Trap-assisted creation of giant molecules and Rydberg-mediated coherent charge transfer in a Penning trap

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 time scales on which the dynamics of the nuclei can be considered frozen and radiative decay can be neglected. The present study can be regarded as a first step toward the implementation of electronic Hubbard models in an ion-trap setup.