Abstract
We consider the interatomic Casimir-Polder interaction energy between two
neutral ground-state atoms moving in the vacuum space with the same uniform
acceleration. We assume the acceleration orthogonal to their separation, so
that their mutual distance remains constant. Using a model of the
Casimir-Polder interaction based on the interaction between the instantaneous
atomic dipole moments, which are induced and correlated by the zero-point field
fluctuations, we evaluate the interaction energy between the two accelerating
atoms in terms of quantities expressed in the laboratory reference frame. We
find that the dependence of the Casimir-Polder interaction between the atoms
from the distance is different with respect to the case of atoms at rest, and
the relation of our results with the Unruh effect is discussed. We show that in
the near zone a new term proportional to $R^-5$ adds to the usual $R^-6$
behavior, and in the far zone a term proportional to $R^-6$ adds to the usual
$R^-7$ behavior, making the interaction of a longer range. We also find that
the interaction energy is time-dependent, and the physical meaning of this
result is discussed. In particular, we find acceleration-dependent corrections
to the $R^-7$ (far zone) and $R^-6$ (near zone) proportional to
$a^2t^2/c^2$; this suggests that significant changes to the Casimir-Polder
interaction between the atoms could be obtained if sufficiently long times are
taken, without necessity of the extremely high accelerations required by other
known manifestations of the Unruh effect.
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