Absolute Ranging with Time Delay Interferometry for Space-Borne Gravitational Wave Detection.

In future space-borne gravitational wave (GW) detectors, time delay interferometry (TDI) will be utilized to reduce the overwhelming noise, including the laser frequency noise and the clock noise etc., by time shifting and recombining the data streams in post-processing. The successful operation of TDI relies on absolute inter-satellite ranging with meter-level precision. In this work, we numerically and experimentally demonstrate a strategy for inter-satellite distance measurement. The distances can be coarsely determined using the technique of arm-locking ranging with a large non-ambiguity range, and subsequently TDI can be used for precise distance measurement (TDI ranging) by finding the minimum value of the power of the residual noises. The measurement principle is introduced. We carry out the numerical simulations, and the results show millimeter-level precision. Further, we perform the experimental verifications based on the fiber link, and the distances can be measured with better than 0.05 m uncertainty, which can well satisfy the requirement of time delay interferometry.

Time delay interferometry with a transfer oscillator.

In this work, we experimentally perform time delay interferometry by using a transfer oscillator, which is capable of reducing the laser frequency noise and the clock noise simultaneously in the post processing. The iodine frequency reference is coherently downconverted to the microwave frequency using a laser frequency comb. The residual noise of the downconversion network is 5 × 10-6Hz/Hz1/2 at 0.7 mHz, and 4 × 10-6Hz/Hz1/2 at 0.1 Hz, indicating high homology between the optical frequency and the microwave frequency. We carry out time delay interferometry with the aid of the electrical delay module, which can introduce large time delays. The results show that the laser frequency noise and the clock noise can be reduced simultaneously by ten and three orders of magnitude, respectively, in the frequency band from 0.1 mHz to 0.1 Hz. The performance of the noise reduction can reach 6 × 10-8Hz/Hz1/2 at 0.1 mHz, and 7 × 10-7Hz/Hz1/2 at 1 mHz, meeting the requirements of the space-borne gravitational wave detection. Our work will be able to offer an alternative method for the frequency comb-based time delay interferometry in the future space-borne gravitational wave detectors.

Weak-Light Phase-Locking Time Delay Interferometry with Optical Frequency Combs.

In the future space-borne gravitational wave (GW) detector, the optical transponder scheme, i.e., the phase-locking scheme, will be utilized so as to maintain the signal-to-noise ratio (SNR). In this case, the whole constellation will share one common laser equivalently, which enables the considerable simplification of time delay interferometry (TDI) combinations. Recently, and remarkably, the unique combination of TDI and optical frequency comb (OFC) has shown a bright prospect for the future space-borne missions. When the laser frequency noise and the clock noise are synchronized using OFC as the bridge, the data streams will be reasonably simplified. However, in the optical transponder scheme, the weak-light phase-locking (WLPL) loops could bring additional noises. In this work, we analyze the phase-locking scheme with OFC and transfer characteristics of the noises including the WLPL noise. We show that the WLPL noise can be efficiently reduced by using the specific TDI combination, and the cooperation of phase-locking and frequency combs can greatly simplify the post-processing.

Constraining the Symmetron Model with the HUST-2020 Torsion Pendulum Experiment.

The search for dynamically screening the coupling between the scalar field and matter in high-density environment is achievable with the symmetron model. The high-accuracy and short-range gravity experiment is proposed to test the symmetron model. In this Letter, the data of the HUST-2020 torsion pendulum experiment testing the inverse-square law at submillimeter range is analyzed to constrain the symmetron model. The results show that the HUST-2020 experiment is uniquely sensitive to probe the symmetron model with a mass scale of µ=7.2×10^{-3} eV, and the self-coupling parameter λ≲105 is excluded at mass scale M=0.3 TeV. Especially, at the dark energy scale µ=2.4×10^{-3} eV, the constraint at M=1.3 TeV is improved by about 10 times the previous constraints on the torsion pendulum experiment.

Arm locking using laser frequency comb.

