Recent progress in testing Newtonian inverse square law at short range
Authors: Tan Wen-Hai  , Wang Jian-Bo  , Shao Cheng-Gang  , Tu Liang-Cheng  , Yang Shan-Qing  , Luo Peng-Shun  , Luo Jun  ,   MOE Key Laboratory of Fundamental Physical Quantities Measurements, Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China;,   TianQin Research Center for Gravitational Physics, Sun Yat-sen University, Zhuhai 519082, China
Published: December 2020

Many theoretical speculations assume that the Newtonian inverse square law (ISL) needs to be modified in short range, such as the modifications due to gravitation propagating in extra dimensions and the hypothetical interactions mediated by bosons predicted by the physics beyond the standard model. High precision tests of the non-Newtonian gravitational forces are important for verifying the proposed models and help us to further understand gravity. Scientists have performed many tests in different interaction ranges by using different techniques and have not find any nonNewtonian gravitational force up to now. Adopting a gap modulation scheme, the experimental group in Huazhong University of Science and Technology had accomplished the tests of ISL in the millimeter and submillimeter range with torsional balance. The experiment in the millimeter range set the strongest constraints on the Yukawa-type violation from ISL. Recently, they have conducted two other tests in the submillimeter and micrometer range by modulating the density of the source attractor. In the submillimeter range, torsional balance is used to measure the torque acting on the pendulum by a rotating density modulated source attractor. The Newtonian gravitational torque at the frequency of interest is suppressed below the thermal noise of the pendulum by a dual compensation design, whereas the nonNewtonian gravitational torque is preserved if it exists, so that a “Null” test can be realized. The experimental system is verified by comparing the theoretical torque with the measured one when intentionally shifting the attractor away from the position for “Null” test. The strongest constraints on the Yukawa-type violation are achieved in a range of 70-300 μm in this experiment. In the micrometer range, an isoelectronic test of the non-Newtonian forces is performed by sensing the lateral force between a gold sphere and a density modulated source attractor by using a soft cantilever. The attractor is fabricated based on silicon-on-insulator wafer to make its surface isoelectronic and possess a density modulated structure underneath. Two-dimensional (2D) mapping of the force signal indicates that the experimental sensitivity is mainly limited by the electrostatic force arising from the surface patch charges. We analyze the 2D mapping data by using maximum likelihood estimation method and set constraints on the Yukawa-type non-Newtonian gravitational forces without subtracting the model-dependent Casimir force or electrostatic force background. Both experiments show no sign of the non-Newtonian gravitational force, and further experiments with high precision are required to explore the unconstrained parameter space.