  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 (1 Tesla) and with a
relatively high temperature (100 K). 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.
