Parametric symmetry breaking in a nonlinear resonator

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.

5 pages, 4 figures

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• Distinctive class of dissipation-induced phase transitions and their universal characteristics
• Observation of first- and second-order dissipative phase transitions in a two-photon driven Kerr resonator
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• Dissipative phase transitions in $n$-photon driven quantum nonlinear resonators
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• Generation and propagation of topological solitons in a chain of coupled parametric-micromechanical-resonator arrays
• Spontaneous parametric down-conversion induced by optomechanical gradient forces in nanophotonic waveguides
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• Three Strongly Coupled Kerr Parametric Oscillators Forming a Boltzmann Machine
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• Quantum Dynamical Signatures of Topological Flow Transitions in Limit Cycle Phases
• The effects of nonlinear damping on degenerate parametric amplification
• Families of Skyrmions in Two-Dimensional Spin-1/2 Systems
• Controlled bit-flip of period-doubling and discrete time crystalline states in open systems