Route to hyperchaos in quadratic optomechanics

TL;DR

This paper demonstrates the emergence of hyperchaos in quadratic optomechanical systems, showing that such complex chaotic behavior can be achieved with current experimental setups, and provides detailed analysis of its characteristics.

Contribution

It introduces hyperchaos in cavity optomechanics with quadratic coupling, including Lyapunov exponents and correlation dimension analysis, and suggests experimental feasibility.

Findings

Hyperchaos can arise in quadratic optomechanical systems.

Two positive Lyapunov exponents confirm hyperchaotic behavior.

Full reconstruction of hyperchaotic attractors is possible in these systems.

Abstract

Hyperchaos is a qualitatively stronger form of chaos, in which several degrees of freedom contribute simultaneously to exponential divergence of small changes. A hyperchaotic dynamical system is therefore even more unpredictable than a chaotic one, and has a higher fractal dimension. While hyperchaos has been studied extensively over the last decades, only a few experimental systems are known to exhibit hyperchaotic dynamics. Here we introduce hyperchaos in the context of cavity optomechanics, in which light inside an optical resonator interacts with a suspended oscillating mass. We show that hyperchaos can arise in optomechanical systems with quadratic coupling and is well within reach of current experiments. We compute the two positive Lyapunov exponents, characteristic of hyperchaos, and independently verify the correlation dimension. We also identify a possible mechanism for the emergence of hyperchaos. As systems designed for high-precision measurements, optomechanical systems enable direct measurement of all four dynamical variables and therefore the full reconstruction of the hyperchaotic attractor. Our results may contribute to better understanding of nonlinear systems and the chaos-hyperchaos transition, and allow the study of hyperchaos in the quantum regime.