Ultra-high Precision Measurements Research Articles

Parametric control of quasi-zero stiffness mechanisms for vibration isolation at near-zero frequencies

Infra-frequency vibration, including near-zero frequencies, has become a critical limiting factor for developers of next-generation ultra-high precision measurement systems. Mechanisms involving quasi-zero stiffness show potential to solve this new vibration problem. An approach for designing a novel type of the mechanisms for this class is presented. An algorithm is developed and tested for numerical solution of nonlinear elasticity problem in designing the mechanism structural and parametric elements based on FEM models. The elements are spatially prestressed multi-layer designs of polymer composites for modeling elastic postbuckling in large and the effect of a “floating” binder. An algorithm and models following the Nelder-Mead method are used for optimizing the designs. Examples of Euler-beam-shaped composite elements under postbuckling demonstrate a qualitative leap in mechanisms design and efficiency, specifically, in terms of compactness, lightness, and strength. A dramatically expanded control range for the linear section of operating travel with quasi-zero stiffness is obtained. A damping threshold is evaluated, and an optimal type diagram of the mechanism is designed and enumerated as necessary conditions for vibration isolation at near-zero frequencies. The validity and effectiveness of the approach are demonstrated with the results of theoretical design and testing of the prototype for vibration isolation of the ultra-high precision optical system. The learning capability of the mechanisms is estimated by an adapted version of the Levenberg-Marquardt algorithm with stepwise refinement in the test mode using Rosenbrock’s function.

Optimizing frequency noise calibration and manipulation in an active feedback control loop

Frequency noise is a key limitation factor for frequency sensitive ultra-high precision measurement. An excellent methodology for its calibration is the error signal extracting from a cavity length locking process via Pound–Drever–Hall (PDH) technique, and also can be applied as a noise discriminator for active feedback control. However, the stabilized laser frequency noise performance was poor to meet the applications for ultra-high precision measurement, and no literature has analyzed the cause in detail. In this Letter, we found that various of noise floors in the in-loop sensing and modulation depth in the PDH error signal should be responsible for the poor noise performance. Meanwhile, differing from the theoretical prediction (1.08), the modulation depth in frequency noise feedback controlling should be optimized by simultaneously considering the detector’s gain and saturation power, cavity impedance matching, and control loop gain. In our case, it was fixed to be 0.17. The experimental results confirm our theoretical analysis well. Finally, the stabilized laser frequency noises are reduced to 10−1Hz/Hz for out-of-loop and 3×10−2Hz/Hz for in-loop. The results demonstrate an efficient settlement solution for active frequency noise feedback control.

Measurement and Characterization of Rotational Errors of Aerostatic Bearings in Subnanometer Accuracy.

Measuring the running accuracy of aerostatic bearings is challenging because of the high-precision requirements in rotational motion. This paper presents an ultra-high precision measurement method for aerostatic bearings using atomic force microscopy (AFM) as the displacement sensor. The Donaldson reversal method was used to separate the artifact form errors from the measurement results. A measurement system was developed with the integration of an AFM module. The effects of sensor nonlinearity, environmental noise, and structural vibration on the measurement results were effectively suppressed in the system. The experimental results show that the measurement achieves up to subnanometer accuracy.

Higher-Order Optomechanical Nonlinearity Based on the Mechanical Effect of Light

Nonlinear cavity optomechanics based on the mechanical effect of light has recently received considerable attention due to its potential applications in high-precision metrology. In this work, we theoretically studied the third-order optomechanical nonlinearity by using a perturbative approach, and an analytical solution is given, which can be extended to cases of higher-order optomechanical nonlinearity. Furthermore, the generation of a third-order sideband is analyzed in detail, and the results show that the amplitude of the third-order sideband shows a high dependence on the control field detuning, suggesting that the high-order nonlinear intensity can be enhanced by properly adjusting the detuning of the laser field rather than by a strong laser drive. In addition to providing insight into optomechanical nonlinearity, the analytical description of third-order optomechanical nonlinearity based on the mechanical effects of light may find applications in ultra-high precision measurement under low power conditions.

