Suspended Mirrors Research Articles

Nanomechanical Crystalline AlN Resonators with High Quality Factors for Quantum Optoelectromechanics.

High-quality factor (Qm) mechanical resonators are crucial for applications where low noise and long coherence time are required, as mirror suspensions, quantum cavity optomechanical devices, or nanomechanical sensors. Tensile strain in the material enables the use of dissipation dilution and strain engineering techniques, which increase the mechanical quality factor. These techniques have been employed for high-Qm mechanical resonators made from amorphous materials and, recently, from crystalline materials such as InGaP, SiC, and Si. A strained crystalline film exhibiting substantial piezoelectricity expands the capability of high-Qm nanomechanical resonators to directly utilize electronic degrees of freedom. In this work, nanomechanical resonators with Qm up to 2.9 × 107 made from tensile-strained 290 nm-thick AlN are realized. AlN is an epitaxially-grown crystalline material offering strong piezoelectricity. Nanomechanical resonators that exploit dissipation dilution and strain engineering to reach a Qm × fm-product approaching 1013 Hz at room temperature are demonstrated. A novel resonator geometry is realized, triangline, whose shape follows the Al-N bonds and offers a central pad patterned with a photonic crystal. This allows to reach an optical reflectivity above 80% for efficient coupling to out-of-plane light. The presented results pave the way for quantum optoelectromechanical devices at room temperature based on tensile-strainedAlN.

Temperature Dependence of the Mechanical Dissipation of Gallium Bonds for Use in Gravitational Wave Detectors.

The mirror suspensions in gravitational wave detectors demand low mechanical loss jointing to ensure good enough detector performance and to enable the detection of gravitational waves. Hydroxide catalysis bonds have been used in the fused silica suspensions of the GEO600, Advanced LIGO, and Advanced Virgo detectors. Future detectors may use cryogenic cooling of the mirror suspensions and this leads to a potential change of mirror material and suspension design. Other bonding techniques that could replace or be used alongside hydroxide catalysis bonding are of interest. A design that incorporates repair scenarios is highly desirable. Indeed, the mirror suspensions in KAGRA, which is made from sapphire and operated at cryogenic temperatures, have used a combination of hydroxide catalysis bonding and gallium bonding. This Letter presents the first measurements of the mechanical loss of a gallium bond measured between 10K and 295K. It is shown that the loss, which decreases with temperature down to the level of (1.8±0.3)×10^{-4} at 10K, is comparable to that of a hydroxide catalysis bond.

Dissipative and dispersive cavity optomechanics with a frequency-dependent mirror

An optomechanical microcavity can considerably enhance the interaction between light and mechanical motion by confining light to a subwavelength volume. However, this comes at the cost of an increased optical loss rate. Therefore, microcavity-based optomechanical systems are placed in the unresolved-sideband regime, preventing sideband-based ground-state cooling. A pathway to reduce optical loss in such systems is to engineer the cavity mirrors, i.e., the optical modes that interact with the mechanical resonator. In our work, we analyze such an optomechanical system, whereby one of the mirrors is strongly frequency dependent, i.e., a suspended Fano mirror. This optomechanical system consists of two optical modes that couple to the motion of the suspended Fano mirror. We formulate a quantum-coupled-mode description that includes both the standard dispersive optomechanical coupling as well as dissipative coupling. We solve the Langevin equations of the system dynamics in the linear regime showing that ground-state cooling from room temperature can be achieved even if the cavity is not in the resolved-sideband regime, but achieves effective sideband resolution through strong-optical-mode coupling. Importantly, we find that the cavity output spectrum needs to be properly analyzed with respect to the effective laser detuning to infer the phonon occupation of the mechanical resonator. Our work also predicts how to reach the regime of nonlinear quantum optomechanics in a Fano-based microcavity by engineering the properties of the Fano mirror. Published by the American Physical Society 2024

Simulation of crucible-free growth of monocrystalline silicon fibres for mirror suspension in gravitational-wave detectors

Monocrystalline silicon fibres are a promising candidate to support the test mass needed in gravitational-wave detectors. Stringent requirements on material purity and fibre diameter underscore the imperative for crucible-free crystal growth methods, such as Pedestal and Floating Zone techniques. We developed a multiphysics numerical model that simulates the coupling between electromagnetism, heat transfer, fluid flow and phase boundaries for these techniques within the same mathematical framework, which facilitates direct comparisons of both growth techniques. Model validation was addressed using experimental measurements and other simulation tools, and satisfactory agreement was obtained. Our findings indicate that electromagnetic forces are the primary mechanism responsible for stirring the molten silicon at small crystal diameters. The resulting fluid velocity develops slightly transient behaviour, although this has little impact on the phase boundary shapes. The understanding of the growth process enabled by the model will facilitate future optimization of crystal quality and diameter stability.

