Title: Universal experimental test for the role of free charge carriers in thermal Casimir effect within a micrometer separation range,
Abstract: We propose a universal experiment to measure the differential Casimir force
between a Au-coated sphere and two halves of a structured plate covered with a
P-doped Si overlayer. The concentration of free charge carriers in the
overlayer is chosen slightly below the critical one, f or which the phase
transition from dielectric to metal occurs. One ha f of the structured plate is
insulating, while its second half is made of gold. For the former we consider
two different structures, one consisting of bulk high-resistivity Si and the
other of a layer of silica followed by bulk high-resistivity Si. The
differential Casimir force is computed within the Lifshitz theory using four
approaches that have been proposed in the literature to account for the role of
free charge carriers in metallic and dielectric materials interacting with
quantum fluctuations. According to these approaches, Au at low frequencies is
described by either the Drude or the plasma model, whereas the free charge
carriers in dielectric materials at room temperature are either taken into
account or disregarded. It is shown that the values of differential Casimir
forces, computed in the micrometer separation range using these four
approaches, are widely distinct from each other and can be easily discriminated
experimentally. It is shown that for all approaches the thermal component of
the differential Casimir force is sufficiently large for direct observation.
The possible errors and uncertainties in the proposed experiment are estimated
and its importance for the theory of quantum fluctuations is discussed.