  We study two ions confined in a Penning trap. We show that electronically
highly excited states exist in which an electron is delocalized among the two
ions forming a giant molecule of several micrometer size. At energies close to
the top of the Coulomb barrier these molecular states can be regarded as
superpositions of Rydberg states of individual ions. We illuminate the
possibility to observe coherent charge transfer between the ions. Beyond a
critical principal quantum number the electron can coherently tunnel through
the Coulomb barrier to an adjacent doubly charged ion. The tunneling occurs on
timescales on which the dynamics of the nuclei can be considered frozen and
radiative decay can be neglected.
