Optical Spring Effect Research Articles

Surpassing the Standard Quantum Limit Using an Optical Spring.

Quantum mechanics places noise limits and sensitivity restrictions on physical measurements. The balance between unwanted backaction and the precision of optical measurements imposes a standard quantum limit (SQL) on interferometric systems. In order to realize a sensitivity below the SQL, it is necessary to leverage a backaction evading measurement technique, reduce thermal noise to below the level of backaction, and exploit cancellations of any excess noise contributions at the detector. Many proof of principle experiments have been performed, but only recently has an experiment achieved sensitivity below the SQL. In this work, we extend that initial demonstration and realize sub-SQL sensitivity nearly two times better than previous measurements, and with an architecture applicable to interferometric gravitational wave detectors. In fact, this technique is directly applicable to Advanced LIGO, which could observe similar effects with a detuned signal recycling cavity. We measure a total sensitivity below the SQL by 2.8dB, corresponding to a reduction in the noise power by 72±5.1% below the quantum limit. Through the use of a detuned cavity and the optical spring effect, this noise reduction is tunable, allowing us to choose the desired range of frequencies that fall below the SQL. This result demonstrates access to sensitivities well below the SQL at frequencies applicable to LIGO, with the potential to extend the reach of gravitational wave detectors further into the Universe.

Radiation Pressure Backaction on a Hexagonal Boron Nitride Nanomechanical Resonator.

Hexagonal boron nitride (hBN) is a van der Waals material with excellent mechanical properties hosting quantum emitters and optically active spin defects, with several of them being sensitive to strain. Establishing optomechanical control of hBN will enable hybrid quantum devices that combine the spin degree of freedom with the cavity optomechanical toolbox. In this Letter, we report the first observation of radiation pressure backaction at telecom wavelengths with a hBN drum-head mechanical resonator. The thermomechanical motion of the resonator is coupled to the optical mode of a high finesse fiber-based Fabry-Pérot microcavity in a membrane-in-the-middle configuration. We are able to resolve the optical spring effect and optomechanical damping with a single photon coupling strength of g0/2π = 1200 Hz. Our results pave the way for tailoring the mechanical properties of hBN resonators with light.

Optical spring effect enhanced by optical parametric amplifier

We experimentally demonstrate that the optical spring effect can be modified using an optical parametric amplifier in an opto-mechanical cavity. The theoretical analysis shows that both the gain and phase of the optical parametric amplifier can modify the frequency of a mechanical resonator in an opto-mechanical cavity. This modification could be used to tune the frequency of peak sensitivity of gravitational wave detectors. The experimental results show a factor of 1.2 ± 0.8 increase in mechanical resonator frequency shift induced by optical spring by tuning the optical parametric amplifier gain.

Giant optomechanical spring effect in plasmonic nano- and picocavities probed by surface-enhanced Raman scattering

Molecular vibrations couple to visible light only weakly, have small mutual interactions, and hence are often ignored for non-linear optics. Here we show the extreme confinement provided by plasmonic nano- and pico-cavities can sufficiently enhance optomechanical coupling so that intense laser illumination drastically softens the molecular bonds. This optomechanical pumping regime produces strong distortions of the Raman vibrational spectrum related to giant vibrational frequency shifts from an optical spring effect which is hundred-fold larger than in traditional cavities. The theoretical simulations accounting for the multimodal nanocavity response and near-field-induced collective phonon interactions are consistent with the experimentally-observed non-linear behavior exhibited in the Raman spectra of nanoparticle-on-mirror constructs illuminated by ultrafast laser pulses. Further, we show indications that plasmonic picocavities allow us to access the optical spring effect in single molecules with continuous illumination. Driving the collective phonon in the nanocavity paves the way to control reversible bond softening, as well as irreversible chemistry.

Optomechanically induced thermal bistability in an optical microresonator

Optomechanical systems have attracted considerable attention due to their wide applications in hybrid transduction systems, sensors, and quantum measurements. Classical optomechanical systems have various dynamical regimes that depend on the parameters, and the situation can be even more complicated when incorporated with other nonlinearities, such as the thermal nonlinearity that is common in optical resonators. Here, we experimentally and theoretically study the thermal bistability induced by optomechanical effect in a whispering-gallery mode microresonator. The mechanical oscillation modulates the intracavity photon number and modifies the thermal stability of states under a blue-detuned pump laser. Utilizing a silica microtip to suppress the mechanical motion, we identify the regions where the optical cavity temperature and detuning change due to the onset of oscillation and characterize the shifts in the detuning quantitatively. Hysteretic response in the mechanical frequency shifts (optical spring effect) to the pump wavelength is also observed to confirm the presence of bistability. The thermal dynamics discussed here is essentially different from the optomechanical heating and cooling of the effective temperature of the mechanical oscillator. This discovery shows that the thermal nonlinearity, which has been used for locking the pump frequency in the optomechanical systems, may also make some detuning states thermally unstable. Our study demonstrates an approach to characterize the detuning of the pump laser in an optomechanical resonator with thermal nonlinearity and also lays the groundwork for further understanding of dynamical effects induced by optomechanical effects.

