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.

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Abstract.Measurements of the Casimir force require the elimination of electrostatic interactions between the surfaces. However, due to electrostatic patch potentials, the voltage required to minimize the total force may not be sufficient to completely nullify the electrostatic interaction. Thus, these surface potential variations cause an additional force, which can obscure the Casimir force signal. In this paper, we inspect the spatially varying surface potential (SP) of e-beamed, sputtered, sputtered and annealed, and template stripped gold surfaces with Heterodyne Amplitude Modulated Kelvin Probe Force Microscopy (HAM-KPFM). It is demonstrated that HAM-KPFM improves the spatial resolution of surface potential measurements compared to Amplitude Modulated Kelvin Probe Force Microscopy (AM-KPFM). We find that patch potentials vary depending on sample preparation, and that the calculated pressure can be similar to the pressure difference between Casimir force calculations employing the plasma and Drude models.

We present a calculation of the Casimir torque acting on a liquid crystal near a birefringent crystal. In this system, a liquid crystal bulk is uniformly aligned at one surface and is twisted at the other surface by a birefringent crystal, e.g. barium titanate. The liquid crystal is separated from the solid crystal by an isotropic, transparent material such as SiO2. By varying the thickness of the deposited layer, we can observe the effect of retardation on the torque (which differentiates it from the close-range van der Waals torque). We find that a barium titanate slab would cause 5CB (4-cyano-4 -pentylbiphenyl) liquid crystal to rotate by 10 • through its bulk when separated by 35 nm of SiO2. The optical technique for measuring this twist is also outlined.

We investigate two effects that lead to a surprising increase in the calculated Casimir-Lifshitz torque between anisotropic, planar, semi-infinite slabs. Retardation effects, which account for the finite speed of light, are generally assumed to decrease the strength of Casimir-Lifshitz interactions. However, the nonretarded approximation underestimates the Casimir-Lifshitz torque at small separations by as much as an order of magnitude. Also, Casimir-Lifshitz forces are typically weakened with the insertion of an intervening dielectric. However, a dielectric medium can increase the short-range Casimir-Lifshitz torque by as much as a factor of 2. The combined effects of retardation and an intervening dielectric dramatically enhance the Casimir-Lifshitz torque in the experimentally accessible regime and should not be neglected in calculation or experimental design.