Temperature dependence of the thermal conductivity of hydroxide catalysis bonds between silicon substrates

Future generations of gravitational wave detectors plan to use cryogenics in order to further reduce thermal noise associated with the mirror test masses and their suspensions. It is important that the thermal conductivity of candidate materials for these mirror suspension systems, and any additional thermal resistance associated with the required bonding/jointing, is characterised. Results are presented here for composite single-crystal silicon substrates, with multiple hydroxide catalysis bonds present, in order to assess the thermal conductivity of the bond layers. An average bond thickness of nm is observed within the oxide-bond-oxide interfaces, with a calculated thermal conductivity rising from Wm−1K−1 across a temperature range of K. This confirms that the thermal conductance through hydroxide catalysis bonds, with geometries being considered for third generation gravitational wave detectors operating at 20 K or 125 K, would have a negligible impact on the required heat extraction for cryogenic operation. Therefore, the use of hydroxide catalysis bonding, as successfully demonstrated within room temperature gravitational wave detectors, remains an attractive solution for building future cryogenic instruments with reduced thermal noise and enhanced astrophysical reach.

Integrated microcavity optomechanics with a suspended photonic crystal mirror above a distributed Bragg reflector.

Increasing the interaction between light and mechanical resonators is an ongoing endeavor in the field of cavity optomechanics. Optical microcavities allow for boosting the interaction strength through their strong spatial confinement of the optical field. In this work, we follow this approach by realizing a sub-wavelength-long, free-space optomechanical microcavity on-chip fabricated from an (Al,Ga)As heterostructure. A suspended GaAs photonic crystal mirror is acting as a highly reflective mechanical resonator, which together with a distributed Bragg (DBR) reflector forms an optomechanical microcavity. We demonstrate precise control over the microcavity resonance by change of the photonic crystal parameters. We find that the microcavity mode can strongly couple to the transmissive modes of the DBR. The interplay between the microcavity mode and a guided resonance of the photonic crystal modifies the cavity response and results in a stronger dynamical backaction on the mechanical resonator compared to conventional optomechanical dynamics.

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.

Instrumented baffle for the Advanced Virgo input mode cleaner end mirror

A novel instrumented baffle surrounding the suspended end mirror in the input mode cleaner cavity of the Virgo interferometer was installed in spring 2021. Since then, the device has been regularly operated in the experiment and the obtained results indicate a good agreement with simulations of the stray light inside the optical cavity. The baffle will operate in the upcoming O4 observation run, serving as a demonstrator of the technology designed to instrument the baffles in front of the main mirrors in time for O5. In this paper we present a detailed description of the baffle design, including mechanics, front-end electronics, data acquisition, as well as optical and vacuum tests, calibration and installation procedures, and performance results.

Optomechanical sideband asymmetry explained by stochastic electrodynamics

Within the framework of stochastic electrodynamics we derive the noise spectrum of a laser beam reflected from a suspended mirror. The electromagnetic field follows Maxwell's equations and is described by a deterministic part that accounts for the laser field and a stochastic part that accounts for thermal and zero-point background fluctuations.Likewise, the mirror motion satisfies Newton's equation of motion and is composed of deterministic and stochastic parts, similar to a Langevin equation. We consider a photodetector that records the power of the field reflected from the mirror interfering with a frequency-shifted reference beam (heterodyne interferometry). We theoretically show that the power spectral density of the photodetector signal is composed of four parts: (i) a deterministic term with beat notes, (ii) shot noise, (iii) the actual heterodyne signal of the mirror motion and (iv) a cross term resulting from the correlation between measurement noise (shot noise) and backaction noise (radiation pressure shot noise). The latter gives rise to the Raman sideband asymmetry observed with ultracold atoms, cavity optomechanics and with levitated nanoparticles. Our classical theory fully reproduces experimental observations and agrees with the results obtained by a quantum theoretical treatment.

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.

Measurement of the stray light in the Advanced Virgo input mode cleaner cavity using an instrumented baffle

A new instrumented baffle was installed in Spring 2021 at Virgo surrounding the suspended mirror in the input mode cleaner triangular cavity. It serves as a demonstrator of the technology designed to instrument the baffles in the main arms in the near future. We present, for the first time, results on the measured scattered light distribution inside the cavity as determined by the new device using data collected between May and July 2021, with Virgo in commissioning phase and operating with an input laser power in the cavity of 28.5 W. The sensitivity of the baffle is discussed and the data is compared to scattered light simulations.

