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

• URL: http://arxiv.org/abs/2511.01985v1
• Date: Mon, 03 Nov 2025 19:00:24 GMT
• Title: Dynamical Phase Transitions Across Slow and Fast Regimes in a Two-Tone Driven Duffing Resonator
• Authors: Soumya S. Kumar, Javier del Pino, Letizia Catalini, Alexander Eichler, Oded Zilberberg,
• Abstract summary: We study a Duffing resonator under bichromatic excitation and identify a competition between the two drives.<n>In the slow-beating regime, where the tones are closely spaced, the secondary drive acts as a modulation that induces dynamical phase transitions.<n>Our results provide a framework for controlling driven nonlinear systems, enabling state manipulation, and sensing in nanomechanical, optical, and superconducting circuit platforms.
• Score: 36.94429692322632
• License: http://creativecommons.org/licenses/by/4.0/
• 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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