  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.
