Nonlinear dynamics of weakly dissipative optomechanical systems

• Published in: New journal of physics Vol. 22; no. 1; pp. 13049 - 13064
• Main Authors: Roque, Thales Figueiredo, Marquardt, Florian, Yevtushenko, Oleg M
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.01.2020
• Subjects: attractors; Bifurcations; chaos; Chaos theory; Dynamical systems; Hybrid systems; Initial conditions; Nonlinear dynamics; optomechanical systems; Physics; Quantum theory; Sidebands; Toruses
• DOI: 10.1088/1367-2630/ab6522
• ISSN: 1367-2630

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.