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The positronium (Ps) $n=2$ fine structure intervals can be used to test bound-state quantum electrodynamics (QED) [1], with current measurements using microwave waveguides at a precision of 100 parts-per-million (ppm) [2]. However, the 10 mm scale of waveguides in the GHz regime results in short transit times and low phase acceptance of the fast and divergent Ps beam. We therefore use free-space radiation in our experiment to target the entire Ps ensemble and minimise transit-time broadening, also greatly simplifying the required vacuum setup.
Linearly polarised microwave radiation was applied using a horn antenna placed outside the vacuum chamber containing metastable Ps* atoms. The $>$50 MHz wide $2\,^3$S$_1 \rightarrow 2\,^3$P$_J~(J = 1, 2)$ transitions were driven in two separate experiments. We measured apparent shifts in the $J = 2$ transition which varied by up to 500 ppm [3]. This was due to reflections of the microwave radiation from the apparatus causing frequency dependent field strength. We also observed the excitation of polarisation-forbidden excitation pathways of the $J = 1$ transition due to reflections causing incomplete polarisation of the microwave radiation.
These effects make precision measurements of broad energy intervals using free-space microwave radiation challenging, but offer insight into effects which may not be observed in narrower resonances (e.g. [4]) until a higher level of precision is achieved.
[1] G. S. Adkins et al., Phys. Rep. 975, 1 (2022).
[2] R. E. Sheldon et al., Phys. Rev. Lett. 131, 043001 (2023).
[3] R. E. Sheldon et al., Phys. Rev. A 107, 042810 (2023).
[4] R. A. Brienza et al., Phys. Rev. A 108, 022815 (2023).