Orbital-angular-momentum beams-based Fizeau interferometer using the advanced azimuthal-phase-demodulation method

A stably acquiring and accurately demodulating interferogram is crucial for the interferometer to achieve ultra-high precision and sensitivity measurements. In this study, a robust orbital angular momentum (OAM) beams-based Fizeau interferometer is proposed and experimentally demonstrated, which is more compact and stable than the OAM interferometers with other structures due to the common optical path characteristic. In accordance with such an interferometric scheme, a phase-demodulation method operated in the domain of the OAM complex spectrum is also proposed and demonstrated in this study. In contrast to other phase-demodulation techniques, the proposed phase-demodulation technique neither requires phase shifters or phase modulators nor brings spectral leakage, which provides a robust alternative enabling to accurately and quickly extract the phase from the OAM interferogram. As a proof-of-concept of the proposed scheme, tiny displacements ranging from 0 to 800 nm were measured. The proposed OAM beams-based Fizeau interferometer and the corresponding azimuthal phase demodulation method may provide a feasible way for exploring further applications of the OAM-based interferometer in metrology.

Sub-femto-Newton sensing torsion pendulum for detection of light force.

Mechanical oscillators are widely used in many fields of physics, including ultrahigh precision measurements, gravity experiments, and optical mechanical systems. A sub-gram-scale silicon wafer is suspended by a tungsten wire with a diameter of 8 µm, forming a torsion pendulum to detect the laser radiation pressure. We demonstrate the application of a low-frequency, highly sensitive torsion pendulum for the measurement of light forces. In the feedback cooling state, the system exhibits a force sensitivity at the end of the pendulum close to 0.1 fN, approaches the thermal noise limit, and reaches the detection level of the laser radiation pressure of 60 nW.

Measurement method of spindle motion error based on composite laser target

The primary component of ultra-precision machining machines and measuring instruments is a high-precision spindle, and spindle error affects the accuracy of these machines. Traditional spindle error measurement methods often require a standard device as a reference, which inevitably reduces the accuracy of spindle error measurement, while the error separation technique is tedious and time-consuming. This study proposed a spindle error measurement method based on a composite laser target, which can measure the motion error of the spindle, including axial, radial, and tilt error in terms of five degrees of freedom. In this method, a composite laser target containing a laser point source and laser collimated beam was constructed and mounted on the spindle as a reference frame to mark the position of the spindle during rotation. Consequently, the error of the spindle was obtained via measurements of the position and angle of the composite laser target. Differential confocal microscopy technique was employed for measuring the axial position of the laser point source to obtain the axial error of the spindle, whereas the radial position was measured using a conventional microscope optical path to obtain the radial error of the spindle. Further, the angle of laser collimation was measured using a collimation measurement optical path to obtain the tilt error of the spindle. The measurement resolution of the proposed method for spindle error was verified through suitable experiments, yielding resolutions of 4 and 2 nm for axial and radial errors, respectively, and 0.2 μrad in case of tilt error. In addition, the method was tested on an air spindle to demonstrate the feasibility of using the method on machines. Thus, it was demonstrated that the proposed method can be used to obtain the spindle error by optical standard devices without additional error separation techniques, particularly for a spindle in ultra-high precision measurement equipment. Further, it facilitates real time monitoring or evaluation and calibration of the spindle error. This method is expected to serve several important practical applications in the field of ultra-precision machining and measurement. • Spindle error measurement method based on a composite laser target proposed. • Method eliminates reliance of accuracy on standard device used. • Motion error of spindle: axial, radial, tilt in terms of five degrees of freedom. • Resolution of proposed method verified through suitable experiments. • Practical applications in the field of ultra-precision machining and measurement.

Advances on Mode-Coupling Theories, Fabrication Techniques, and Applications of the Helical Long-Period Fiber Gratings: A Review

In this paper, we have briefly review the developing history and recent advances made with regard to helical long-period fiber gratings (HLPGs) in three aspects, i.e., the mode-coupling theories, the fabrication techniques, and the applications. It is shown that, due to the intrinsic helicity characteristics, which are especially suitable to control the loss, polarization, and orbit-angular-momentum (OAM) states of the light in optical fiber, HLPGs have recently attracted great research interest and have found various applications, such as the mode-converters, the torsion sensors, the band-rejection filters, wave plates, linear- and circular-light polarizers, and OAM mode generators, etc. It is believed that HLPGs and the HLPGs-based devices would find further applications to not only the fields of optical sensors and optical communication, but also other fields such as ultrahigh precision measurement, quantum optics, and biochemistry, etc.

Producing high intensity muon, antiproton beams and related physical researches in the HIAF accelerators

The high intensity frontier in particle physics would reveal physics beyond standard model, and is one of the most sensitive probing tools for particle physics at very high energy scales. In this paper, the high intensity frontier in particle physics is reviewed from the perspective of muon and antiproton physics and the experiments like charged lepton flavor violation are summarized. The possible utilization of HIAF accelerators in muon electron conversion searching and ultra-high precision measurement of muon anomalous magnetic moment is demonstrated. The preliminary analysis considering solely the signal statistics indicates that the muon and antiproton beams produced by the experimental platform of the HIAF accelerators would be quite competitive compared to the available beams around the world. By employing HIAF accelerators, the upper limit of muon electron conversion branching ratio could be pushed to the order of 10−19, and the measurement of muon anomalous magnetic moment would be potentially improved to the precision of 0.07 ppm.

