Long-range interactions and state characteristics of interacting Rydberg atoms

We study the long-range interaction between mutually excited hydrogen atoms in principal quantum numbers n = 4, 8, 16. The quasimolecular states are constructed from the basis of hydrogen-like product states with the configuration interaction method and with the inclusion of all order multipole moments of the total electrostatic interaction. Several common features appear, which are n-insensitive, and will thus remain relevant for the coherent control of cold Rydberg systems with higher values of n. The energy curves are shown to be attractive and repulsive, generally non-intersecting and the repulsion splitting is stronger than the attractive. The electronic probability densities of the selected states are studied as well as their relation to the single product states consisting of linear Stark states (most aligned) on each atom. One of the observed features is that the least bound states are always characterized by a high degree of polarization favoured towards the molecular centre, and therefore well approximated by a product of two Stark states. The most bound states are similarly expressed as a coherent combination of such states which secure symmetry with respect to electron exchange and parity. Coherent control between the attractive and repulsive states can be obtained with almost 100% probability in time-dependent resonant monochromatic microwave fields.