  Casimir interaction between two media of ground-state atoms is well described
with the help of Lifshitz formula depending upon permittivity of media. We will
show that this formula is in contradiction with experimental evidence for
excited atoms. We calculate Casimir force between two atoms if one of them or
both atoms are excited. We use methods of quantum electrodynamics specially
derived for the problem. It enables us to take into account excited-state
radiation widths of atoms. Then we calculate the force between excited atom and
medium of ground-state atoms. The results are in agreement with the ones,
obtained by other authors using perturbation theory or linear response theory.
Generalization of our results to the case of interaction between two media of
excited atoms results in a formula, which is in not only in quantitative, but
in qualitative contradiction with Lifshits formula. This contradiction
disappears if media of ground-state atoms are taken. Moreover, our result does
not include permittivity of the media. It includes the quantity which differs
from the permittivity only for excited atoms. The main features of our results
are as follows. The interaction is resonant; the force may be either attractive
or repulsive depending on resonant frequencies of the atoms of different media;
the value of Casimir force may be several orders of magnitude lager than that
predicted by Lifshitz formula. The features mentioned here are in agreement
with known experimental and theoretical evidences obtained by many authors for
interaction of a single excited atom with dielectric media.