Ultrahigh-precision measurement timing jitter based on self-reference source

Ultrahigh-precision measurement timing jitter based on self-reference source

Phase-Imaging Ion-Cyclotron-Resonance technique at the JYFLTRAP double Penning trap mass spectrometer

The Phase-Imaging Ion-Cyclotron-Resonance (PI-ICR) technique has been commissioned at the JYFLTRAP double Penning trap mass spectrometer. This technique is based on projecting the ion motion in the Penning trap onto a position-sensitive multichannel-plate ion detector. Mass measurements of stable 85 Rb $ ^{+}$ and 87 Rb $ ^{+}$ ions with well-known mass values show that relative uncertainties $ \Delta m/m \leq 7\cdot 10^{-10}$ are possible to reach with the PI-ICR technique at JYFLTRAP. The significant improvement both in resolving power and in precision compared to the conventional Time-of-Flight Ion Cyclotron Resonance technique will enable measurements of close-lying isomeric states and of more exotic isotopes as well as ultra-high precision measurements required, e.g., for neutrino physics. In addition, a new phase-dependent cleaning method based on the differences in the accumulated cyclotron motion phases has been demonstrated with short-lived 127 In $ ^{+}$ and 127m In $ ^{+}$ ions.

Status of the radio technique for cosmic-ray induced air showers

Radio measurements yield calorimetric information on the electromagnetic shower component around the clock. However, until recently it was not clear whether radio measurements can compete in accuracy with established night-time techniques like air-Cherenkov or air-fluorescence detection. Due to recent progress in the radio technique as well as in the understanding of the emission mechanisms, the performance of current radio experiments has significantly improved. Above 100 PeV, digital, state-of-the-art antenna arrays achieve a reconstruction accuracy for the energy similar to that of other techniques, and can provide an independent measurement of the absolute energy scale. Furthermore, radio measurements are sensitive to the mass composition of the primary particles: First, the position of the shower maximum can be reconstructed from the radio signal. Second, in combination with muon detectors the measurement of the electromagnetic component provides complementary information on the primary mass. Since the radio footprint is huge for inclined showers, and the radio signal does not suffer absorption in the atmosphere, future radio arrays either focus on inclined showers at the highest energy, or on ultra-high precision measurements with extremely dense arrays. This proceeding reviews the current status of radio experiments and simulations as well as future plans.

Generalized hyper-Ramsey resonance with separated oscillating fields

An exact generalization of the Ramsey transition probability is derived to improve ultra-high precision measurement and quantum state engineering when a particle is subjected to independently-tailored separated oscillating fields. The phase-shift accumulated at the end of the interrogation scheme offering high-level control of quantum states throughout various laser parameters conditions. The Generalized Hyper-Ramsey Resonance based on independent manipulation of interaction time, field amplitude, phase and frequency detuning is presented to increase the performance of next generation of atomic, molecular and nuclear clocks, to upgrade high resolution frequency measurement in Penning trap mass spectrometry and for a better control of light induced frequency shifts in matter wave interferometers or quantum information processing.

Quantum cascade laser frequency stabilization at the sub-Hz level

Quantum Cascade Lasers (QCL) are increasingly being used to probe the mid-infrared "molecular fingerprint" region. This prompted efforts towards improving their spectral performance, in order to reach ever-higher resolution and precision. Here, we report the stabilisation of a QCL onto an optical frequency comb. We demonstrate a relative stability and accuracy of 2x10-15 and 10-14, respectively. The comb is stabilised to a remote near-infrared ultra-stable laser referenced to frequency primary standards, whose signal is transferred via an optical fibre link. The stability and frequency traceability of our QCL exceed those demonstrated so far by two orders of magnitude. As a demonstration of its capability, we then use it to perform high-resolution molecular spectroscopy. We measure absorption frequencies with an 8x10-13 relative uncertainty. This confirms the potential of this setup for ultra-high precision measurements with molecules, such as our ongoing effort towards testing the parity symmetry by probing chiral species.

