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Shaping the void

par Paul INDELICATO - 19 septembre 2008

Quantum vacuum may be devoid of matter but its shape is still important. The strength of the Casimir force caused by quantum fluctuations in the space between surfaces critically depends on their nano-scale shape. As recently published in Physical Review Letters, the geometrical approximation which is widely used to calculate the shape influence completely fails in this situation.

Two reflecting plates in quantum vacuum attract each other. This startling vacuum force is called the Casimir force named after the Dutch physicist Hendrik Casimir who discovered it in 1948. Its origin is quantum mechanical : it arises because quantum vacuum is not entirely empty but filled with zero point fluctuations of the electromagnetic field. The reflecting plates provide boundaries which change the mode density of vacuum fluctuations in the gap compared to the unrestricted vacuum outside the plates. This results in the Casimir force which scales with the fourth power of the inverse distance between the plates.

The Casimir force is highly versatile and tailoring it could potentially be useful in the design and control of micro- and nanomachines. While the material dependence of the Casimir force has been thoroughly studied between two plane mirrors, for other geometries exact calculations exist only for perfectly reflecting boundaries. If material properties are taken into account, the shape dependence of the Casimir force is usually treated using a geometrical approximation, the so-called proximity force approximation (PFA) which amounts to summing up contributions at different distances as if they were independent.

While PFA works well to estimate the force between a sphere and a flat surface, it completely fails when the Casimir plates are nanostructured, as has been recently shown by theorists at the Laboratoire Kastler Brossel. When testing PFA against their exact calculations in a configuration where two Silicon plates with nanotrenches face each other, they found a Casimir force 25% smaller than calculated from PFA. Their calculations explain a recent experiment by Chan et al. (Phys. Rev. Lett. 101, 030401 (2008)) discussed in Nature News and Views 454, 836 (2008), where the Casimir force is measured between different nanostructured silicon surfaces and a gold sphere.

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