Enhancement and manipulation of optical interaction between coupled nano-waveguides in hollow-core fibers

Optomechanical forces between evanescently coupled nano-waveguides serve as useful mechanisms to configure versatile functionalities of macro- and nano-devices. Strategies for boosting the optomechanical interaction strength are particularly compelling for the field of nanotechnologies. Here we show that the optical coupling strength between nano-waveguides can be enhanced by orders of magnitude when they are confined in hollow-core fibers. The presence of hollow core greatly increases the overlap integral between the nano-waveguides through excitation of the core modes. The excited higher-order core modes are able to mediate a long-range optomechanical interaction between the waveguides even though they are separated by tens of optical wavelength. It is found that the optical forces between the nanofibers can be switched from attractive to repulsive ones purely by tuning the gap between the nanofibers due to the optomechanical back-action effect induced by the higher-order core modes. The enhanced optomechanical coupling can be exploited to manipulate the collective eigenfrequencies of the coupled nano-waveguides via the optical spring effect. Our observation may find applications on the design of waveguide couplers embedded in the hollow core, or to realize miniaturized acoustic sensors.

Passive laser power stabilization via an optical spring.

Metrology experiments can be limited by the noise produced by the laser involved via small fluctuations in the laser's power or frequency. Typically, active power stabilization schemes consisting of an in-loop sensor and a feedback control loop are employed. Those schemes are fundamentally limited by shot noise coupling at the in-loop sensor. In this Letter, we propose to use the optical spring effect to passively stabilize the classical power fluctuations of a laser beam. In a proof of principle experiment, we show that the relative power noise of the laser is stabilized from approximately 2 × 10-5 Hz-1/2 to a minimum value of 1.6 × 10-7 Hz-1/2, corresponding to the power noise reduction by a factor of 125. The bandwidth at which stabilization occurs ranges from 400 Hz to 100 kHz. The work reported in this Letter further paves the way for high power laser stability techniques which could be implemented in optomechanical experiments and in gravitational wave detectors.

Vibrational Kerr Solitons in an Optomechanical Microresonator.

Kerr soliton microcombs in microresonators have been a prominent miniaturized coherent light source. Here, for the first time, we demonstrate the existence of Kerr solitons in an optomechanical microresonator, for which a nonlinear model is built by incorporating a single mechanical mode and multiple optical modes. Interestingly, an exotic vibrational Kerr soliton state is found, which is modulated by a self-sustained mechanical oscillation. Besides, the soliton provides extra mechanical gain through the optical spring effect, and results in phonon lasing with a red-detuned pump. Various nonlinear dynamics is also observed, including limit cycle, higher periodicity, and transient chaos. This work provides a guidance for not only exploring many-body nonlinear interactions, but also promoting precision measurements by featuring superiority of both frequency combs and optomechanics.

Reduction of quantum noise using the quantum locking with an optical spring for gravitational wave detectors

In our previous research, simulation showed that a quantum locking scheme with homodyne detection in sub-cavities is effective in surpassing the quantum noise limit for Deci-hertz Interferometer Gravitational Wave Observatory (DECIGO) in a limited frequency range. This time we have simulated an optical spring effect in the sub-cavities of the quantum locking scheme. We found that the optimized total quantum noise is reduced in a broader frequency band, compared to the case without the optical spring effect significantly improving the sensitivity of DECIGO to the primordial gravitational waves.

Tunable Exciton-Optomechanical Coupling in Suspended Monolayer MoSe2.

