Measuring gravity with small test masses is a key program for both tabletop fundamental physics and commercial sensor technology. Here, we explore inertial sensing with a 10 Hz, 0.1 mg torsion pendulum with an ultralow damping rate of 10 mu Hz and a thermal acceleration sensitivity of similar to 1 ng0/root Hz (g(0) = 9.8 ms-2), formed by suspending a Si microchip from a high-stress (sigma approximate to 1GPa) Si3N4 nanoribbon. Previous studies of this device focused on its operation as a semi-absolute clock gravimeter, demonstrating bias stabilities as low as 500 ng(0) at 1000 s by frequency tracking. In this work, we operate it as spring-mass accelerometer read out with an optical lever. We demonstrate similar to 100ng(0)/root Hz sensitivity between 0.1 and 100 Hz (as little as 40ng(0)/root Hz near resonance), limited by vibration isolation and thermal drift-sufficient to observe the ocean wave microseism from our laboratory in Tucson. We present progress towards improved sensitivity based on cross-spectral analysis with a commercial seismometer, measurement-based feedback cooling, and active vibration isolation. Longer term goals include measuring the Earth's tides and integration with a source mass for short-range gravity measurements.

Flexures in torsion balances and precision mechanisms often exhibit extreme aspect ratios, causing exponential scaling in Euler-Bernoulli bending models. Standard double-precision arithmetic cannot resolve the small initial conditions required for accurate solutions. This paper presents a semi-analytic method combining an efficient 1D bending model with adaptive Runge-Kutta-Fehlberg integration in arbitrary precision that overcomes this limitation. A quantitative criterion is established when extended precision becomes necessary. Furthermore, an open-source Python implementation is provided, which remains stable even for flexures with extreme aspect ratios.

Chip-scale optomechanical devices are driving the miniaturization of inertial sensors and next generation fundamental physics experiments. However, precision at the theoretical limit is often unattainable due to extraneous vibrations. One solution is tailoring the device to isolate a degree of freedom from the environment while maintaining coupling to the signal of interest. To this end, we introduce a dual milligram-mass torsion oscillator, formed by mass loading a strained silicon nitride nanoribbon. The antisymmetric torsion mode suppresses vibrations by over an order of magnitude to achieve a thermally limited torque sensitivity of $10^{-18}$ Nm/$\sqrt{\rm Hz}$ while maintaining ultralow loss. We demonstrate the sensing ability by detecting an optical radiation pressure torque of $10^{-16}$ Nm over a 30 Hz bandwidth. We also characterize the device for frequency-based gravimetry, demonstrating $10^{-6}g_0$ ($g_0=9.8$ $\rm m s^{-2}$) precision in 30 seconds with an oscillation amplitude of only 100 $μ$rad. This device demonstrates a technique for overcoming vibration noise, with broad implications for optomechanical sensing from commercial applications to fundamental physics experiments.

Measurement of mutual gravitation on laboratory scales is an outstanding challenge and a prerequisite to probing theories of quantum gravity. A leading technology in tabletop gravity experiments is the torsion balance, with limitations due to thermal decoherence. Recent demonstrations of lithographically defined suspensions in thin-film silicon nitride with macroscale test masses suggest a path forward, as torsion pendulums dominated by gravitational stiffness may achieve higher mechanical quality factors through dilution of material losses. Here, we demonstrate a 250 & micro;m & times; 5 mm & times; 1.8 & micro;m torsion fiber supporting 87 g and forming a Cavendish-style torsion pendulum with tungsten test masses that is the largest thin-film silicon-nitride-based oscillator to date. Torsion pendulums with thin-film nanofabricated suspensions provide a test bed for near-term tabletop experiments probing classical and quantum gravitational interaction between oscillators.

We derive a nonlinear equation of motion for a chip-scale pendulum comprising a thick plate suspended from a tensioned nanoribbon. Recently, we explored the use of such a device as a clock gravimeter, exploiting the parametric coupling of its frequency to the local acceleration of gravity and demonstrating micro-g resolution with a silicon nitride prototype. Here we consider the restoring torque arising from the mid-plane stretching of the nanoribbon, finding it is a hardening spring that can be used to counteract the softening of gravitational torques, reducing parametric frequency noise and extending the range of isochronous pendulation. Using the method of multiple scales, we predict that parametric frequency-amplitude coupling can be driven to zero by exploiting fabrication tolerances available using modern nanolithography.

