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arXiv:2605.00338

Staircase mechanical energy growth in optomechanical systems of median mechanical frequencies

Yi Xiao, Yi Wu, Qi-Kai Zhan, Jin Lian Zhang, Bing He, Qing Lin

physics.opticsquant-phSubmitted May 1, 2026• Announced May 4, 2026
arXivHTMLPDF

Abstract

Owing to the radiation-force-induced nonlinearity, cavity optomechanical systems (COMS) exhibit dynamical phenomena such as back-action induced oscillation, chaos, mechanical amplitude locking, and anomalous stabilization, which occur under different driving conditions and different system parameters. We here identify a previously unknown dynamical pattern of staircase evolution for the energy of mechanical resonator, when a COMS with neither very large nor very small built-in mechanical frequency is driven by a two-tone field, which satisfies a condition that the frequency difference of the two tones matches the built-in mechanical frequency. The properties of this phenomenon are analyzed for the different system parameters due to fabrication such as mechanical frequencies and quality factors, as well as under the varied driving conditions such as unequal drive tone powers and mismatched drive tone difference from the mechanical frequency. Some special features, such as an emergent bifurcation due to the tone power difference, together with the totally different responses of the system to the drive tone mismatches of opposite signs, are discovered to exist only in this type of COMS with median mechanical frequencies. This work fills a gap in the study of the dynamics of COMS under two-tone drives. In the aspect of applications, the rapid increase of mechanical energy exhibited in the phenomenon promises phonon laser generation, and the sensitive dynamical response to the drive tone mismatches offers a potential approach to high-precision sensing.

