Optical Spring Research Articles

Optical Spring Tracking for Enhancing Quantum-Limited Interferometers

Optical Spring Tracking for Enhancing Quantum-Limited Interferometers

New double-pass type of the optical spring

New double-pass type of the optical spring

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.

Kerr-Enhanced Optical Spring.

We propose and experimentally demonstrate the generation of enhanced optical springs using the optical Kerr effect. A nonlinear optical crystal is inserted into a Fabry-Perot cavity with a movable mirror, and a chain of second-order nonlinear optical effects in the phase-mismatched condition induces the Kerr effect. The optical spring constant is enhanced by a factor of 1.6±0.1 over linear theory. To our knowledge, this is the first realization of optomechanical coupling enhancement using a nonlinear optical effect, which has been theoretically investigated to overcome the performance limitations of linear optomechanical systems. The tunable nonlinearity of demonstrated system has a wide range of potential applications, from observing gravitational waves emitted by binary neutron star postmerger remnants to cooling macroscopic oscillators to their quantum ground state.

Optimization of Quantum Noise in Space Gravitational-Wave Antenna DECIGO with Optical-Spring Quantum Locking Considering Mixture of Vacuum Fluctuations in Homodyne Detection

Quantum locking using optical spring and homodyne detection has been devised to reduce the quantum noise that limits the sensitivity of the DECIGO, a space-based gravitational-wave antenna in the frequency band around 0.1 Hz for the detection of primordial gravitational waves. The reduction in the upper limit of energy density ΩGW from 2×10−15 to 1×10−16, as inferred from recent observations, necessitates improved sensitivity in the DECIGO to meet its primary science goals. To accurately evaluate the effectiveness of this method, this paper considers a detection mechanism that takes into account the influence of vacuum fluctuations on homodyne detection. In addition, an advanced signal processing method is devised to efficiently utilize signals from each photodetector, and design parameters for this configuration are optimized for the quantum noise. Our results show that this method is effective in reducing quantum noise, despite the detrimental impact of vacuum fluctuations on its sensitivity.

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.

Effective description of a suspended mirror coupled to cavity light: Limitations of Q enhancement due to normal-mode splitting by an optical spring

Pendulums have long been used as force sensors due to their ultimately low dissipation (high-quality factor) characteristic. They are widely used in the measurement of the gravitational constant, detection of gravitational waves, and determination of ultralight dark matter. Furthermore, it is expected that the quantum nature of gravity will be demonstrated by performing quantum control for macroscopic pendulums. Recently, we have demonstrated that quantum entanglement between two pendulums can be generated using an optical spring [D. Miki, N. Matsumoto, A. Matsumura, T. Shichijo, Y. Sugiyama, K. Yamamoto, and N. Yamamoto, arXiv:2210.13169 (2022)]; however, we have ignored that an optical spring can reduce the quality factor (Q-factor) by applying normal-mode splitting between the pendulum and rotational modes possessing relatively high dissipation. Herein, we analyze a system composed of a cylinder suspended using a beam (a suspended mirror, i.e., a pendulum) and an optical spring to consider normal-mode splitting. The reduction in Q-factor is determined only by the beam parameters: the ratio of the radius of the mirror to the length of the beam, and the ratio of the frequency of the rotational mode to the pendulum mode in the absence of cavity photons. In our analysis, we find that the reduction factor $4.38$ is reproduced, which is consistent with the experimental result in Matsumoto \textit{et al.} [N. Matsumoto, S. B. Catan$\tilde{\text{o}}$-Lopez, M. Sugawara, S. Suzuki, N. Abe, K. Komori, Y. Michimura, Y. Aso, and K. Edamatsu, Phys. Rev. Lett. 122, 071101 (2019)]. Our analysis shows that low dissipation (high quality) can be reached using an optical spring for the realistic pendulum system considering the rotational degree of freedom.

