Laser excitation of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math>level of positronium for antihydrogen production

We demonstrate the laser excitation of the $n=3$ state of positronium (Ps) in vacuum. A combination of a specially designed pulsed slow positron beam and a high-efficiency converter target was used to produce Ps. Its annihilation was recorded by single-shot positronium annihilation lifetime spectroscopy. Pulsed laser excitation of the $n=3$ level at a wavelength $\ensuremath{\lambda}\ensuremath{\approx}205$ nm was monitored via Ps photoionization induced by a second intense laser pulse at $\ensuremath{\lambda}=1064$ nm. About 15% of the overall positronium emitted into vacuum was excited to $n=3$ and photoionized. Saturation of both the $n=3$ excitation and the following photoionization was observed and explained by a simple rate equation model. The positronium's transverse temperature was extracted by measuring the width of the Doppler-broadened absorption line. Moreover, excitation to Rydberg states $n=15$ and 16 using $n=3$ as the intermediate level was observed, giving an independent confirmation of excitation to the $3^{3}P$ state.