator under bichromatic excitation and show even a weak secondary drive induces dynamical phase transitions between the system's coexisting stationary states. We present a phase diagram that maps the dynamic regimes, capturing the asymmetry observed for blue vs red detuning in the experiment. Our central result is a model that links the onset of these transitions to the resonance properties of the nonlinear stationary mode of the system. Our results provide a framework for controlling driven nonlinear systems and enabling state manipulation in driven optomechanical, photonic, and circuit QED systems.