Synchronization of Optomechanical Nanobeams by Mechanical Interaction

Floquet Control of Optomechanical Bistability in Multimode Systems

Cavity optomechanical systems make possible the fine manipulation of mechanical degrees of freedom with light, adding functionality and having broad appeal in photonic technologies. We show that distinct mechanical modes can be exploited with a temporally modulated Floquet drive to steer between distinct steady states induced by changes of cavity radiation pressure. We investigate the additional influence of the thermo-optic nonlinearity on these dynamics and find that it can suppress or amplify the control mechanism in contrast to its often performance-limiting character. Our results provide new techniques for the characterization of thermal properties of optomechanical systems and their control, sensing and computational applications.

All-Optical Synchronization of Remote Optomechanical Systems

Synchronization and frequency locking between remote mechanical oscillators are of scientific and technological importance. The key challenges are to align the oscillation frequencies and realize strong nonlinear interaction of both oscillators to a common carrier capable of long-distance transmission. Here, we experimentally realize the all-optical synchronization between two different optomechanical systems, a microsphere and a microdisk. The mechanical oscillation of the microsphere induced by the radiation pressure is loaded onto the pump laser via the optomechanical interaction, which is directly transmitted through a 5-km-long single-mode fiber to excite the mechanical oscillation of the microdisk. By finely tuning both the optical and mechanical frequencies of the two microresonators, the oscillation of the microdisk is injection locked to the microsphere, resulting in a synchronized phase relation of the two systems. Our results push a step forward the long-distance synchronization network using optomechanical microresonators.

A definition of the asymptotic phase for quantum nonlinear oscillators from the Koopman operator viewpoint

We propose a definition of the asymptotic phase for quantum nonlinear oscillators from the viewpoint of the Koopman operator theory. The asymptotic phase is a fundamental quantity for the analysis of classical limit-cycle oscillators, but it has not been defined explicitly for quantum nonlinear oscillators. In this study, we define the asymptotic phase for quantum oscillatory systems by using the eigenoperator of the backward Liouville operator associated with the fundamental oscillation frequency. By using the quantum van der Pol oscillator with a Kerr effect as an example, we illustrate that the proposed asymptotic phase appropriately yields isochronous phase values in both semiclassical and strong quantum regimes.

Two-Membrane Cavity Optomechanics: Linear and Non-Linear Dynamics

In this paper, we review the linear and non-linear dynamics of an optomechanical system made of a two-membrane etalon in a high-finesse Fabry–Pérot cavity. This two-membrane setup has the capacity to modify on demand the single-photon optomechanical coupling, and in the linearized interaction regime to cool simultaneously two mechanical oscillators. It is a promising platform for realizing cavity optomechanics with multiple resonators. In the non-linear regime, an analytical approach based on slowly varying amplitude equations allows us to derive a consistent and full characterization of the non-linear displacement detection, enabling a truthful detection of membrane displacements much above the usual linear sensing limited by the cavity linewidth. Such a high quality system also shows a pre-synchronization regime.

Mode-localized accelerometer in the nonlinear Duffing regime with 75 ng bias instability and 95 ng/√Hz noise floor

Mode-localized sensors have attracted attention because of their high parametric sensitivity and first-order common-mode rejection to temperature drift. The high-fidelity detection of resonator amplitude is critical to determining the resolution of mode-localized sensors where the measured amplitude ratio in a system of coupled resonators represents the output metric. Operation at specific bifurcation points in a nonlinear regime can potentially improve the amplitude bias stability; however, the amplitude ratio scale factor to the input measurand in a nonlinear regime has not been fully investigated. This paper theoretically and experimentally elucidates the operation of mode-localized sensors with respect to stiffness perturbations (or an external acceleration field) in a nonlinear Duffing regime. The operation of a mode-localized accelerometer is optimized with the benefit of the insights gained from theoretical analysis with operation in the nonlinear regime close to the top critical bifurcation point. The phase portraits of the amplitudes of the two resonators under different drive forces are recorded to support the experimentally observed improvements for velocity random walk. Employing temperature control to suppress the phase and amplitude variations induced by the temperature drift, 1/f noise at the operation frequency is significantly reduced. A prototype accelerometer device demonstrates a noise floor of 95 ng/√Hz and a bias instability of 75 ng, establishing a new benchmark for accelerometers employing vibration mode localization as a sensing paradigm. A mode-localized accelerometer is first employed to record microseismic noise in a university laboratory environment.