Improving the stability of frequency-dependent squeezing with bichromatic control of filter cavity length, alignment, and incident beam pointing

Frequency dependent squeezing is the main upgrade for achieving broadband quantum noise reduction in upcoming observation runs of gravitational wave detectors. The proper frequency dependence of the squeezed quadrature is obtained by reflecting squeezed vacuum from a Fabry-Perot filter cavity detuned by half of its linewidth. However, since the squeezed vacuum contains no classical amplitude, co-propagating auxiliary control beams are required to achieve the filter cavity's length, alignment, and incident beam pointing stability. In our frequency dependent squeezing experiment at the National Astronomical Observatory of Japan, we used a control beam at a harmonic of squeezed vacuum wavelength and found visible detuning variation related to the suspended mirrors angular drift. These variations can degrade interferometer quantum noise reduction. We investigated various mechanisms that can cause the filter cavity detuning variation. The detuning drift is found to be mitigated sufficiently by fixing the incident beam pointing and applying filter cavity automatic alignment. It was also found that there is an optimal position of the beam on the filter cavity mirror that helps to reduce the detuning fluctuations. Here we report a stabilized filter cavity detuning variation of less than 10$\,$Hz compared to the 113$\,$Hz cavity linewidth. Compared to previously published results [Phys. Rev. Lett. 124, 171101 (2020)], such detuning stability would be sufficient to make filter cavity detuning drift induced gravitational wave detector detection range fluctuation reduce from $11\%$ to within $2\%$.

Observing the optical modes of parametric instability.

Parametric instability (PI) is a phenomenon that results from resonant interactions between optical and acoustic modes of a laser cavity. This is problematic in gravitational wave interferometers where the high intracavity power and low mechanical loss mirror suspension systems create an environment where three-mode PI will occur without intervention. We demonstrate a technique for real-time imaging of the amplitude and phase of the optical modes of PI yielding, to the best of the authors' knowledge, the first ever images of this phenomenon which could form part of active control strategies for future detectors.

Strained crystalline nanomechanical resonators with quality factors above 10 billion

In strained mechanical resonators, the concurrence of tensile stress and geometric nonlinearity dramatically reduces dissipation. This phenomenon, called dissipation dilution, is employed in mirror suspensions of gravitational-wave interferometers and at the nanoscale, where soft clamping and strain engineering have allowed extremely high quality factors. However, these techniques have so far been applied only to amorphous materials, specifically Si3N4. Crystalline materials exhibit substantially lower intrinsic damping at cryogenic temperatures. Applying dissipation dilution engineering to strained crystalline materials could, therefore, enable extremely low loss nanomechanical resonators, as they combine low internal friction, high intrinsic strain and high yield strength. This potential has not yet been fully exploited. Here we demonstrate that single-crystal strained silicon—a material developed for high-mobility transistors—can be used to realize mechanical resonators with ultralow dissipation. We fabricate strained silicon nanostrings with high aspect ratios supporting megahertz mechanical modes with quality factors exceeding 1010 at 7 K, a tenfold improvement over values reported in Si3N4. We estimate a thermal-noise-limited force sensitivity of (5 ± 2) × 10–20 N Hz–1/2 at 7 K—approaching that of carbon nanotubes—and a heating rate of only 60 quanta per second. The low mass and high quality factors of our nanomechanical resonators make them particularly promising for quantum sensing and transduction. Soft clamping reduces the dissipation of nanomechanical resonators, but this method has been limited to amorphous materials. When applied in crystalline silicon, it enables resonators with quality factors beyond ten billion.

Large-scale Monolithic Fused-Silica Mirror Suspension for Third-Generation Gravitational-Wave Detectors

Thermal noise from the suspension fibers used in the mirror pendulums in current gravitational-wave detectors is a critical noise source. Future detectors will require improved suspension performance with the specific ability to suspend much heavier masses to reduce radiation pressure noise, while retaining good thermal noise performance. In this paper we propose and experimentally demonstrate a design for a large-scale fused-silica suspension, demonstrating its suitability for holding an increased mass of 160 kg. We demonstrate the concepts for improving thermal noise via longer suspension fibers supporting a higher static stress. We present a full thermal noise analysis of our prototype, meeting requirements for conceptual third-generation detector designs such as the high frequency interferometer of the Einstein Telescope, and closely approaching that required for Cosmic Explorer.

