Gradient of the Casimir force between Au surfaces of a sphere and a plate measured using an atomic force microscope in a frequency-shift technique

Abstract

We present measurement results for the gradient of the Casimir force between an Au-coated sphere and an Au-coated plate obtained by means of an atomic force microscope operated in a frequency shift technique. This experiment was performed at a pressure of 3 × 10 −8 Torr with hollow glass sphere of 41.3 µm radius. Special attention is paid to electrostatic calibrations including the problem of electrostatic patches. All calibration parameters are shown to be separationindependent after the corrections for mechanical drift are included. The gradient of the Casimir force was measured in two ways with applied compensating voltage to the plate and with different applied voltages and subsequent subtraction of electric forces. The obtained mean gradients are shown to be in mutual agreement and in agreement with previous experiments performed using a micromachined oscillator. The obtained data are compared with theoretical predictions of the Lifshitz theory including corrections beyond the proximity force approximation. An independent comparison with no fitting parameters demonstrated that the Drude model approach is excluded by the data at a 67% confidence level over the separation region from 235 to 420 nm. The theoretical approach using the generalized plasma-like model is shown to be consistent with the data over the entire measurement range. Corrections due to the nonlinearity of oscillator are calculated and the application region of the linear regime is determined. A conclusion is made that the results of several performed experiments call for a thorough analysis of the basics of the theory of dispersion forces.

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

“…It is well known that the standard Lifshitz theory at thermal equilibrium faces problems in describing the Casimir free energy and the pressure between two metallic plates (see reviews [24,25] and the monograph [26]). Specifically, it turns out that the results for the Casimir interaction obtained by all high-precision experiments at separations below 1.1 µm are in conflict with theoretical predictions taking into account the relaxation properties of conduction electrons [27][28][29][30][31][32][33][34][35][36][37][38]. If these relaxation properties are disregarded in computations, the Lifshitz theory is brought to a very good agreement with the measurement data [27][28][29][30][31][32][33][34][35][36][37][38].…”

Casimir force, causality, and the Gurzhi model

“…Then, the dielectric permittivity along the imaginary frequency axis is found from Eq. (15). This is called the plasma model approach to the calculation of the Casimir force.…”

“…Taking into consideration that the difference between two alternative theoretical predictions at the experimental separations of Refs. [11][12][13][14][15][16][17][18][19][20][21] was below a few percent, attempts of solving the problem at the expense of some background effects or computational inaccuracies have been undertaken (see, e.g.,…”

Charging of graphene by a magnetic field and the mechanical effect of magnetic oscillations

“…As a byproduct, we note that the newly-developed mechanical method 8,16,17 may lead to the precise measurement of density of states if sample is additionally gated.…”