Femto-Newton light force measurement at the thermal noise limit

The measurement of very small light forces has wide applications in many fields of physics. A common measurement method for small force detection is the determination of changes in the dynamic behavior of mechanical oscillators, either in amplitude or in frequency. The detection of slowly varying forces mostly requires long period oscillators, such as a torsion pendulum. We demonstrate the application of a macroscopic, low-noise, torsion balance oscillator for the detection of radiation pressure forces at the femto-Newton level. The system is "precooled" (removing excess seimic noise) to be only thermal noise limited. The demonstrated force sensitivity reaches the thermal limit.     

Determination of the thermal noise limit in test of weak equivalence principle with a rotating torsion pendulum

Thermal noise is one of the most fundamental limits to the sensitivity in weak equivalence principle test with a rotating torsion pendulum. Velocity damping and internal damping are two of many contributions at the thermal noise, and which one mainly limits the torsion pendulum in low frequency is difficult to be verified by experiment. Based on the conventional method of fast Fourier transform, we propose a developed method to determine the thermal noise limit and then obtain the precise power spectrum density of the pendulum motion signal. The experiment result verifies that the thermal noise is mainly contributed by the internal damping in the fiber in the low frequency torsion pendulum experiment with a high vacuum. Quantitative data analysis shows that the basic noise level in the experiment is about one to two times of the theoretical value of internal damping thermal noise.     

Correlation method estimation of the modulation signal in the weak equivalence principle test

In a test of the weak equivalence principle(WEP) with a rotating torsion pendulum, it is important to estimate the amplitude of the modulation signal with high precision. We use a torsional filter to remove the free oscillation signal and employ the correlation method to estimate the amplitude of the modulation signal. The data analysis of an experiment shows that the uncertainties of amplitude components of the modulation signal obtained by the correlation method are in agreement with those due to white noise. The power spectral density of the modulation signal obtained by the correlation method is about one order higher than the thermal noise limit. It indicates that the correlation method is an effective way to estimate the amplitude of the modulation signal and it is instructive to conduct a high-accuracy WEP test.     

Influence of the colored noise on determining the period of a torsion pendulum

Based on statistical properties, two typical models are considered to calculate the uncertainties for some random noise sequences on the period extraction of a torsion pendulum, which is important and instructive in the measurement of gravitational constant G with the time-of-swing method. An expression of the uncertainty for the period measurement is obtained, which is dependent on the ratio ?t/(1/λ) where ?t is the interval of the sample time and 1/λ is the length of the correlation time. The result of processing experimental data shows that as the interval of the sample time ?t gradually shortens, the uncertainty of the period becomes smaller, and further when the ratio ?t/(1/λ) is less than 1, the uncertainty remains substantially unchanged.     

Achieving geodetic motion for LISA test masses: ground testing results

The low-frequency resolution of space-based gravitational wave observatories such as LISA (Laser Interferometry Space Antenna) hinges on the orbital purity of a free-falling reference test mass inside a satellite shield. We present here a torsion pendulum study of the forces that will disturb an orbiting test mass inside a LISA capacitive position sensor. The pendulum, with a measured torque noise floor below 10 fN m/square root of Hz from 0.6 to 10 mHz, has allowed placement of an upper limit on sensor force noise contributions, measurement of the sensor electrostatic stiffness at the 5% level, and detection and compensation of stray dc electrostatic biases at the millivolt level.     

Influence of the Earth's rotation on measurement of gravitational constant G with the time-of-swing method

In the measurement of the Newtonian gravitational constant G with the time-of-swing method,the influence of the Earth's rotation has been roughly estimated before,which is far beyond the current experimental precision.Here,we present a more complete theoretical modeling and assessment process.To figure out this effect,we use the relativistic Lagrangian expression to derive the motion equations of the torsion pendulum.With the correlation method and typical parameters,we estimate that the influence of the Earths rotation on G measurement is far less than 1 ppm,which may need to be considered in the future high-accuracy experiments of determining the gravitational constant G.     

