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arXiv · 2511.01985

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

Soumya S. Kumar·Javier del Pino·Letizia Catalini·Alexander Eichler·Oded Zilberberg
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Abstract

The response of nonlinear resonators to multifrequency driving reveals rich dynamics beyond conventional single-tone theory. We study a Duffing resonator under bichromatic excitation and identify a competition between the two drives, governed by their detuning and relative amplitudes. In the slow-beating regime, where the tones are closely spaced, the secondary drive acts as a modulation that induces dynamical phase transitions between coexisting stationary states. We introduce the cycle-averaged amplitude as an order parameter and map the resulting phase diagram as a function of the drive detuning and amplitude ratio, capturing the pronounced asymmetry observed for blue versus red detuning in experiment. We devise a model to link the onset of these transitions to the resonance properties around the nonlinear stationary mode of the system. Our results provide a framework for controlling driven nonlinear systems, enabling state manipulation, and sensing in nanomechanical, optical, and superconducting circuit platforms.

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Soumya S. Kumar, Javier del Pino, Letizia Catalini, Alexander Eichler, Oded Zilberberg. 2025-11-03. Dynamical Phase Transitions Across Slow and Fast Regimes in a Two-Tone Driven Duffing Resonator. https://arxiv.org/abs/2511.01985

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