Nonlinearity-induced symmetry breaking in a system of two parametrically driven Kerr-Duffing oscillators

TL;DR

This paper investigates how nonlinearity can induce symmetry breaking in a coupled system of Kerr-Duffing oscillators under parametric drive, revealing transitions from symmetric to asymmetric states through analytical analysis.

Contribution

It introduces a detailed analysis of symmetry breaking in coupled Kerr-Duffing oscillators under parametric drive, highlighting the role of nonlinearity and detuning in state transitions.

Findings

Symmetry breaking occurs even with identical parametric drives.

Transitions from symmetric to asymmetric solutions are driven by detuning.

The analysis uses the rotating wave approximation to identify steady states.

Abstract

We study the classical dynamics of a system comprising a pair of Kerr-Duffing nonlinear oscillators, which are coupled through a nonlinear interaction and subjected to a parametric drive. Using the rotating wave approximation (RWA), we analyze the steady-state solutions for the amplitudes of the two oscillators. For the case of almost identical oscillators, we investigate separately the cases in which only one oscillator is parametrically driven and in which both oscillators are simultaneously driven. In the latter regime, we demonstrate that even when the parametric drives acting on the two oscillators are identical, the system can transition from a stable Nesymmetric solution to a broken-symmetry solution as the detuning is varied.