Precision limit of atomic magnetometers in the presence of spin-destruction collisions

Ultra sensitive detection and high precision measurement of magnetic fields have been of great importance for both fundamental physics and practical applications. Recent developments in the technology of atomic magnetometers have enabled the spin-exchange relaxation free (SERF) atomic magnetometers as the most sensitive devices for detecting and measuring static or quasi-static magnetic fields. In this paper, we analyze the effect of the most prominent relaxation mechanism (i.e., the spin-destruction collisions) on the precision of SERF magnetometers. For static magnetic fields, it is explicitly demonstrated how the spin-destruction collisions degrade the precision of the SERF magnetometers from the Heisenberg limit to the standard limit even with quantum resources being employed.

Note: High precision measurements using high frequency gigahertz signals.

Generalized lock-in amplifiers use digital cavities with Q-factors as high as 5 × 10(8) to measure signals with very high precision. In this Note, we show that generalized lock-in amplifiers can be used to analyze microwave (giga-hertz) signals with a precision of few tens of hertz. We propose that the physical changes in the medium of propagation can be measured precisely by the ultra-high precision measurement of the signal. We provide evidence to our proposition by verifying the Newton's law of cooling by measuring the effect of change in temperature on the phase and amplitude of the signals propagating through two calibrated cables. The technique could be used to precisely measure different physical properties of the propagation medium, for example, the change in length, resistance, etc. Real time implementation of the technique can open up new methodologies of in situ virtual metrology in material design.

Future large scale accelerator projects for particle physics

The discovery of a new particle, the properties of which are compatible with the expected Brout–Englert–Higgs scalar field in the Standard Model (SM), is the starting point of an intense program for studying its couplings. With this particle, all the components of the SM have now been unraveled. Yet, the existence of dark matter, baryon asymmetry of the Universe and neutrino mass call for new physics at an energy scale, which is not determined so far. Therefore, new large scale accelerators are needed to investigate these mysteries through ultra-high precision measurements and/or the exploration of higher energy frontiers. In the following, we discuss the various accelerator projects aimed at the achievement of the above objectives. The physics reach of these facilities will be briefly described as well as their main technical features and related challenges, highlighting the importance of accelerator R&D not only for the benefit of particle physics but also for other fields of research, and more generally for the society.

The trap design of PENTATRAP

A novel Penning trap tower consisting of five compensated cylindrical Penning traps is developed for the PENTATRAP mass spectrometer at the Max-Planck-Institut f\"ur Kernphysik in Heidelberg, Germany. An analytical expression for the electrostatic potential inside the trap tower is derived to calculate standard Penning trap properties like the compensation of anharmonicities and an orthogonal geometry of the trap electrodes. Since the PENTATRAP project described in the preceding article aims for ultra high-precision mass-ratio measurements of highly charged ions up to uranium, systematic effects for highly charged ions inside the trap tower are considered for the design process as well. Finally, a limit due to remaining anharmonic shifts at large amplitudes is estimated for the resulting geometry, which is important for phase-sensitive measurements of the reduced cyclotron frequency of the ions.

Magnetic Field Stabilization for 129Xe EDM Search Experiment

Magnetic field stabilization is a crucial condition parameter for many kinds of ultra-high precision measurements such as a search for an electric dipole moment (EDM). The instability of magnetic field strength often arises from the drift of current flow in a solenoid coil to generate the magnetic field. For our EDM search experiment with maser oscillating diamagnetic 129Xe atoms, we have developed a new stabilized current source based on a feedback system which is devised to correct the amount of current flow measured precisely with high-precision digital multimeter and standard resistor. Using this new current source, we have successfully reduced the drifts of coil current by at least a factor of 100 compared to commercially available current sources.

Magnetic Fields in B, (peculiar) A, and F stars - recent results from MuSiCoS Data

Ultra-high precision measurements of Stokes V Zeeman signatures have been obtained using the MuSiCoS spectropolarimeter (Donati et al. 1999) at the Pic du Midi obseravtory, aimed at studying the distribution of weak and tangled magnetic fields in F, A, and late-B type stars. We will discuss recent results obtained from these data, including the complete absence of magnetic fields (with an upper limit of around 25 G) in the non-Ap/Bp sample, and the relatively easy detection of magnetic fields in nearly all of the Ap/Bp stars. In addition polarimetric data in all four Stokes parameters ( I , V , Q , and U ) has been obtained for a sample of roAp stars, a pulsating subgroup within the magnetic Cp stars, with the aim to study vertical (stratification) and horizontal ( via Zeeman Doppler Imaging) abundance characteristics and their relation to the magnetic field geometry. We will present results of our data analysis, using the Least Squares Deconvolution (LSD) technique (Donati et al. 1997) and with the goal of determining the surface abundance distribution of rare earth elements and the magnetic field geometry of these stars.