Self-sustained oscillation and harmonic generation in optomechanical systems with quadratic couplings

Abstract

Many works are based on the steady-state analysis of mean-value dynamics in electro-or optomechanical systems to explore vibration cooling, squeezing, and quantum-state controlling of massive objects. These studies are always conducted in a red-detuned pumping field under a lower power to maintain a stable situation. In this paper we consider self-sustained oscillations of a cavity-field-driven oscillator combined with quadratic coupling in a blue-detuned regime above a pumping threshold. Our study finds that the oscillator will be far away from its steady-state behavior by conducting a self-sustained oscillation with a discrete amplitude locking effect producing a rich energy-balanced structure. The dynamical backaction of this self-oscillation on the field mode induces a multipeak field spectrum, which implies an efficient harmonic generation with its intensity modified not only by the displacement x 0 but also by the amplitude A of the mechanical oscillation. The corresponding nonlinear field spectrum and its magnitude are analytically analyzed with quadratic coupling when the mechanical oscillator is dynamically locked to a self-sustained oscillation.

Photon–phonon parametric oscillation induced by quadratic coupling in an optomechanical resonator

“…The nonlinear static responses modified by the quadratic coupling can be understood by the adiabatic potential generated by the cavity mode when the field modulation is much faster than the motion of the mechanical resonator. Then the total adiabatic potential felt by the resonator is [15] U (x, τ ) = 1 2…”

“…The above nonlinear steady-state responses influenced by the quadratic coupling are based on the steady-state analysis without considering any dynamical stabilities of the system. However, when the pumping field is above a threshold power, the static behaviors shown in Fig.1 will lose their stabilities and run into a limit-circle motion via a Hopf bifurcation [13][14][15], which is often identified as the SSO emerged in many nonlinear systems [17]. Fig.3 displays the typical dynamic orbits of the res- onator and the corresponding cavity field in phase space starting from ground states in a red-detuned pumping field.…”

“…which supports the self-oscillation with step-like amplitudes with different x 0 determined by the pumping power. A detailed analysis of the discrete amplitudes in this case should resort to the power balance of ẍẋ = 0 for the resonator [19], which gives [15] A ≈…”

“…The nonlinear behavior with a large-amplitude of motion is dominated by the mean-field dynamics of the resonator and it is critical to explore new features of practical applications. One important nonlinear behavior found in the optomechanical systems is that the system can support stable self-sustained oscillations (SSOs) [11][12][13][14] and a highefficiency broadband high-order harmonic oscillation can be generated in this case [15,16]. An easily controlled * Electronic address: zhanglincn@snnu.edu.cn SSO working at different power levels is the physical foundation for many practical applications such as developing force sensors or information processors based on nonlinear photon-phonon interactions [17].…”

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

“…As a solid-state quantum platform, the optomechanical system has exhibited both great potential for testing fundamental problems in quantum mechanics and wide applications in quantum information processing and quantum precise measurement (see reviews [1][2][3]). Because of the radiation-pressureinduced nonlinearity between optics and mechanics, cavity optomechanical systems allow the study of a variety of nonlinear phenomena, such as bistability [4,5], multi-stability [6][7][8], selfsustained oscillations [6,9,10], and chaotic motion [11,12]. However, noise is unavoidable in open optomechanical systems, and compared to all-optical systems the mechanical freedom in an optomechanical system is more sensitive to thermal noise because of its relatively low resonance frequency.…”