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.
Highlights
Cavity optomechanics [1] aims to explore and exploit the interaction between radiation fields and mechanical vibrations, with important applications ranging from sensitive measurements to quantum communication
Besides being significantly faster than commonly used methods based on the calculation of the maximal Lyapunov exponent (LE), the modified generalized alignment index (GALI) method provides an efficient tool to learn the dimensionality of the attractors
To prove that our implementation of the GALI method yields reliable results, we show in figure 5(c) a similar diagram which has been obtained by calculating the maximal Lyapunov exponent (mLE)
Summary
Cavity optomechanics [1] aims to explore and exploit the interaction between radiation fields and mechanical vibrations, with important applications ranging from sensitive measurements to quantum communication. Most state-of-the-art experiments reach the resolved sideband regime and deal with substantially larger mechanical quality factors, ranging from 104 to 109 (see figures 11 and 10 in [1]) These experiments raise a natural question: do such weakly dissipative systems show something qualitatively new in their classical dynamics? Besides being significantly faster than commonly used methods based on the calculation of the maximal Lyapunov exponent (LE), the modified GALI method provides an efficient tool to learn the dimensionality of the attractors This has allowed us to explore the OM attractors in a large range of parameters and to reveal important phenomena which are well-known in nonlinear science but have been overlooked so far in optomechanics.
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