Saturation effects in experiments on the thermal Casimir effect

We address three different problematic Casimir experiments in this work. The first is the classical Casimir force measured between two metal half spaces; here in the form of the Casimir pressure measurement between a gold sphere and a gold plate as performed by Decca et al. [Phys. Rev. D 75, 077101 (2007)]; theory predicts a large negative thermal correction, absent in the high precision experiment. The second experiment is the measurement of the Casimir force between a metal plate and a laser irradiated semiconductor membrane as performed by Chen et al. [Phys. Rev. B 76, 035338 (2007)]; the change in force with laser intensity is larger than predicted by theory. The third experiment is the measurement of the Casimir force between an atom and a wall in the form of the measurement by Obrecht et al. [Phys. Rev. Lett. 98 063201 (2007)] of the change in oscillation frequency of a Rb Bose-Einstein condensate trapped to a fused silica wall; the change is smaller than predicted by theory. We show that saturation effects can explain the discrepancies between theory and experiment observed in all these cases.