Noise-induced temporal regularity and signal amplification in an optomechanical system with parametric instability

Abstract

Noise usually has an unwelcome influence on system performance. For instance, noise inevitably affects the low-frequency mechanical freedom in optomechanical experiments. However, we investigate here the beneficial effects of thermal noise on a basic optomechanical system with parametric instability. In a regime near parametric instability, it is found that thermal noise in the mechanical freedom can sustain long-term quasi-coherent oscillations when the system would otherwise remain in the equilibrium state. In an overlapping regime of parametric instability and bistability, intermittent switching between a self-sustained oscillating state and an equilibrium can be induced by adding a certain amount of noise. When a subthreshold periodic signal is applied to the mechanics, the switching between the self-sustained oscillations and the equilibrium exhibits good periodicity at a rate that is synchronized to the signal frequency, resulting in a significant amplification of the signal. Our results deepen the understanding of the interplay between optomechanical nonlinearity and noise and provide theoretical guidance for experimental observation of noise-induced beneficial phenomena in optomechanics.

Quantum pure noise-induced transitions: A truly nonclassical limit cycle sensitive to number parity

“…There has also been some recent results on noise-induced oscillations and transitions, including quantum systems, but in a different sense [63][64][65][66]. These results, which we shall discuss now, do not qualify as pure noise-induced transitions because they investigate phenomena whereby additive noise (which are system independent) induces the system to jump in and out of preexisting states.…”

“…induced or stochastic limit cycles [67,68,84,85], and was recently studied in open quantum systems [63,64]. Some authors have in fact defined a noise-induced "limit cycle" by using only a local basin of attraction and the destabilizing effect of additive noise [65].…”

Quantum Coherence Resonance

“…Coherence resonance was first demonstrated near a saddle-node on invariant circle (SNIC) bifurcation [20] and also near a supercritical Hopf bifurcation [19] of limit cycles. Since then, a number of theoretical investigations have been carried out for various dynamical systems [3,21], including chaotic systems [22], spatially extended systems [23], and realistic models of microscale devices such as semiconductor superlattices [24] and optomechanical systems [25]. It has also been used to model the periodic calcium release from the endoplasmic reticulum in a living cell [26,27].…”

Pure and truly nonclassical noise-induced transitions at the microscopic scale

“…There has also been some recent results on noiseinduced oscillations and transitions, including quantum systems, but in a different sense [62][63][64][65]. This literature investigates phenomena whereby additive noise (which are system independent) induces the system to jump in and out of preexisting states.…”

“…In the case of coherence resonance, pulses resembling limit-cycle oscillations are produced using noise-activated escape in a system whose deterministic dynamics already contains a limit cycle (an excitable system [82]). Such pulsations have also come un-der the name of noise-induced or stochastic limit cycles [66,67,83,84], and was recently studied in open quantum systems [64,65]. Some authors have in fact defined a noise-induced "limit cycle" by using only a local basin of attraction and the destabilizing effect of additive noise [62].…”