The space-borne gravitational wave (GW) detectors, e.g., LISA, TaiJi, and TianQin, will open the window in the low-frequency regime (0.1 mHz to 1 Hz) to study the highly energetic cosmic events, such as coalescences and mergers of binary black holes and neutron stars. For the sake of successful observatory of GWs, the required strain sensitivity of the detector is approximately 10-21/Hz1/2 in the science band, 7 orders of magnitude better than the state of the art of the ultra-stable laser. Arm locking is therefore proposed to reduce the laser phase noise by a few orders of magnitude to relax the burden of time delay interferometry. During the past two decades, various schemes have been demonstrated by using single or dual arms between the spacecraft, with consideration of the gain, the nulls in the science band, and the frequency pulling characteristics, etc. In this work, we describe an updated version of single arm locking, and the noise amplification due to the nulls can be flexibly restricted with the help of optical frequency comb. We show that the laser phase noise can be divided by a specific factor with optical frequency comb as the bridge. The analytical results indicate that, the peaks in the science band have been greatly reduced. The performance of the noise suppression shows that the total noise after arm locking can well satisfy the requirement of time delay interferometry, even with the free-running laser source. When the laser source is pre-stabilized to a Fabry-Perot cavity or a Mach-Zehnder interferometer, the noise can reach the floor determined by the clock noise, the spacecraft motion, and the shot noise. We also estimate the frequency pulling characteristics of the updated single arm locking, and the results suggest that the pulling rate can be tolerated, without the risk of mode hopping. Arm locking will be a valuable solution for the noise reduction in the space-borne GW detectors. We demonstrate that, with the precise control of the returned laser phase noise, the noise amplification in the science band can be efficiently suppressed based on the updated single arm locking. Not only does our method allow the suppression of the peaks, the high gain, and low pulling rate, it can also serve for full year, without the potential risk of locking failure due to the arm length mismatch. We then discuss the unified demonstration of the updated single arm locking, where both the local and the returned laser phase noises can be tuned to generate the expected arm-locking sensor actually. Finally, the time-series simulations in Simulink have been carried out, and the results indicate a good agreement with the theory, showing that the presented method is reasonable and feasible. Our work could provide a back-up strategy for the arm locking in the future space-borne GW detectors.

Combined Test of the Gravitational Inverse-Square Law at the Centimeter Range.

Experiments measuring the Newtonian gravitational constant G can offer uniquely sensitive probes of the test of the gravitational inverse-square law. An analysis of the non-Newtonian effect in two independent experiments measuring G is presented, which permits a test of the 1/r^{2} law at the centimeter range. This work establishes the strongest bound on the magnitude α of Yukawa-type deviations from Newtonian gravity in the range of 5-500 mm and improves the previous bounds by up to a factor of 7 at the length range of 60-100 mm.

Influence of the tilt error motion of the rotation axis on the test of the equivalence principle with a rotating torsion pendulum.

Improving the precision of current tests of the equivalence principle with a rotating torsion pendulum requires a more complete analysis of systematic effects. Here, we discuss in detail one of the important systematic effects, the influence from the tilt error motion of the rotation axis of a rotary stage, namely, wandering of the instantaneous rotation axis around its average direction. Its influence on the rotating torsion pendulum is modeled phenomenologically, and the parameters in the model are calibrated. It is shown that the influence can contribute a correction of η ≈ 5 × 10-13 to the equivalence-principle violating parameter for a rotary stage whose tilt error motion of interest is about 31 nrad in magnitude. We also show that such an influence can be reduced to the level of η ≈ 1 × 10-14 by means of active compensation of the tilt error motion using a set of piezoelectric actuators placed under the stage stator.

Improvement for Testing the Gravitational Inverse-Square Law at the Submillimeter Range.

We improve the test of the gravitational inverse-square law at the submillimeter range by suppressing the vibration of the electrostatic shielding membrane to reduce the disturbance coupled from the residual surface potential. The result shows that, at a 95% confidence level, the gravitational inverse-square law holds (|α|≤1) down to a length scale λ=48 µm. This work establishes the strongest bound on the magnitude α of the Yukawa violation in the range of 40-350 µm, and improves the previous bounds by up to a factor of 3 at the length scale λ≈70 µm. Furthermore, the constraints on the power-law potentials are improved by about a factor of 2 for k=4 and 5.

Precision measurement of the Newtonian gravitational constant.

The Newtonian gravitational constant G, which is one of the most important fundamental physical constants in nature, plays a significant role in the fields of theoretical physics, geophysics, astrophysics and astronomy. Although G was the first physical constant to be introduced in the history of science, it is considered to be one of the most difficult to measure accurately so far. Over the past two decades, eleven precision measurements of the gravitational constant have been performed, and the latest recommended value for G published by the Committee on Data for Science and Technology (CODATA) is (6.674 08 ± 0.000 31) × 10-11 m3 kg-1 s-2 with a relative uncertainty of 47 parts per million. This uncertainty is the smallest compared with previous CODATA recommended values of G; however, it remains a relatively large uncertainty among other fundamental physical constants. In this paper we briefly review the history of the G measurement, and introduce eleven values of G adopted in CODATA 2014 after 2000 and our latest two values published in 2018 using two independent methods.

