Efficient production of Rydberg positronium

We demonstrate experimentally the production of Rydberg positronium (Ps) atoms in a two-step process, comprising incoherent laser excitation, first to the 2(3)P state and then to states with principal quantum numbers ranging from 10 to 25. We find that excitation of 2(3)P atoms to Rydberg levels occurs very efficiently (~90%) and that the ~25% overall efficiency of the production of Rydberg atoms is determined almost entirely by the spectral overlap of the primary excitation laser and the Doppler broadened width of the 1 (3)S-2(3)P transition. The observed efficiency of Rydberg Ps production can be explained if stimulated emission back to the 2P states is suppressed, for example, by intermixing of the Rydberg state Stark sublevels. The efficient production of long-lived Rydberg Ps in a high magnetic field may make it possible to perform direct measurements of the gravitational free fall of Ps.