Apparatus for Measuring the Thermal Casimir Force at Large Distances

We describe a Casimir apparatus based on a differential force measurement between a Au-coated sphere and a planar slab divided in two regions, one of which is made of high-resistivity (dielectric) Si, and the other of Au. The crucial feature of the setup is a semitransparent plane parallel conducting overlayer, covering both regions. The setup offers two important advantages over existing Casimir setups. On one hand, it leads to a large amplification of the difference between the Drude and the plasma prescriptions that are currently used to compute the thermal Casimir force. On the other hand, thanks to the screening power of the overlayer, it is in principle immune from electrostatic forces caused by potential patches on the plates surfaces, that plague present large distance Casimir experiments. If a semitransparent conductive overlayer with identical patch structure over the Au-Si regions of the plate can be manufactured, similar to the opaque overlayers used in recent searches of non-Newtonian gravitational forces based on the isoelectronic technique, the way will be paved for a clear observation of the thermal Casimir force up to separations of several microns, and an unambiguous discrimination between the Drude and the plasma prescriptions.

Figure 1

The setup consists of a Au-coated sphere above a planar slab divided into two regions, respectively, made of high-resistivity (dielectric) Si and Au. Both the Si and the Au regions are covered with a semitransparent plane-parallel conducting overlayer of uniform thickness $w$ made of low-resistivity Si.

Figure 2

The force difference $\mathrm{\Delta }F$ (in fN) versus separation $a$ (in microns). The red and grey lines correspond to the plasma and Drude prescriptions, respectively. The dashed (dot-dashed) lines show the effect of a 20 nm step (overlayer thickness difference $\delta w=20\mathrm{nm}$) across the Au-Si regions.

Figure 3

Difference of the Casimir force-gradient $\mathrm{\Delta }{F}^{\prime }$ (in units of ${10}^{-8}\mathrm{N}/\mathrm{m}$) versus separation (in $\mu \mathrm{m}$). The red and grey lines correspond to the plasma and Drude prescriptions, respectively. All parameters are as in Fig. 2.