Combined Search for a Lorentz-Violating Force in Short-Range Gravity Varying as the Inverse Sixth Power of Distance.

Precision measurements of the inverse-square law via experiments on short-range gravity provide sensitive tests of Lorentz symmetry. A combined analysis of data from experiments at the Huazhong University of Science and Technology and Indiana University sets simultaneous limits on all 22 coefficients for Lorentz violation correcting the Newton force law as the inverse sixth power of distance. Results are consistent with no effect at the level of 10^{-12} m^{4}.

Measurements of the gravitational constant using two independent methods.

The Newtonian gravitational constant, G, is one of the most fundamental constants of nature, but we still do not have an accurate value for it. Despite two centuries of experimental effort, the value of G remains the least precisely known of the fundamental constants. A discrepancy of up to 0.05 per cent in recent determinations of G suggests that there may be undiscovered systematic errors in the various existing methods. One way to resolve this issue is to measure G using a number of methods that are unlikely to involve the same systematic effects. Here we report two independent determinations of G using torsion pendulum experiments with the time-of-swing method and the angular-acceleration-feedback method. We obtain G values of 6.674184 × 10-11 and 6.674484 × 10-11 cubic metres per kilogram per second squared, with relative standard uncertainties of 11.64 and 11.61 parts per million, respectively. These values have the smallest uncertainties reported until now, and both agree with the latest recommended value within two standard deviations.

Magnetic effect in the test of the weak equivalence principle using a rotating torsion pendulum.

The high precision test of the weak equivalence principle (WEP) using a rotating torsion pendulum requires thorough analysis of systematic effects. Here we investigate one of the main systematic effects, the coupling of the ambient magnetic field to the pendulum. It is shown that the dominant term, the interaction between the average magnetic field and the magnetic dipole of the pendulum, is decreased by a factor of 1.1 × 104 with multi-layer magnetic shield shells. The shield shells reduce the magnetic field to 1.9 × 10-9 T in the transverse direction so that the dipole-interaction limited WEP test is expected at η ≲ 10-14 for a pendulum dipole less than 10-9 A m2. The high-order effect, the coupling of the magnetic field gradient to the magnetic quadrupole of the pendulum, would also contribute to the systematic errors for a test precision down to η ∼ 10-14.

Extraction and detection of bisphenol A in human serum and urine by aptamer-functionalized magnetic nanoparticles.

A new type of magnetic nanoparticles (MNPs), as the absorbents of bisphenol A (BPA), was prepared by functionalization of Fe3O4@SiO2 with BPA-specific aptamer in this work. ssDNA aptamer was immobilized on the Fe3O4@SiO2 surface through biotin-avidin interactions, playing a role of the specific probe for BPA. The resultant materials (Apt-MNPs) exhibited outstanding magnetic responsibility and can be separated efficiently by the magnetic field. Experimental results also showed that Apt-MNPs had large adsorption capacity and high competitive selectivity for the targeted compound BPA. Furthermore, Apt-MNPs were adopted as the specific absorbents to extract and enrich BPA from human serum and urine samples. Therefore, an efficient detection method of BPA was developed in combination with high-performance liquid chromatography (HPLC). The linearity of the method was over a range of 5-10,000 ng mL-1 with a correlation coefficient of 0.99997, and the limit of detections (LODs) for serum and urine were 2.0 and 1.0 ng mL-1, respectively. The recoveries of BPA in the spiked human serum and urine samples were 90.8 ± 7.3% (RSD) and 92.3 ± 1.5%, respectively. Our results demonstrated that Apt-MNPs were high-performance adsorbents for extracting and enriching BPA, resulting in fast and efficient detection of BPA in serum and urine samples. Graphical abstract Aptamer-MNPs were effective for BPA separation from serum and urine.

Test of the Equivalence Principle with Chiral Masses Using a Rotating Torsion Pendulum.

Here we present a new test of the equivalence principle designed to search for the possible violation of gravitational parity using test bodies with different chiralities. The test bodies are a pair of left- and right-handed quartz crystals, whose gravitational acceleration difference is measured by a rotating torsion pendulum. The result shows that the acceleration difference towards Earth Δa_{left-right}=[-1.7±4.1(stat)±4.4(syst)]×10^{-15} m s^{-2} (1-σ statistical uncertainty), correspondingly the Eötvös parameter η=[-1.2±2.8(stat)±3.0(syst)]×10^{-13}. This is the first reported experimental test of the equivalence principle for chiral masses and opens a new way to the search for the possible parity-violating gravitation.