The strong excitonic effect in monolayer transition metal dichalcogenide (TMD) semiconductors has enabled many fascinating light-matter interaction phenomena. Examples include strongly coupled exciton-polaritons and nearly perfect atomic monolayer mirrors. The strong light-matter interaction also opens the door for dynamical control of mechanical motion through the exciton resonance of monolayer TMDs. Here, we report the observation of exciton-optomechanical coupling in a suspended monolayer MoSe2 mechanical resonator. By moderate optical pumping near the MoSe2 exciton resonance, we have observed optical damping and antidamping of mechanical vibrations as well as the optical spring effect. The exciton-optomechanical coupling strength is also gate-tunable. Our observations can be understood in a model based on photothermal backaction and gate-induced mirror symmetry breaking in the device structure. The observation of gate-tunable exciton-optomechanical coupling in a monolayer semiconductor may find applications in nanoelectromechanical systems (NEMS) and in exciton-optomechanics.

Optical back-action on the photothermal relaxation rate

Photothermal effects can alter the response of an optical cavity, for example, by inducing self-locking behavior or unstable anomalies. The consequences of these effects are often regarded as parasitic and generally cause limited operational performance of the cavity. Despite their importance, however, photothermal parameters are usually hard to characterize precisely. In this work, we use an optical cavity strongly coupled to photothermal effects to experimentally observe an optical back-action on the photothermal relaxation rate. This effect, reminiscent of the radiation-pressure-induced optical spring effect in cavity optomechanical systems, uses optical detuning as a fine control to change the photothermal relaxation process. The photothermal relaxation rate of the system can be accordingly modified by more than an order of magnitude. This approach offers an opportunity to obtain precise in situ estimations of the parameters of the cavity in a way that is compatible with a wide range of optical resonator platforms. Through this back-action effect, we are able to determine the natural photothermal relaxation rate and the effective thermal conductivity of cavity mirrors with unprecedented resolution.

Observation of nonlinear dynamics in an optical levitation system

Optical levitation of mechanical oscillators has been suggested as a promising way to decouple the environmental noise and increase the mechanical quality factor. Here, we investigate the dynamics of a free-standing mirror acting as the top reflector of a vertical optical cavity, designed as a testbed for a tripod cavity optical levitation setup. To reach the regime of levitation for a milligram-scale mirror, the optical intensity of the intracavity optical field approaches 3 MW cm−2. We identify three distinct optomechanical effects: excitation of acoustic vibrations, expansion due to photothermal absorption, and partial lift-off of the mirror due to radiation pressure force. These effects are intercoupled via the intracavity optical field and induce complex system dynamics inclusive of high-order sideband generation, optical bistability, parametric amplification, and the optical spring effect. We modify the response of the mirror with active feedback control to improve the overall stability of the system.

A cavity optomechanical locking scheme based on the optical spring effect.

We present a novel locking scheme for active length-stabilization and frequency detuning of a cavity optomechanical device based on the optical spring effect. The error signal is generated by utilizing the position measurement of a thermally driven intra-cavity nanomechanical device and employing its detuning-dependent frequency shift caused by the dispersive coupling to the cavity field. The scheme neither requires external modulation of the laser or the cavity nor does it demand for additional error signal readout, rendering its technical implementation rather simple for a large variety of existing optomechanical devices. Specifically, for large-linewidth microcavities or in situations where other locking schemes appear unfavorable conceptually or are hard to realize technically, the optical spring lock represents a potential alternative for stabilizing the cavity length. We explain the functional principle of the lock and characterize its performance in terms of bandwidth and gain profile.

Linear analytical approach to dispersive, external dissipative, and intrinsic dissipative couplings in optomechanical systems

We present a theoretical study of optomechanical systems in which the mechanical resonator modulates both the resonant frequency (dispersive coupling) and the decay rates (dissipative coupling) of the optical cavity. We extend the generic dispersive framework to a more general case in which the dissipative coupling is split between its external and intrinsic contribution. We report a complete analysis of the influence of each kind of optical losses (intrinsic and external) on the three coupling mechanisms and highlight the interest of each external decay rate regime. The basic tools to experimentally identify the three couplings and their relative influence on the optical response are presented. We demonstrate the general expression of the optical spring effect and optomechanical damping. Comparison between experimental measurements in photonic crystal systems from the literature and our theoretical modal yields good agreement.

High-Q Milligram-Scale Monolithic Pendulum for Quantum-Limited Gravity Measurements.

We present the development of a high-Q monolithic silica pendulum weighing 7milligram. The measured Q value for the pendulum mode at 2.2Hz was 2.0×10^{6}. To the best of our knowledge this is the lowest dissipative milligram-scale mechanical oscillator to date. By employing this suspension system, the optomechanical displacement sensor for gravity measurements we recently reported in Matsumoto et al. [Phys. Rev. Lett. 122, 071101 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.071101] can be improved to realize quantum-noise-limited sensing at several hundred hertz. In combination with the optical spring effect, the amount of intrinsic dissipation measured in the pendulum mode is enough to satisfy requirements for measurement-based quantum control of a massive pendulum confined in an optical potential. This paves the way for not only testing dark matter via quantum-limited force sensors, but also Newtonian interaction in quantum regimes, namely, between two milligram-scale oscillators in quantum states, as well as improving the sensitivity of gravitational-wave detectors.

