Test Of Non-newtonian Gravitational Forces At Micrometer Range

Unifying the four fundamental interactions of nature,the gravitation,electromagnetic interaction,strong interaction and weak interaction,has received a great deal of attention in the past decades.Among the unified theories,many of them have predicted that the gravitational force would deviate from Newton's inverse square law at millimeter range or closer,or there may exist non-Newtonian gravitational forces.Those predictions have inspired intense experimental efforts to test the Newton's inverse square law at different interaction ranges and to search for the non-Newtonian forces.We performed an isoelectronic test of non-Newtonian forces at micrometer range by sensing the lateral force between a gold sphere and a density modulation source mass using a soft cantilever.With an optimal drive amplitude,the non-Newtonian force signal is expected to be significant at the 8th harmonics of the drive frequency,so the disturbance signal can be separated effectively.The cantilever is placed normal to the source mass surface to minimize the contribution of the force background dominated in normal direction.The gold sphere was made by melting a high purity gold wire using hydrogen flame,then glued to the end of a soft cantilever under an optical microscope.The probe minimum detectable force at the signal frequency is estimated to be 5.7 fN/(?)Hz.The density modulation source mass was fabricated on a silicon-on-insulator wafer.The imprint of the modulation structure on the surface has be controlled under?3 nm in amplitude on average.Two-dimensional force mapping,in combination with in situ topographic imaging,is applied to verify the isoelectronic property of the surface.The force signal is found to be electrostatic force dominated,which is correlated with the density modulation structure for thinner gold coating and reduced by thicker gold coating and thermal annealing.Maximum likelihood estimation is used to extract the constraint on the hypothetical force based on the 2D data.The constraint on the Yukawa force is set by the up-bound a value at 95%confidence level without subtraction of the model dependent force background.This result would be a meaningful complementary to previous tests with different methods.