The Casimir-Polder effect for a stack of conductive planes

TL;DR

This paper investigates the Casimir-Polder interaction between an atom and a multilayered system of graphene sheets, deriving asymptotic expressions and exploring how conductivity models influence the interaction, with implications for experimental manipulation.

Contribution

It provides new asymptotic formulas for atom-graphene interactions and analyzes the effects of different conductivity models on the Casimir-Polder force.

Findings

Retardation effects are significant at large separations.

The van der Waals coefficient depends on the number of graphene layers.

Conductivity models influence the magnitude of the Casimir-Polder energy.

Abstract

The Casimir-Polder interaction between an atom and a multilayered system composed of infinitely thin planes is considered using the zeta-function regularization approach with summation of the zero-point energies. As a prototype material, each plane is represented by a graphene sheet whose optical response is described by a constant conductivity or Drude-Lorentz model conductivity. Asymptotic expressions for various separations are derived and compared to numerical calculations. We distinguish between large atom/plane limit, where retardation effects are prominent, and small atom/plane limit, where the typical van der Waals coefficient is found to be dependent on the number of graphenes and characteristic distances. The calculated energies for different atoms and graphene conductivity models brings forward the basic science of the Casimir-Polder effect and suggests ways to manipulate this interaction experimentally.