An improved correlation method for amplitude estimation of gravitational background signal with time-varying frequency.

In the measurement of the gravitational constant G with angular acceleration method, the accurate estimation of the amplitude of the useful angular acceleration generated by source masses depends on the effective subtraction of the spurious gravitational signal caused by room fixed background masses. The gravitational background signal is of time-varying frequency, and mainly consists of the prominent fundamental frequency and second harmonic components. We propose an improved correlation method to estimate the amplitudes of the prominent components of the gravitational background signal with high precision. The improved correlation method converts a sinusoidal signal with time-varying frequency into a standard sinusoidal signal by means of the stretch processing of time. Based on Gaussian white noise model, the theoretical result shows the uncertainty of the estimated amplitude is proportional to σNT, where σ and N are the standard deviation of noise and the number of the useful signal period T, respectively.

Influence of tungsten fiber's slow drift on the measurement of G with angular acceleration method.

In the measurement of the gravitational constant G with angular acceleration method, the equilibrium position of torsion pendulum with tungsten fiber undergoes a linear slow drift, which results in a quadratic slow drift on the angular velocity of the torsion balance turntable under feedback control unit. The accurate amplitude determination of the useful angular acceleration signal with known frequency is biased by the linear slow drift and the coupling effect of the drifting equilibrium position and the room fixed gravitational background signal. We calculate the influences of the linear slow drift and the complex coupling effect on the value of G, respectively. The result shows that the bias of the linear slow drift on G is 7 ppm, and the influence of the coupling effect is less than 1 ppm.

Combined Search for Lorentz Violation in Short-Range Gravity.

Short-range experiments testing the gravitational inverse-square law at the submillimeter scale offer uniquely sensitive probes of Lorentz invariance. A combined analysis of results from the short-range gravity experiments HUST-2015, HUST-2011, IU-2012, and IU-2002 permits the first independent measurements of the 14 nonrelativistic coefficients for Lorentz violation in the pure-gravity sector at the level of 10^{-9} m^{2}, improving by an order of magnitude the sensitivity to numerous types of Lorentz violation involving quadratic curvature derivatives and curvature couplings.

Test of the Universality of Free Fall with Atoms in Different Spin Orientations.

We report a test of the universality of free fall by comparing the gravity acceleration of the ^{87}Rb atoms in m_{F}=+1 versus those in m_{F}=-1, of which the corresponding spin orientations are opposite. A Mach-Zehnder-type atom interferometer is exploited to alternately measure the free fall acceleration of the atoms in these two magnetic sublevels, and the resultant Eötvös ratio is η_{S}=(0.2±1.2)×10^{-7}. This also gives an upper limit of 5.4×10^{-6} m^{-2} for a possible gradient field of the spacetime torsion. The interferometer using atoms in m_{F}=±1 is highly sensitive to the magnetic field inhomogeneity. A double differential measurement method is developed to alleviate the inhomogeneity influence, of which the effectiveness is validated by a magnetic field modulating experiment.

New Test of the Gravitational Inverse-Square Law at the Submillimeter Range with Dual Modulation and Compensation.

By using a torsion pendulum and a rotating eightfold symmetric attractor with dual modulation of both the interested signal and the gravitational calibration signal, a new test of the gravitational inverse-square law at separations down to 295 µm is presented. A dual-compensation design by adding masses on both the pendulum and the attractor was adopted to realize a null experiment. The experimental result shows that, at a 95% confidence level, the gravitational inverse-square law holds (|α|≤1) down to a length scale λ=59 µm. This work establishes the strongest bound on the magnitude α of Yukawa-type deviations from Newtonian gravity in the range of 70-300 µm, and improves the previous bounds by up to a factor of 2 at the length scale λ≈160 µm.

Influence of temperature on period of torsion pendulum with a high-Q fused silica fiber.

Due to the high-Q fused silica fiber's extreme sensitivity to temperature change, the period estimation of torsion pendulum with high precision depends on the effective correction of the thermoelastic effect. In the measurement of G with the time-of-swing method, we analyze the complex relation between temperature and the pendulum's period and propose a developed method to find the shear thermoelasticity coefficient as well as isolate the influence of temperature on period alone. The result shows that the shear thermoelasticity coefficient is 101(2) × 10(-6)/°C, the resultant correction to Δ(ω(2)) is 9.16(0.18) ppm, and the relative uncertainty to G is less than 1 ppm.