Casimir pressure between metallic plates out of thermal equilibrium: Proposed test for the relaxation properties of free electrons

Abstract

We propose a test on the role of relaxation properties of conduction electrons in the Casimir pressure between two parallel metal-coated plates kept at different temperatures. It is shown that for sufficiently thick metallic coatings the Casimir pressure and pressure gradient are determined by the mean of the equilibrium contributions calculated at temperatures of the two plates and by the term independent on separation. Numerical computations of the nonequilibrium pressures are performed for two parallel Au plates of finite thickness as a function of separation and temperature of one of the plates using the plasma and Drude models for extrapolation of the optical data of Au to low frequencies. The obtained results essentially depend on the extrapolation used.Modifications of the CANNEX setup, originally developed to measure the Casimir pressure and pressure gradient in thermal equilibrium, are suggested, which allow different temperatures of one of the plates. Computations of the nonequilibrium pressure and pressure gradient are performed for a realistic experimental configuration. According to our results, even with only a 10 K difference in temperature between the plates, the experiment could discriminate between different theoretical predictions for the total pressure and its gradient, as well as for the contributions to them due to nonequilibrium, at high confidence.

Nonequilibrium effects in the Casimir force between two similar metallic plates kept at different temperatures

“…These effects could be observed using the experimental setup described in Refs. [43,52], where the upper plate plays the role of a sensor suspended by the springs and the lower plate is mounted on a piezo-electric stage. Taking into account that an immediate application of the above computational results requires the vacuum conditions outside of both plates, their thickness should be chosen sufficiently large (typically more than 0.5 µm) in order that a material underlying the lower plate will not impact on the nonequilibrium pressure.…”

“…Then, the pressure on the upper plate kept at the temperature of the environment T 1 contains an additional contribution from the environmental black-body radiation pressure [18,43]…”

“…This line of attack was already used in Refs. [42,43] where the nonequilibrium Casimir force between metallic test bodies was calculated with and without taking into account relaxation properties of the conduction electrons and different possibilities to measure it were proposed. Arguing that corrections due to the temperature dependence of the dielectric permittivity would be small compared to the effect of a temperature difference between the plates, the dielectric permittivity was assumed to be temperature-independent.…”

Precision measurements of the gradient of the Casimir force between ultraclean metallic surfaces at larger separations

“…This made harder the theoretical solution to the problem and called for precise measurements of the Casimir interaction in the micrometer separation range. Several experiments of this kind directed to the resolution of the Casimir puzzle and Casimir conundrum have been proposed recently[79][80][81][82][83].The main improvements made in the experiment presented here are the use of much softer cantilever, which allowed the increase of the calibration constant by up to an order of magnitude, and implementation of the two-step cleaning procedure by means of the UV light and Ar ions, which resulted in ultra clean surfaces of both the internal walls of vacuum chamber and of the test bodies at ultrahigh (< 5 × 10 −9 Torr ≈ 0.7 × 10 −6 Pa) and stable vacuum. This allowed to reach low (a few mV) and stable residual potential difference which was independent of separation for the regular (not specially selected) samples.…”

“…Thus, by the results of measurements with 10and 20-nm oscillation amplitudes of the cantilever the Drude model approach is excluded by the data over the separation range from 250 to 1100 nm.The problem of why the Lifshitz theory is in contradiction with the measurement data when it takes into account the relaxation properties of conduction electrons at low frequencies is discussed in the literature but there is yet no consensus on how this puzzle can be explained. In Refs [61,83,84]. it was hypothesized that a material system might not respond similarly to electromagnetic fields with nonzero field strength and to fluctuations with zero field strength but nonzero dispersion.…”