Ultralight dark matter searches with KAGRA gravitational wave telescope

Among various dark matter candidates, bosonic ultralight fields with masses below 1eV are well motivated. Recently, a number of novel approaches have been put forward to search for ultralight dark matter candidates using laser interferometers at various scales. Those include our proposals to search for axion-like particles (ALPs) and vector fields with laser interferometric gravitational wave detectors. ALPs can be searched for by measuring the oscillating polarization rotation of laser light. Massive vector fields weakly coupled to the standard model sector can also be searched for by measuring the oscillating forces acting on the suspended mirrors of the interferometers. In this paper, the current status of the activities to search for such ultralight dark matter candidates using a gravitational wave detector in Japan, KAGRA, is reviewed. The analysis of data from KAGRA’s observing run in 2020 to search for vector dark matter, and the installation of polarization optics to the arm cavity transmission ports of the interferometer to search for ALPs in future observing runs are underway.

Squeezed light at 2128 nm for future gravitational-wave observatories

All gravitational-wave observatories (GWOs) have been using the laser wavelength of 1064 nm. Ultra-stable laser devices are at the sites of GEO 600, Kagra, LIGO, and Virgo. Since 2019, not only GEO 600, but also LIGO and Virgo have been using separate devices for squeezing the uncertainty of the light, so-called squeeze lasers. The sensitivities of future GWOs will strongly gain from reducing the thermal noise of the suspended mirrors, which involves shifting the wavelength into the 2 µm region. This Letter aims to reuse the existing high-performance lasers at 1064 nm. Here we report the realization of a squeeze laser at 2128 nm that uses pump light at 1064 nm. We achieve the direct observation of 7.2 dB of squeezing as the first step at megahertz sideband frequencies. The squeeze factor achieved is mainly limited by the photodiode's quantum efficiency, which we estimated to (92±3)%. Reaching larger squeeze factors seems feasible also in the required audio and sub-audio sideband, provided photo diodes with sufficiently low dark noise will be available. Our result promotes 2128 nm as the new, to the best of our knowledge, cost-efficient wavelength of GWOs.

LIGO’s quantum response to squeezed states

Gravitational Wave interferometers achieve their profound sensitivity by combining a Michelson interferometer with optical cavities, suspended masses, and now, squeezed quantum states of light. These states modify the measurement process of the LIGO, VIRGO and GEO600 interferometers to reduce the quantum noise that masks astrophysical signals; thus, improvements to squeezing are essential to further expand our gravitational view of the universe. Further reducing quantum noise will require both lowering decoherence from losses as well more sophisticated manipulations to counter the quantum back-action from radiation pressure. Both tasks require fully understanding the physical interactions between squeezed light and the many components of km-scale interferometers. To this end, data from both LIGO observatories in observing run three are expressed using frequency-dependent metrics to analyze each detector's quantum response to squeezed states. The response metrics are derived and used to concisely describe physical mechanisms behind squeezing's simultaneous interaction with transverse-mode selective optical cavities and the quantum radiation pressure noise of suspended mirrors. These metrics and related analysis are broadly applicable for cavity-enhanced optomechanics experiments that incorporate external squeezing, and -- for the first time -- give physical descriptions of every feature so far observed in the quantum noise of the LIGO detectors.

Investigation of crackling noise in the vibration isolation systems of the KAGRA gravitational wave detector

Gravitational wave detectors, such as KAGRA, require complex mirror suspension systems to reach high sensitivity. One particular concern in these suspensions is the presence of crackling noise, where motion of the steel crystal structure disturbs material defects, causing impulse force release and exciting mirror motion. Crackling in the Geometric Anti Spring filters (GAS) in KAGRA's suspension system could introduce noise in the gravitational wave detection band. We investigate crackling noise in a miniature GAS with a low-frequency cyclical stress. We developed a scaling law between miniature and KAGRA GAS. Applying experimental results to the scaling law allows us to estimate the upper limit of crackling noise in KAGRA. It is found that crackling noise should be below the target sensitivity for gravitational waves above 60 Hz.

Approaching the motional ground state of a 10-kg object.

The motion of a mechanical object, even a human-sized object, should be governed by the rules of quantum mechanics. Coaxing them into a quantum state is, however, difficult because the thermal environment masks any quantum signature of the object's motion. The thermal environment also masks the effects of proposed modifications of quantum mechanics at large mass scales. We prepared the center-of-mass motion of a 10-kilogram mechanical oscillator in a state with an average phonon occupation of 10.8. The reduction in temperature, from room temperature to 77 nanokelvin, is commensurate with an 11 orders-of-magnitude suppression of quantum back-action by feedback and a 13 orders-of-magnitude increase in the mass of an object prepared close to its motional ground state. Our approach will enable the possibility of probing gravity on massive quantum systems.