扭摆法验证平行轴定理实验的改进

转动惯量是物体定轴转动中的重要物理量,物体的转动惯量测量的常用方法有三线摆法与扭摆法。扭摆法通常测量物体通过质心转轴的转动惯量,所以用扭摆法验证平行轴定理一直不怎么直观,本文就是在已有的基础上进行一些改进,已达到更好、更直观验证平行轴定理。     

DETERMINATION OF THE PERIOD OF A TORSION PENDULUM BY THE FITTING METHOD IN REAL TIME

A phenomenological study on the fitting method in real time has been done, and the method was applied to process and analyze the extensive data of a long period torsion pendulum used to determine Newtonian gravitational constant G. The result shows that the fitting method in real time is effective to determine the period of a torsion pendulum with a relative precision of 10^-5 orders.     

Optical phase estimation in the presence of phase diffusion

The measurement problem for the optical phase has been traditionally attacked for noiseless schemes or in the presence of amplitude or detection noise. Here we address the estimation of phase in the presence of phase diffusion and evaluate the ultimate quantum limits to precision for phase-shifted Gaussian states. We look for the optimal detection scheme and derive approximate scaling laws for the quantum Fisher information and the optimal squeezing fraction in terms of the total energy and the amount of noise. We also find that homodyne detection is a nearly optimal detection scheme in the limit of very small and large noise.     

Numerical modeling of the motion of a torsion balance in the problem of measuring the Newtonian gravitational constant

The motion of a torsion balance with five degrees of freedom has been numerically simulated. It has been shown that the oscillations along the swing degrees of freedom are excited by the random noise of the seismic origin and their amplitude varies with time. It has been shown also that the nonlinear couplings between the swing and torsion degrees of freedom result in the appearance of combination oscillations. The methods for effectively suppressing these combination oscillations have been considered.     

Precise Determination of Period of a Torsion Pendulum in Measurement of Gravitational Constant

The period of a torsion pendulum would vary under the disturbances of environmental noise factors. In order to subtract the period of the pendulum from external influence, we employ the correlation method to determine the period with a high precision. Theoretical analysis shows that the relative precision is improved to be proportional to 1/m^3/2 with the number of the period m, compared with the conventional statistical mean that is proportional to 1/m^1/2, which is significant for the determination of gravitational constant with the swing time method.     

Thermal noise limit in measuring the gravitational constant G using the angular acceleration method and the dynamic deflection method

A general comparison is made between two methods of measuring the gravitational constant G. The angular acceleration method can avoid the anelasticity effect since the torsion fiber is not twisted. The dynamic deflection method is similar in principle but it does not use feedback, therefore a major noise introduced by the feedback control system in the angular acceleration method can be avoided. Both methods have their advantages and can be performed with the same device. Based on different expressions of G, we have expressed the signal-to-noise ratio and calculated the thermal noise limit for both methods. In order to get a lower thermal noise limit, the dynamic deflection method should avoid resonance.     

激光单脉冲冲量的扭摆测量方法

 激光脉冲作用于工质，使工质烧蚀反喷，产生微小冲量。研究了扭摆微小冲量测量方法，提出了在激光烧蚀反喷作用力下扭摆的运动方程，激光单脉冲作用下冲量所满足的积分方程。进一步通过积分方程的离散化方法，提出了激光单脉冲冲量的计算方法，并且进行了精度分析。为采用扭摆测量激光单脉冲冲量，提供了工程测量和计算方法。     

Experimental control for initiating and maintaining rotation of parametric pendulum

In this paper, the authors have studied experimentally the control methods of a parametric pendulum excited harmonically to initiate and maintain a period one rotation – the most superior response for energy harvesting. For initiating the period one rotation inherent in the system, first the bang-bang method is applied. Then a new method where velocity is monitored is proposed and applied and finally the time-delayed feedback method with multi-switching is considered. Ultimately the problem of maintaining the rotation of the pendulum is addressed. For first time, robustness and sensitivity of the latter method to change of frequency and amplitude of excitation and added noise are studied. Finally, it has been demonstrated how the delayed feedback method can be applied in a system of two pendula to ensure synchronized rotation.     

