Constraints on spatially oscillating sub-mm forces from the Stanford Optically Levitated Microsphere Experiment data

A recent analysis by one of the authors [L. Perivolaropoulos, Phys. Rev. D 95, 084050 (2017)] has indicated the presence of a 2 sigma signal of spatially oscillating new force residuals in the torsion balance data of the Washington experiment. We extend that study and analyze the data of the Stanford Optically Levitated Microsphere Experiment (SOLME) [A. D. Rider et al., Phys. Rev. Lett. 117, 101101 (2016)] (kindly provided by A. D. Rider et al.) searching for sub-mm spatially oscillating new force signals. We find a statistically significant oscillating signal for a force residual of the form F(z) = alpha cos( 2 pi/lambda z+c) where z is the distance between the macroscopic interacting masses (levitated microsphere and cantilever). The best fit parameter values are alpha = (1.1 +/- 0.4) x 10(-17) N, lambda = (35.2 +/- 0.6) mu m. Monte Carlo simulation of the SOLME data under the assumption of zero force residuals has indicated that the statistical significance of this signal is at about 2 sigma level. The improvement of the chi(2) fit compared to the null hypothesis (zero residual force) corresponds to Delta chi(2) = 13.1. There are indications(1) that this previously unnoticed signal is indeed in the data but is most probably induced by a systematic effect caused by diffraction of non-Gaussian tails of the laser beam. Thus the amplitude of this detected signal can only be useful as an upper bound to the amplitude of new spatially oscillating forces on sub-mm scales. In the context of gravitational origin of the signal emerging from a fundamental modification of the Newtonian potential of the form V-eff(r) = -GM/r (1 + alpha(0) cos(2 pi/lambda r + theta)) = V-N (r) + V-osc (r), we evaluate the source integral of the oscillating macroscopically induced force. If the origin of the SOLME oscillating signal is systematic, the parameter alpha(0) is bounded as alpha(0) < 10(7) for lambda similar or equal to 35 mu m. Thus, the SOLME data cannot provide useful constraints on the modified gravity parameter alpha(0). However, the constraints on the general phenomenological parameter alpha (alpha < 0.3 x 10(-17) N at 2 sigma) can be useful in constraining other fifth force models related to dark energy (chameleon oscillating potentials etc.).