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

TL;DR

This paper investigates how a nonlinear Duffing resonator responds to two-tone driving, revealing dynamical phase transitions influenced by drive detuning and amplitude, with implications for controlling nonlinear systems in various technological platforms.

Contribution

It introduces a phase diagram based on cycle-averaged amplitude to characterize dynamical phase transitions in bichromatically driven Duffing resonators, linking them to resonance properties.

Findings

Dynamical phase transitions occur between coexisting stationary states.

Asymmetry in phase diagram depends on blue versus red detuning.

Model links transition onset to nonlinear stationary mode resonance.

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.