Hetero-Optomechanical Crystal Zipper Cavity for Multimode Optomechanics

Multimode optomechanics exhibiting several intriguing phenomena, such as coherent wavelength conversion, optomechanical synchronization, and mechanical entanglements, has garnered considerable research interest for realizing a new generation of information processing devices and exploring macroscopic quantum effect. In this study, we proposed and designed a hetero-optomechanical crystal (OMC) zipper cavity comprising double OMC nanobeams as a versatile platform for multimode optomechanics. Herein, the heterostructure and breathing modes with high mechanical frequency ensured the operation of the zipper cavity at the deep-sideband-resolved regime and the mechanical coherence. Consequently, the mechanical breathing mode at 5.741 GHz and optical odd mode with an intrinsic optical Q factor of 3.93 × 105 were experimentally demonstrated with an optomechanical coupling rate g0 = 0.73 MHz between them, which is comparable to state-of-the-art properties of the reported OMC. In addition, the hetero-zipper cavity structure exhibited adequate degrees of freedom for designing multiple mechanical and optical modes. Thus, the proposed cavity will provide a playground for studying multimode optomechanics in both the classical and quantum regimes.

Optomechanical synchronization across multi-octave frequency spans

Experimental exploration of synchronization in scalable oscillator microsystems has unfolded a deeper understanding of networks, collective phenomena, and signal processing. Cavity optomechanical devices have played an important role in this scenario, with the perspective of bridging optical and radio frequencies through nonlinear classical and quantum synchronization concepts. In its simplest form, synchronization occurs when an oscillator is entrained by a signal with frequency nearby the oscillator’s tone, and becomes increasingly challenging as their frequency detuning increases. Here, we experimentally demonstrate entrainment of a silicon-nitride optomechanical oscillator driven up to the fourth harmonic of its 32 MHz fundamental frequency. Exploring this effect, we also experimentally demonstrate a purely optomechanical RF frequency divider, where we performed frequency division up to a 4:1 ratio, i.e., from 128 MHz to 32 MHz. Further developments could harness these effects towards frequency synthesizers, phase-sensitive amplification and nonlinear sensing.

Higher order synchronization in optomechanical devices is relatively unexplored. Here the authors use nonlinear parametric effects to entrain an optomechanical oscillator with a drive signal several octaves away from the oscillation frequency, and demonstrate RF frequency division.

Floquet Phonon Lasing in Multimode Optomechanical Systems

Dynamical radiation pressure effects in cavity optomechanical systems give rise to self-sustained oscillations or 'phonon lasing' behavior, producing stable oscillators up to GHz frequencies in nanoscale devices. Like in photonic lasers, phonon lasing normally occurs in a single mechanical mode. We show here that mode-locked, multimode phonon lasing can be established in a multimode optomechanical system through Floquet dynamics induced by a temporally modulated laser drive. We demonstrate this concept in a suitably engineered silicon photonic nanocavity coupled to multiple GHz-frequency mechanical modes. We find that the long-term frequency stability is significantly improved in the multimode lasing state as a result of the mode locking. These results provide a path toward highly stable ultracompact oscillators, pulsed phonon lasing, coherent waveform synthesis, and emergent many-mode phenomena in oscillator arrays.

