Nonlinear dynamics of weakly dissipative optomechanical systems

Abstract

Optomechanical systems attract a lot of attention because they provide a novel platform for quantum measurements, transduction, hybrid systems, and fundamental studies of quantum physics. Their classical nonlinear dynamics is surprisingly rich and so far remains underexplored. Works devoted to this subject have typically focussed on dissipation constants which are substantially larger than those encountered in current experiments, such that the nonlinear dynamics of weakly dissipative optomechanical systems is almost uncharted waters. In this work, we fill this gap and investigate the regular and chaotic dynamics in this important regime. To analyze the dynamical attractors, we have extended the "Generalized Alignment Index" method to dissipative systems. We show that, even when chaotic motion is absent, the dynamics in the weakly dissipative regime is extremely sensitive to initial conditions. We argue that reducing dissipation allows chaotic dynamics to appear at a substantially smaller driving strength and enables various routes to chaos. We identify three generic features in weakly dissipative classical optomechanical nonlinear dynamics: the Neimark-Sacker bifurcation between limit cycles and limit tori (leading to a comb of sidebands in the spectrum), the quasiperiodic route to chaos, and the existence of transient chaos.

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Cited by in corpus (15)

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• Optomechanical parametric oscillation of a quantum light-fluid lattice
• Quantum entanglement assisted via Duffing nonlinearity
• Instabilities near ultrastrong coupling in microwave optomechanical cavity
• Dissipative phase transitions in optomechanical systems
• Parametric control of self-sustained and self-modulated optomechanical oscillations
• Observation of Nonlinear Dynamics in an Optical Levitation System
• Hybrid coupling optomechanically assisted nonreciprocal photon blockade
• The Josephson junction as a quantum engine
• Chaos in Optomechanical Systems coupled to a Non-Markovian environment
• Highly correlated optomechanical oscillations manifested by an anomalous stabilization
• Quantum signatures of bistability and limit cycle in Kerr-modified cavity magnomechanics
• Dynamics of Onsager vortex clustering in decaying turbulent polariton quantum fluids
• Route to hyperchaos in quadratic optomechanics
• Mechanically Modulated Sideband and Squeezing Effects of Membrane Resonators