Measuring gravitational interactions on sub-100-mu m length scales offers a window into physics beyond the Standard Model. However, short-range gravity experiments are limited by the ability to position sufficiently massive objects to within small separation distances. Here we propose mass-loaded silicon nitride ribbons as a platform for testing the gravitational inverse square law at separations currently inaccessible with traditional torsion balances. These microscale torsion resonators benefit from low thermal noise due to strain-induced dissipation dilution while maintaining compact size (< 100 g) to allow close approach. Considering an experiment combining a 40 mu g torsion resonator with a source mass of comparable size (130 mu g) at separations down to 25 mu m, and including limits from thermomechanical noise and systematic uncertainty, we predict these devices can set novel constraints on Yukawa interactions within the 1-100 mu m range.

We show that torsion resonators can experience massive dissipation dilution due to nanoscale strain, and draw a connection to a century-old theory from the torsion balance community which suggests that a simple torsion ribbon is naturally soft-clamped. By disrupting a commonly held belief in the nanomechanics community, our findings invite a rethinking of strategies towards quantum experiments and precision measurement with nanomechanical resonators. For example, we revisit the optical lever technique for monitoring displacement, and find that the rotation of a strained nanobeam can be resolved with an imprecision smaller than the zero-point motion of its fundamental torsional mode, without the use of a cavity or interferometric stability. We also find that a strained torsion ribbon can be mass-loaded without changing its $Q$ factor. We use this strategy to engineer a chip-scale torsion balance whose resonance frequency is sensitive to micro-$g$ fluctuations of the local gravitational field. Enabling both these advances is the fabrication of high-stress Si$_3$N$_4$ nanobeams with width-to-thickness ratios of $10^4$ and the recognition that their torsional modes have $Q$ factors scaling as their width-to-thickness ratio squared, yielding $Q$ factors as high as $10^8$ and $Q$-frequency products as high as $10^{13}$ Hz.

Torsion resonators loom large in the history of precision measurement; however their role in modern nanomechanics experiments is limited. In this presentation I will describe a new class of ultra-high-Q torsion nanoresonators fashioned from strained nanoribbons, and how they might be used for imaging-based quantum optomechanics experiments and chip-scale intertial sensing. Specifically, using an optical lever, we have resolved the rotation of one such nanoribbon with an imprecision 100 times smaller than the zero-point motion of its fundamental torsion mode, paving the way towards observation of radiation pressure shot noise in torque. We have also found that a strained nanoribbon can be mass-loaded without changing its torsional Q. We have used this strategy to engineer a chip-scale torsion pendulum with an ultralow damping rate of 7 micro-hertz, sufficient to resolve micro-g fluctuations of the local gravitational field.

We present a new class of ultra-high-Q nanomechanical resonators based on torsion modes of high-stress nanoribbons, and explore their application for quantum optomechanics experiments and precision optomechanical sensing. Specifically, we show that nanoribbons made of high stress silicon nitride support torsion modes which are naturally soft-clamped, yielding dissipation dilution factors as high as 10^4 and Q factors as high as 10^8 for the fundamental mode. We show that these modes can be read out with optical lever measurements with an imprecision below that at the standard quantum limit, paving the way for a new branch of torsional quantum optomechanics. We also show that nanoribbons can be mass-loaded without changing their torsional Q factor. We use this strategy to engineer a chip-scale torsion balance with an damping rate of 10 micro-hertz. We use this torsion balance as a clock gravimeter to sence micro-g fluctuation in the local gravitational field strength.

We show that torsion modes of strained nanoribbons can have ultrahigh Q-factors, are naturally soft-clamped, and can be mass-loaded without changing their Q. We leverage these insights to realize sub-SQL optical lever measurements and chip-scale torsion pendula with µHz damping rates.

Optomechanical accelerometers offer in situ traceability to the international system of units through laser interferometry, providing an alternative to a calibration chain using instrumented shakers. Here, we examine the ‘self-calibrating’ property of a prototype optomechanical accelerometer for use as a seismic reference. We report the optomechanically derived sensitivity of the accelerometer and compare this in situ calibrated output to input accelerations from an instrumented shaker, finding agreement to be within ±1%. The comparison spanned frequencies between 3 Hz and 30 Hz, and for sinusoidal accelerations with amplitudes ranging from 0.01 m s −2 to 0.6 m s −2 . These results are evidence that optomechanically derived sensitivity calibration can be equivalent to established international methods for primary calibration.

A new paradigm in laser power metrology has recently evolved. The measurement of photon pressure forces from the reflection of a laser from a high reflectivity mirror provides a means to quantify optical power in a fashion similar to methods used to realize the mass unit in the redefined SI. Because photon pressure forces are typically quite small, an electrostatic force balance (EFB) can be effectively used to interconvert between force and laser power within the International System of Units (SI). In this work, a portable version of the EFB is constructed and tested. The balance will be used to measure a photon pressure equivalent to 10 kilowatts of laser power (approximately 60 micronewtons) with an uncertainty on the order of 0.01 %. A preliminary demonstration shows sufficient resolution for the required application.