On Weakly Coupled Resonant MEMS Transducers Operating in the Modal Overlap Regime

Miniaturized physical transducers based on weakly coupled resonators have previously demonstrated the twin benefits of high parametric sensitivity and the first-order common-mode rejection of environmental effects. Current approaches to sensing based on coupled resonator transducers employ strong coupling where the modal overlap of the responses is avoided. This strong coupling limits the sensitivity for such mode-localized sensors that utilize an amplitude ratio (AR) output metric as opposed to tracking resonant frequency shifts. In this article, this limitation is broken through by theoretically and experimentally demonstrating the operation of the weakly coupled resonators in the weak-coupling (modal overlap) regime. Especially, a prototype microelectromechanical systems (MEMS) sensor based on this principle is employed to detect shifts in stiffness, with a stiffness bias instability of [Formula: see text]/m (9.5 ppb) and a corresponding noise floor of [Formula: see text]/m/ √ Hz (6.8 ppb/ √ Hz). The linear dynamic range of such AR readout sensors is first explored and found to be defined by the dynamic range of the secondary resonator. The proposed method provides a promising approach for high-performance resonant force and inertial sensors.

Generalized synchronization on the onset of auxiliary system approach

Generalized synchronization is an emergent functional relationship between the states of the interacting dynamical systems. To analyze the stability of a generalized synchronization state, the auxiliary system technique is a seminal approach that is broadly used nowadays. However, a few controversies have recently arisen concerning the applicability of this method. In this study, we systematically analyze the applicability of the auxiliary system approach for various coupling configurations. We analytically derive the auxiliary system approach for a drive-response coupling configuration from the definition of the generalized synchronization state. Numerically, we show that this technique is not always applicable for two bidirectionally coupled systems. Finally, we analytically derive the inapplicability of this approach for the network of coupled oscillators and also numerically verify it with an appropriate example.

Dispersive optomechanics of supercavity modes in high-index disks

In this work, we study the dispersive coupling between optical quasi-bound states in the continuum at telecom wavelengths and GHz-mechanical modes in high-index wavelength-sized disks. We show that such cavities can display values of the optomechanical coupling rate on par with optomechanical crystal cavities (g₀/2π≃800kHz). Interestingly, optomechanical coupling of optical resonances with mechanical modes at frequencies well above 10 GHz seems attainable. We also show that mechanical leakage in the substrate can be extremely reduced by placing the disk over a thin silica pedestal. Our results suggest a new route for ultra-compact optomechanical cavities that can potentially be arranged in massive arrays forming optomechanical metasurfaces for application in signal processing or sensing.

Coordinating an Ensemble of Chemical Micromotors via Spontaneous Synchronization

Spatiotemporal coordination of a nanorobot ensemble is critical for their operation in complex environments, such as tissue removal or drug delivery. Current strategies of achieving this task, however, rely heavily on sophisticated, external manipulation. We here present an alternative, biomimetic strategy by which oscillating Ag Janus micromotors spontaneously synchronize their dynamics as chemically coupled oscillators. By quantitatively tracking the kinetics at both an individual and cluster level, we find that synchronization emerges as the oscillating entities are increasingly coupled as they approach each other. In addition, the synchronized beating of a cluster of these oscillating colloids was found to be dominated by substrate electroosmosis, revealed with the help of an acoustic trapping technique. This quantitative, systematic study of synchronizing micromotors could facilitate the design of biomimetic nanorobots that spontaneously communicate and organize at micro- and nanoscales. It also serves as a model system for nonlinear active matter.

Self-Organized Synchronization of Phonon Lasers

Self-organized synchronization is a ubiquitous collective phenomenon, in which each unit adjusts their rhythms to achieve synchrony through mutual interactions. The optomechanical systems, due to their inherently engineerable nonlinearities, provide an ideal platform to study self-organized synchronization. Here, we demonstrate the self-organized synchronization of phonon lasers in a two-membrane-in-the-middle optomechanical system. The probe of each individual membrane enables us to monitor the real-time transient dynamics of synchronization, which reveals that the system enters into the synchronization regime via a torus birth bifurcation line. The phase-locking phenomenon and the transition between in-phase and antiphase regimes are directly observed. Moreover, such a system greatly facilitates the controllable synchronous states, and consequently a phononic memory is realized by tuning the system parameters. This result is an important step towards the future studies of many-body collective behaviors in multiresonator optomechanics with long distances, and might find potential applications in quantum information processing and complex networks.