  We find that energy surfaces of more than two atoms or molecules interacting
via dipole-dipole po- tentials generically possess conical intersections (CIs).
Typically only few atoms participate strongly in such an intersection. For the
fundamental case, a circular trimer, we show how the CI affects adiabatic
excitation transport via electronic decoherence or geometric phase
interference. These phe- nomena may be experimentally accessible if the trimer
is realized by light alkali atoms in a ring trap, whose dipole-dipole
interactions are induced by off-resonant dressing with Rydberg states. Such a
setup promises a direct probe of the full many-body density dynamics near a
conical intersection.
