The Casimir force is a quantum effect that strongly depends on not only the material properties but also the shape of the boundary of the interacting objects. The majority of past experiments focused on simple geometries such as plate-sphere, two parallel plates or two cylinders, where the interactions are not expected to deviate significantly from the pairwise additive approximation (PAA) and proximity force approximation (PFA). To demonstrate the strong shape dependence of the Casimir force, we measure the Casimir force between a gold sphere and artificial strongly deformed surfaces which consist of nano-scale, periodic rectangular trenches.
A microelectromechanical torsional oscillator was used in our experiments to precisely measure the force. To improve the detection sensitivity, we use a dynamic approach, where the Casimir force gradient is measured by the shifts in the resonant frequency of the oscillator.
At distance between 150 nm and 500 nm, the measured force gradient shows significant deviations from the value expected from the PAA and the PFA. The observed deviation has a good agreement with the theoretical calculations based on scattering theory that includes the finite conductivity of the material, demonstrating the strong shape dependence of the Casimir force. Compared to the calculated values for perfectly conducting surfaces, the deviation is ∼50% smaller, revealing the interplay between the material and the geometry effects.