On the use of hydrogen switchable mirrors in Casimir force experiments

Hydrogen switchable mirrors (HSMs) are shiny metals that become optically transparent upon exposure to hydrogen. The Casimir force between HSMs is thus supposed to be stronger in air than in hydrogen. A few years ago, an experiment designed to measure this effect gave an unexpected result (Iannuzzi, Lisanti and Capasso 2004 Proc. Natl Acad. Sci. USA 101 4019-23): no change of the force was observed upon hydrogenation. Qualitative arguments show that this result is reasonable if HSMs do not switch at long wavelengths, where no measurements of the dielectric function are available. Because the exact composition of the mirrors used in that experiment is not known, a more quantitative comparison of the data with theory is not possible. Still, calculations of the Casimir force in the presence of similar HSMs of known composition might provide new insights for the interpretation of the experimental result and may suggest precious hints for the development of future analogous experiments. In this paper, we present calculations of the Casimir attraction between Mg2Ni mirrors in air and in hydrogen. Our results clearly indicate that the modulation of the Casimir force with HSMs should be observable with modern set-ups.