Measurement of the Casimir Force between Two Spheres

Complex interaction geometries offer a unique opportunity to modify the strength and sign of the Casimir force. However, measurements have traditionally been limited to sphere-plate or plate-plate configurations. Prior attempts to extend measurements to different geometries relied on either nanofabrication techniques that are limited to only a few materials or slight modifications of the sphere-plate geometry due to alignment difficulties of more intricate configurations. Here, we overcome this obstacle to present measurements of the Casimir force between two gold spheres using an atomic force microscope. Force measurements are alternated with topographical scans in the x-y plane to maintain alignment of the two spheres to within approximately 400 nm (∼1% of the sphere radii). Our experimental results are consistent with Lifshitz's theory using the proximity force approximation (PFA), and corrections to the PFA are bounded using nine sphere-sphere and three sphere-plate measurements with spheres of varying radii.