Constraints on non-Newtonian gravity from measuring the Casimir force in   a configuration with nanoscale rectangular corrugations
  We report constraints on the parameters of Yukawa-type corrections to Newtonian gravity from measurements of the gradient of the Casimir force in the configuration of an Au-coated sphere above a Si plate covered with corrugations of trapezoidal shape. For this purpose, the exact expression for the gradient of Yukawa force in the experimental configuration is derived and compared with that obtained using the proximity force approximation. The reported constraints are of almost the same strength as those found previously from several different experiments on the Casimir force and extend over a wide interaction range from 30 to 1260\,nm. It is discussed how to make them stronger by replacing the material of the plate. 
V. B. Bezerra, G. L. Klimchitskaya, V. M. Mostepanenko, and C. Romero
hep-ph quant-ph