Comments
10 pages. 6 figures

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Owing to the radiation-force-induced nonlinearity, cavity optomechanical systems (COMS) exhibit dynamical phenomena such as back-action induced oscillation, chaos, mechanical amplitude locking, and anomalous stabilization, which occur under different driving conditions and different system parameters. We here identify a previously unknown dynamical pattern of staircase evolution for the energy of mechanical resonator, when a COMS with neither very large nor very small built-in mechanical frequency is driven by a two-tone field, which satisfies a condition that the frequency difference of the two tones matches the built-in mechanical frequency. The properties of this phenomenon are analyzed for the different system parameters due to fabrication such as mechanical frequencies and quality factors, as well as under the varied driving conditions such as unequal drive tone powers and mismatched drive tone difference from the mechanical frequency. Some special features, such as an emergent bifurcation due to the tone power difference, together with the totally different responses of the system to the drive tone mismatches of opposite signs, are discovered to exist only in this type of COMS with median mechanical frequencies. This work fills a gap in the study of the dynamics of COMS under two-tone drives. In the aspect of applications, the rapid increase of mechanical energy exhibited in the phenomenon promises phonon laser generation, and the sensitive dynamical response to the drive tone mismatches offers a potential approach to high-precision sensing.
The nonlinear dynamics of a mechanical resonator in an optomechanical system with linear, quadratic and cubic photon-vibration interactions (with respect to mechanical displacements) in a modulated driving field under conditions of adiabatic elimination of the optical field is studied. Based on the constructed bifurcation diagrams of the mechanical coordinate and the largest Lyapunov exponent as a function of the modulation amplitude, as well as power spectra, phase portraits and Poincare sections, regions of regular and chaotic dynamics of the optomechanical system are identified. It is also shown that for a certain modulation amplitude in the presence of all three types of interactions, chaotic dynamics of the mechanical resonator (oscillator) is realized, which is replaced by quasi-periodic oscillations in the absence of cubic interaction, and the system returns to chaotic behavior if only linear interaction remains. This non-monotonic dependence of chaotic dynamics on the order of nonlinearity originates from the interplay between parametric driving and effective potential reshaping and manifests that nonlinearity does not always enhance chaos. For an optomechanical system in a membrane-in-the-middle configuration, where only quadratic photon-vibration interaction is present, it is demonstrated that at small modulation amplitudes the mechanical oscillator exhibits quasi-periodic motion in each of the wells of a symmetric two-minimum potential, whereas large modulation amplitudes lead to chaotic motion, involving interwell transitions.
We investigate the change in width of transparency windows and the amplification of the probe output spectra in an optomechanical system with multiple mechanical resonators. Each mechanical resonator is driven by a mechanical driving field, and the phases of these mechanical driving fields are different. Via exhibiting the probe output spectra of the system, we find that the number of transparency windows is explicitly decided by the number of mechanical resonators with different frequencies. Meanwhile, we discuss the effect of cavity decay rate on the width of the transparency windows. Moreover, we also investigate the absorption and amplification phenomena with the different phase differences among the pump field, probe field, and mechanical driving fields. By adjusting the phase differences, the fast–slow light transitions can occur. These interesting phenomena can also be exploited to investigate the optical switch and frequency comb generation.
Nonlinearity is a key resource in both classical and quantum signal processing. Nonlinear nanomechanical elements have found applications ranging from sensing to computing, while networks of nonlinear resonators, as well as nonlinearly coupled networks of linear resonators, constitute promising platforms for simulating complex dynamics. Here, we experimentally demonstrate an approach to realizing strong mechanical nonlinearity in nanomechanical resonators, fully controlled through optical laser drives. The mechanism exploits the nonlinearity of the radiation-pressure interaction in a cavity optomechanical system, which gives rise to a nonlinear optical spring effect. The resulting Duffing nonlinearity is conveniently tunable in strength via pump laser power, while its sign is controlled by laser detuning. Moreover, we demonstrate that the nonlinear optical spring mediates effective interactions between mechanical modes coupled to a common cavity, inducing tunable nonlinear interactions between them that impact spectral response and dynamics. These results establish cavity optomechanics as a versatile and in-situ reconfigurable platform for engineering nonlinear dynamics in resonators and networks.
Abstract The generation of large-amplitude coherent states of a massive mechanical resonator, and their quantum-limited detection represent useful tools for quantum sensing and for testing fundamental physics theories. In fact, any weak perturbation may affect the coherent quantum evolution of the prepared state, providing a sensitive probe for such a perturbation. Here we consider a cavity optomechanical setup and the case of the detection of a weak mechanical nonlinearity. We consider different strategies, first focusing on the stationary dynamics in the presence of multiple tones driving the system, and then focusing on non-equilibrium dynamical strategies. These methods can be successfully applied for measuring Duffing-like material nonlinearities, or effective nonlinear corrections associated with quantum gravity theories.
Intrinsic damping rate and quality factor (QQQ) are key parameters in optomechanical systems. However, in high-Q devices, their measurement is often challenging because probe-induced dynamical backaction (DBA) and the need to resolve and accurately track the mechanical resonance limit the performance of state-of-the-art techniques. Here, we introduce an all-optical ringdown method in the unresolved-sideband regime that exploits the nonlinear, time-averaged optical response induced by strong mechanical motion. We derive an analytical model of the time-averaged optical cavity response probed by a weak frequency-scanning laser. During the evolution of the mechanical oscillator, the excited motion modulates the Lorentzian lineshape into a double-horned profile whose peak separation enables an accurate estimation of the modulation amplitude. Tracking this response during the mechanical ringdown allows the intrinsic damping rate to be determined without resolving the mechanical oscillation. We apply the method to a density-modulated phononic crystal membrane placed inside a high-finesse cavity and obtain mechanical quality factors consistent with independent measurements on the same platform. Our method requires a minimal optical setup, while offering an in situ diagnostic and reduced impact from probe-induced DBA and robustness against measurement noise. Finally, the model can describe other resonant systems dispersively coupled to coherent frequency modulations, providing new insights and measurement strategies that expand beyond the optomechanical platform.
An optomechanical cavity driven by a periodically amplitude-modulated laser can generate steady light-mechanical entanglement with time periodicity. Similar results can be alternatively obtained by pumping an especially tuned optical degenerate parametric amplifier (DPA) inside the cavity. While the two laser beams are simultaneously applied, the optomechanical entanglement can exhibit constructive and destructive interference patterns, depending on their cooperative phase, which further gives rise to beating in entanglement dynamics if the two modulation frequencies are slightly different, followed by a beating frequency-dependent dynamical behavior in the energy exchange between light and a mechanical oscillator. The optimal dynamical entanglement goes beyond what is attainable by the scenario with two superimposed cavity drivings, as a result of the specially DPA-modulated quantum dynamics. Moreover, we calculate correlation spectra between the cavity and mechanical modes, and we find correspondence between the light-oscillator entanglement and the correlation spectra under the cooperative effect. The cooperation-enhanced optomechanical entanglement is robust against the thermal temperature, and is potentially useful for continuous variable quantum information processing.