Theory-experiment comparison for the Casimir force between metallic test bodies: A spatially nonlocal dielectric response

Abstract

It is known that the Lifshitz theory of the Casimir force comes into conflict with measurement data if the response of conduction electrons in metals to electromagnetic fluctuations is described by the well-tested dissipative Drude model. The same theory is in very good agreement with measurements of the Casimir force from graphene, whose spatially nonlocal electromagnetic response is derived from the first principles of quantum electrodynamics. Here we propose spatially nonlocal phenomenological dielectric functions of metals which lead to nearly the same response as the standard Drude model to the propagating waves, but to a different response in the case of evanescent waves. Unlike some previous suggestions of this type, the response functions considered here depend on all components of the wave vector, as is most natural in the formalism of specular reflection used. It is shown that these response functions satisfy the Kramers-Kronig relations. We derive respective expressions for the surface impedances and reflection coefficients. The obtained results are used to compute the effective Casimir pressure between two parallel plates, the Casimir force between a sphere and a plate, and the Casimir force gradient in configurations of the most precise experiments performed with both nonmagnetic (Au) and magnetic (Ni) test bodies. It is shown that in all cases (Au-Au, Au-Ni, and Ni-Ni test bodies) the predictions of the Lifshitz theory found by using the dissipative nonlocal response functions are in as good agreement with the measurement data as was reached previously with the dissipationless plasma model. Possible developments and applications of these results are discussed.