COmplex-Model-Based Estimation of thermal noise for fMRI data in the presence of artifacts

Due to the presence of artifacts induced by fast-imaging acquisition in functional magnetic resonance imaging (fMRI) studies, it is very difficult to estimate the variance of thermal noise by traditional methods in magnitude images. Moreover, the existence of incidental phase fluctuations impairs the validity of currently available solutions based on complex datasets. In this article, a time-domain model is proposed to generalize the analysis of complex datasets for nonbrain regions by incorporating artifacts and phase fluctuations. Based on this model, a novel estimation schema has been developed to find an appropriate set of voxels in nonbrain regions according to their levels of artifact and phase fluctuation. In addition, noise intensity from these voxels is estimated. The whole schema is named COmplex-Model-Based Estimation (COMBE). Theoretical and experimental results demonstrate that the proposed COMBE method provides a better estimation of thermal noise in fMRI studies compared with previously proposed methods and suggest that the new method can adapt to a broader range of applications, such as functional connectivity studies, evaluation of sequence designs and reconstruction schemas.     

Interaction between stray electrostatic fields and a charged free-falling test mass

We present an experimental analysis of force noise caused by stray electrostatic fields acting on a charged test mass inside a conducting enclosure, a key problem for precise gravitational experiments. Measurement of the average field that couples to the test mass charge, and its fluctuations, is performed with two independent torsion pendulum techniques, including direct measurement of the forces caused by a change in electrostatic charge. We analyze the problem with an improved electrostatic model that, coupled with the experimental data, also indicates how to correctly measure and null the stray field that interacts with the test mass charge. Our measurements allow a conservative upper limit on acceleration noise, of 2 (fm/s2)/Hz(1/2) for frequencies above 0.1 mHz, for the interaction between stray fields and charge in the LISA gravitational wave mission.     

Measurement of intensity difference squeezing via non-degenerate four-wave mixing process in an atomic vapor

We report the measurement of the intensity difference squeezing via the non-degenerate four-wave mixing process in a rubidium atomic vapor medium. Two pairs of balanced detection systems are employed to measure the probe and the conjugate beams, respectively. It is convenient to get the quantum shot noise limit, the squeezed and the amplified noise power spectra. We also investigate the influence of the input extra quadrature amplitude noise of the probe beam. The influence of the extra noise can be minimized and the squeezing can be optimized under the proper parameter condition. We measure the -3.7-dB intensity difference squeezing when the probe beam has a 3-dB extra quadrature amplitude noise. This result is slightly smaller than -4.1 dB when the ideal coherent light （no extra noise） for the probe beam is used.     

利用智能手机磁传感器研究单摆运动

本文基于Phyphox手机App,利用智能手机中的磁传感器(电子罗盘)研究磁性单摆运动.结果表明,不同最大摆角测量出来的磁感应强度随时间变化规律不同.只有最大摆角小于1°时,单摆才可看作简谐振动.不同最大摆角的磁感应强度随时间变化曲线可以用磁偶极子模型结合大角度单摆公式来描述.利用磁传感器测量的当地重力加速度为9.868m/s 2,由于磁性摆空气阻尼较小,测得的实验误差仅为0.8%.     

浅海波导环境失配下的协方差矩阵拟合稳健匹配场声源功率估计

实际浅海波导中环境噪声为相干噪声,最小方差匹配场声源功率估计方法能在相干噪声背景下准确估计声源辐射功率,但该方法受环境不确定性影响较大;此外,由于最小方差匹配场声源功率估计方法使用信号幅度作为中间量估计声源功率,信号幅度估计误差会二次放大并传递到声源功率估计结果中。本文提出一种协方差矩阵拟合稳健最小方差匹配场声源功率估计方法,该方法引入信道传递函数不确定集,结合协方差矩阵拟合思想将声源功率估计问题建模为在信道传递函数不确定集约束下对函数取极值的问题,使用Lagrange乘子法求解该问题得到信道传递函数估计值和声源辐射功率估计值。环境失配影响声源辐射功率估计性能的根本原因在于信道传递函数偏差较大,协方差矩阵拟合稳健匹配场声源功率估计方法有效减小了环境失配时信道传递函数的偏差,从而显著提升环境失配稳健性。此外,该方法使用权值直接估计声源功率,无需使用信号幅度作为中间量,避免了估计误差的传递。仿真验证了协方差矩阵拟合稳健匹配场声源功率估计方法的环境失配稳健性。     

铝-0.5wt%铜合金在低内耗时的反常振幅效应

用计算机控制的自动倒扭摆测量了轻度冷加工的铝-0.5wt%铜合金试样在室温(20℃)时效24小时后的自由衰减曲线。此时的内耗值虽然很低,但在逐次增加激发振幅进行内耗测量时也观察到一系列的振幅内耗峰。 关键词：