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.

Parametric control of self-sustained and self-modulated optomechanical oscillations

“…1 suggests that dissipation values such as κ = 0.1 and γ = 0.01 enable the existence of a rich set of dynamical features for relatively low values of the injected power P , which is highly desirable for practical applications. Such intermediate values of γ are 2 orders of magnitude higher than previously considered for the existence of complex dynamics [30],…”

“…Multistability may occur under the coexistence of more than one stable attractors of the same or different type. For high power values the coexistence of multiple stable attractors along with the complexity of their basins of attraction, sometimes having a fractal-like topology, results in an exotic dynamical behavior [30], characterized by such a sensitivity with respect to initial conditions that essentially makes the system's response unpredictable.…”

“…The latter consists of a fully nonlinear system of coupled equations, supporting a rich set of complex nonlinear dynamical features, which are of crucial importance to the various applications. This set includes the bistability of steady states [14,15], the existence of self-induced oscillations corresponding to stable limit cycles [16][17][18][19][20][21][22] and related multistability effects [23,24] as well as the existence of self-modulated oscillations corresponding either to stable limit tori or chaotic attractors [25][26][27][28][29][30]. Characteristic features of classical chaos such as period-doubling [31][32][33] and quasiperiodic [30] route to chaos, transient and intermittent chaos [34], and antimonotonicity [35],…”

Observation of nonlinear dynamics in an optical levitation system

“…Similarly to the radiation-pressure induced optical spring effect, the positive photothermal stiffness experienced during self-locking by the system is paralleled by a negative damping coefficient [34,35]. The amount by which the natural damping of the acoustic mode is modified by the photothermal interaction can be estimated by the eigenvalues of the Jacobian matrix [30,[55][56][57][58].…”

HarmonicBalance.jl: A Julia suite for nonlinear dynamics using harmonic balance

“…The package finds all dynamical steady states, identifies the most likely response given a parametric sweep, and supports numerical time-evolution within the harmonic ansatz (introduced in 2.1). time-resolved experiment), only a single steady state is found per run, depending on the initial conditions [16,17]. Therefore, a complete exploration of the solution landscape would require infinite sampling of the continuous space of initial conditions.…”