Parametric symmetry breaking in a nonlinear resonator

TL;DR

This paper explores the complex behavior of a nonlinear resonator with parametric symmetry breaking, revealing a novel double hysteresis phenomenon and providing a theoretical model that explains these dynamics, with implications for sensing and computing.

Contribution

It introduces the first experimental observation of double hysteresis in a nonlinear resonator and develops a theoretical model explaining the symmetry-breaking mechanism involved.

Findings

Observation of double hysteresis in amplitude and phase responses.

Excellent agreement between experimental results and the theoretical model.

Insights into symmetry breaking of parametric phase states.

Abstract

Much of the physical world around us can be described in terms of harmonic oscillators in thermodynamic equilibrium. At the same time, the far from equilibrium behavior of oscillators is important in many aspects of modern physics. Here, we investigate a resonating system subject to a fundamental interplay between intrinsic nonlinearities and a combination of several driving forces. We have constructed a controllable and robust realization of such a system using a macroscopic doubly clamped string. We experimentally observe a hitherto unseen double hysteresis in both the amplitude and the phase of the resonator's response function and present a theoretical model that is in excellent agreement with the experiment. Our work provides a thorough understanding of the double-hysteretic response through a symmetry breaking of parametric phase states that elucidates the selection criteria governing transitions between stable solutions. Our study motivates applications ranging from ultrasensitive force detection to low-energy computing memory units.