First-step experiment for sensitivity improvement of DECIGO: Sensitivity optimization for simulated quantum noise by completing the square

DECi-hertz Interferometer Gravitational Wave Observatory (DECIGO) is a future mission for a space-borne laser interferometer. DECIGO has 1,000-km-long arm cavities mainly to detect the primordial gravitational waves (PGW) at lower frequencies around 0.1 Hz. Observations in the electromagnetic spectrum have lowered the bounds on the upper limit of PGW energy density ($\Omega_{\rm gw} \sim 10^{-15} \to 10^{-16}$). As a result, DECIGO's target sensitivity, which is mainly limited by quantum noise, needs further improvement. To maximize the feasibility of detection while constrained by DECIGO's large diffraction loss, a quantum locking technique with an optical spring was theoretically proposed to improve the signal-to-noise ratio of the PGW. In this paper, we experimentally verify one key element of the optical-spring quantum locking: sensitivity optimization by completing the square of multiple detector outputs. This experiment is operated on a simplified tabletop optical setup with classical noise simulating quantum noise. We succeed in getting the best of the sensitivities with two different laser powers by the square completion method.

Photothermal effect in macroscopic optomechanical systems with an intracavity nonlinear optical crystal.

Intracavity squeezing is a promising technique that may improve the sensitivity of gravitational wave detectors and cool optomechanical oscillators to the ground state. However, the photothermal effect may modify the occurrence of optomechanical coupling due to the presence of a nonlinear optical crystal in an optical cavity. We propose a novel method to predict the influence of the photothermal effect by measuring the susceptibility of the optomechanical oscillator and identifying the net optical spring constant and photothermal absorption rate. Using this method, we succeeded in precisely estimating parameters related to even minor photothermal effects, which could not be measured using a previously developed method.

Tunable mechanical-mode coupling based on nanobeam-double optomechanical cavities

Tunable coupled mechanical resonators with nonequilibrium dynamic phenomena have attracted considerable attention in quantum simulations, quantum computations, and non-Hermitian systems. In this study, we propose tunable mechanical-mode coupling based on nanobeam-double optomechanical cavities. The excited optical mode interacts with both symmetric and antisymmetric mechanical supermodes and mediates coupling at a frequency of approximately 4.96 GHz. The mechanical-mode coupling is tuned through both optical spring and gain effects, and the reduced coupled frequency difference in non-Hermitian parameter space is observed. These results benefit research on the microscopic mechanical parity–time symmetry for topology and on-chip high-sensitivity sensors.

Angular trapping of a linear-cavity mirror with an optical torsional spring

Optomechanical systems have attracted intensive attention in various physical experiments. With an optomechanical system, the displacement of or the force acting on a mechanical oscillator can be precisely measured by utilizing optical interferometry. As a mechanical oscillator, a suspended mirror is often used in over a milligram scale optomechanical systems. However, the tiny suspended mirror in a linear cavity can be unstable in its yaw rotational degree of freedom due to optical radiation pressure. This instability curbs the optical power that the cavity can accumulate in it and imposes a limitation on the sensitivity. Here, we show that the optical radiation pressure can be used to trap the rotational motion of the suspended mirror without additional active feedback control when the $g$ factors of the cavity are negative and one mirror is much heavier than the other one. Furthermore, we demonstrate experimentally the validity of the trapping. We measured the rotational stiffness of a suspended tiny mirror with various intracavity power. The result indicates that the radiation pressure of the laser beam inside the cavity actually works as a positive restoring torque. Moreover, we discuss the feasibility of observing quantum radiation pressure fluctuation with our experimental setup as an application of our trapping configuration.

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.

Improving force sensitivity by amplitude measurements of light reflected from a detuned optomechanical cavity

The measurement of weak continuous forces exerted on a mechanical oscillator is a fundamental problem in various physical experiments. It is fundamentally impeded by quantum back-action from the meter used to sense the displacement of the oscillator. In the context of interferometric displacement measurements, we here propose and demonstrate the working principle of a scheme for coherent back-action cancellation. By measuring the amplitude quadrature of the light reflected from a detuned optomechanical cavity inside which a stiff optical spring is generated, back-action can be cancelled in a narrow band of frequencies. This method provides a simple way to improve the sensitivity in experiments limited by quantum back-action without injection of squeezed light or stable homodyne readout.

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.