Experimental approaches to the difference in the Casimir force due to modifications in the optical properties of the boundary surface

We propose two experiments on the measurement of the Casimir force acting between a gold coated sphere and semiconductor plates with markedly different charge carrier densities. In the first of these experiments a patterned Si plate is used which consists of two sections of different dopant densities and oscillates in the horizontal direction below a sphere. The measurement scheme in this experiment is differential, i.e., it allows the direct high-precision measurement of the difference of the Casimir forces between the sphere and sections of the patterned plate or the difference of the equivalent pressures between Au and patterned parallel plates with static and dynamic techniques, respectively. The second experiment proposes to measure the Casimir force between the same sphere and a $\mathrm{V}{\mathrm{O}}_{2}$ film which undergoes the insulator-metal phase transition with the increase of temperature. We report the present status of the interferometer based variable temperature apparatus developed to perform both experiments and present the first results on the calibration and sensitivity. The magnitudes of the Casimir forces and pressures in the experimental configurations are calculated using different theoretical approaches to the description of optical and conductivity properties of semiconductors at low frequencies proposed in the literature. It is shown that the suggested experiments will aid in the resolution of theoretical problems arising in the application of the Lifshitz theory at nonzero temperature to real materials. They will also open new opportunities in nanotechnology.