Brillouin cavity optomechanics sensing with enhanced dynamical backaction

Based on the dispersive interaction between a high quality factor microcavity and nano-objects, whispering-gallery-mode microcavities have been widely used in highly sensitive sensing. Here, we propose a novel method to enhance the sensitivity of the optical frequency shift and reduce the impact of the laser frequency noise on the detection resolution through Brillouin cavity optomechanics in a parity-time symmetric system. The optical spring effect is sensitive to the perturbation of optical modes around the exceptional point. By monitoring the shift of the mechanical frequency, the detection sensitivity for the optical frequency shift is enhanced by 2 orders of magnitude compared with conventional approaches. We find the optical spring effect is robust to the laser frequency noise around the exceptional point, which can reduce the detection limitation caused by the laser frequency instability. Thus, our method can improve the sensing ability for nano-object sensing and other techniques based on the frequency shift of the optical mode.

Noise suppression of mechanical oscillations in a microcavity for ultrasensitive detection.

Optical microcavities have been widely applied as sensitive detectors due to ultrahigh quality factors and small mode volumes. Besides considering the optical mode as the sensing signal, the optomechanical oscillations induced by the optical spring effect also perform as an elegant sensing signal. However, the minimal size of a detectable analyte is limited by the relatively weak light-matter interaction compared to the experimental noises. To improve the detection limit, many methods have been developed to either enhance device sensitivities or suppress experimental noises. In this work, we present a way to lower the detection limit by suppressing experimental noises of the mechanical frequency by 3 orders of magnitude. Utilizing a fiber tip as a benchmark analyte attaching onto the cavity, the mechanical frequency shift reflects the changes of the optical mode detuning of the cavity, predicting an effective tool for ultrasensitive detection.

Optical Spring Effect in Micro-Bubble Resonators and Its Application for the Effective Mass Measurement of Optomechanical Resonant Mode.

In this work, we present a novel approach for obtaining the effective mass of mechanical vibration mode in micro-bubble resonators (MBRs). To be specific, the effective mass is deduced from the measurement of optical spring effect (OSE) in MBRs. This approach is demonstrated and applied to analyze the effective mass of hollow MBRs and liquid-filled MBRs, respectively. It is found that the liquid-filled MBRs has significantly stronger OSE and a less effective mass than hollow MBRs, both of the extraordinary behaviors can be beneficial for applications such as mass sensing. Larger OSE from higher order harmonics of the mechanical modes is also observed. Our work paves a way towards the developing of OSE-based high sensitive mass sensor in MBRs.

Energy-localization-enhanced ground-state cooling of a mechanical resonator from room temperature in optomechanics using a gain cavity

When a gain system is coupled to a loss system, the energy usually flows from the gain system to the loss one. We here present a counterintuitive theory for the ground-state cooling of the mechanical resonator in optomechanical system via a gain cavity. The energy flows first from the mechanical resonator into the loss cavity, then into the gain cavity, and finally localizes there. The energy localization in the gain cavity dramatically enhances the cooling rate of the mechanical resonator. Moreover, we show that unconventional optical spring effect, e.g., giant frequency shift and optically induced damping of the mechanical resonator, can be realized. Those feature a pre-cooling free ground-state cooling, i.e., the mechanical resonator in thermal excitation at room temperature can directly be cooled to its ground state. This cooling approach has the potential application for fundamental tests of quantum physics without complicated cryogenic setups.

Sensitivity characterisation of a parametric transducer for gravitational wave detection through optical spring effect

We present the characterisation of the most recent parametric transducers designed to enhance the Mario Schenberg gravitational wave detector sensitivity. The transducer is composed of a microwave re-entrant cavity that attaches to the gravitational wave antenna via a rigid spring. It functions as a three-mode mass-spring system; motion of the spherical antenna couples to a 50 μm thick membrane, which converts its mechanical motion into a frequency shift of the cavity resonance. Through the optical spring effect, the microwave transducer frequency-displacement sensitivity was measured to be at 4 K. The spherical antenna detection sensitivity is determined analytically using the transducer amplification gain and equivalent displacement noise in the test setup, which are and , respectively.