Atomic quantum states with maximum localization on classical elliptical orbits

We show how to build atomic states that mimic the classical Bohr-Sommerfeld elliptic orbits with minimum quantum fluctuations. These elliptic states are uniquely defined from symmetry considerations. They are the coherent states of the SO(4) symmetry group of the Coulomb interaction in three dimensions and are superpositions of the usual spherical states with well-defined weights and phases. They can be experimentally produced from laser excitation of Rydberg atoms in crossed electric and magnetic fields. We finally indicate how to build Coulomb wave packets localized both in space and time.