Test of non-Newtonian gravitational forces at micrometer range with two-dimensional force mapping

We report 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. Two-dimensional (2D) 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, and the experiment sets a constraint on the Yukawa type forces without subtraction of the model dependent force background. This result would be a meaningful complementary to previous tests with different methods.