Antihydrogen production by charge exchange reaction between positronium (Ps) atoms and antiprotons requires an efficient excitation of Ps atoms up to high-$n$ levels (Rydberg levels). In this study it is assumed that a Ps cloud is produced within a relatively strong uniform magnetic field $\left(1\mathrm{T}\right)$ and with a relatively high temperature $\left(100\mathrm{K}\right)$. Consequently, the structure of energy levels are deeply modified by Zeeman and motional Stark effects. A two-step laser light excitation, the first one from ground to $n=3$ and the second from this level to a Rydberg level, is proposed and the physics of the problem is discussed. We derive a simple formula giving the absorption probability with substantially incoherent laser pulses. A 30% population deposition in high-$n$ states can be reached with feasible lasers suitably tailored in power and spectral bandwidth.

• Received 30 June 2008

DOI:https://doi.org/10.1103/PhysRevA.78.052512