A tabletop-sized Kibble balance (KIBB-g1) designed to directly realize mass at the gram-level range with uncertainties on the order of parts in 10(6) has been developed at the National Institute of Standards and Technology (NIST). The masses of a nominally 5 g and 1 g weight were determined with standard uncertainties of 9.0 g and 6.7 g, respectively. The corresponding relative uncertainties are and . The construction of the instrument, capabilities, and full uncertainty budgets are presented in this manuscript.

The Consultative Committee for Mass and related quantities (CMM), of the International Committee for Weights and Measures (CPIM), has recently declared the readiness of the community to support the redefinition of the international system of units (SI) at the next meeting of the General Conference on Weights and Measures (CGPM) scheduled for November, 2018. Such redefinition will replace the International Prototype of the Kilogram (IPK), as the definition and sole primary realization of the unit of mass, with a definition involving the Planck constant, h. This redefinition in terms of a fundamental constant of nature will enable widespread primary realizations not only of the kilogram but also of its multiples and sub-multiples, best to address the full range of practical needs in the measurement of mass. We review and discuss the statistical models and statistical data reductions, uncertainty evaluations, and substantive arguments that support the verification of several technical preconditions for the redefinition that the CCM has established, and whose verification the CCM has affirmed. These conditions relate to the accuracy and mutual consistency of qualifying measurement results. We review also an issue that has surfaced only recently, concerning the convergence toward a stable value, of the historical values that the Task Group on Fundamental Constants of the committee on Data for Science and Technology CODATA-TGFC has recommended for h over the years, even though the CCM has not deemed this issue to be relevant. We conclude that no statistically significant trend can be substantiated for these recommended values, but note that cumulative consensus values that may be derived from the historical measurement results for h seem to have converged while continuing to exhibit fluctuations that are typical of a process in statistical control. Finally, we argue that the most recent consensus value derived from the best measurements available for h, obtained using either a Kibble balance or the XRCD method, is reliable and has uncertainty no larger than the uncertainties surrounding the current primary and secondary realizations of the unit of mass, hence that no credible technical impediments stand in the way of the redefinition of the unit of mass in terms of a fixed value of h.

The fourth generation Kibble balance at the National Institute of Standards and Technology (NIST) has been operational and used to measure the value of the Planck constant from Fall 2015 to Spring 2017. Since then, researchers have been working on upgrades and checking the robustness of the experiment in preparation for the redefinition of the SI.

The definition of the kilogram in the International System of Units (SI) is expected to be revised in 2018. The present definition of the kilogram, the mass of the International Prototype of the Kilogram (IPK), adopted in 1889, would then be replaced by a definition based on a fixed numerical value of the Planck constant. The Consultative Committee for Mass and Related Quantities has requested that, as one of the essential steps before the redefinition, a comparison of kilogram realizations based on future realization methods, Kibble(9) balances and x-ray crystal density (XRCD) experiments, be organized. This comparison was carried out during 2016 in the form of a 'Pilot Study'. One aim of the study was to determine the uniformity of mass dissemination after the redefinition by comparing mass calibrations based on different future realization experiments. Another aim was to test the continuity of the mass unit across the redefinition by comparing mass calibrations based on Kibble balances and XRCD experiments with those based on the IPK. This paper describes the organization of the comparison and presents its results.

Researchers at the National Institute of Standards and Technology (NIST) have measured the value of the Planck constant to be h = 6.626 069 934(89) x 10(-34)J s (relative standard uncertainty 13 x 10(-9)). The result is based on over 10 000 weighings of masses with nominal values ranging from 0.5 kg to 2 kg with the Kibble balance NIST-4. The uncertainty has been reduced by more than twofold relative to a previous determination because of three factors: (1) a much larger data set than previously available, allowing a more realistic, and smaller, Type A evaluation; (2) a more comprehensive measurement of the back action of the weighing current on the magnet by weighing masses up to 2 kg, decreasing the uncertainty associated with magnet non-linearity; (3) a rigorous investigation of the dependence of the geometric factor on the coil velocity reducing the uncertainty assigned to time-dependent leakage of current in the coil.

All measurements performed in science and industry are based on the International System of Units, the SI. It has been proposed to revise the SI following an approach which was implemented for the redefinition of the unit of length, the metre, namely to define the SI units by fixing the numerical values of so-called defining constants, including c, h, e, k and NA. We will discuss the reasoning behind the revision, which will likely be put into force in 2018. Precision engineering was crucial to achieve the required small measurement uncertainties and agreement of measurement results for the defining constants.

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