Collisions and interactions in ultracold Rydberg plasmas

A new branch of atomic physics -~the interactions and collisions in ultracold Rydberg plasmas ($T\ll 1 K$) systems-~ has naturally evolved from recent advances in the cooling and trapping of neutral gases. Here we discuss the key collisional processes-- three-body recombination. electron-impact ionization of Rydberg atoms, radiative cascade of Rydberg atoms and Rydberg -Rydberg interactions --important to the evolution of the plasma. Quantal and classical radiative cascades are illustrated, together with the ``trajectory" in $n\ell$ space followed during the cascade. Theory and cross sections for ionization of Rydberg atoms in $n, \ell$ states by collision with electrons is presented. The full dependence of the cross sections on the initial angular momentum $\ell$ of the target is revealed, with interesting physical characteristics. Analytical curvefits for the cross sections are then provided so as to extract the rates for three-body capture into state $n,\ell$ from detailed balance. Three-body recombination followed by Stark mixing produce Rydberg atoms with a broad distribution of $\ell$ states. These states are sufficiently flexible that {\it permanent dipole} and higher {\it permanent multipoles} are created quite easily out of the large number $\sim n^2$ of degenerate angular momentum states $\ell$ within the energy shell. First-order interactions between Rydbergs therefore exist. We present the physics of the first-order long-range interaction between these polar Rydberg atoms and investigate the possible formation of long-range molecules from two Rydberg atoms with the same (or different) principal quantum numbers $n$, but with a broad superposition of many degenerate angular momentum states $\ell$.