Positronium (Ps) is a purely leptonic atom comprising an electron and its antimatter equivalent, the positron, in a quasi-stable bound state. Due to its fundamental nature, Ps is an ideal test bed for bound-state QED.
Recent high-precision spectroscopic experiments reveal a discrepancy in the measurement of the proton charge radius rp, known as the Proton Charge Radius Puzzle. Spectroscopic measurments carried out on hydrogen and muonic hydrogen, the bound state of a muon and a proton, differ from other scattering and other spectroscopic experiments by 3.3σ. The measurement of rp comes from fitting the resulting measurement of either the 1S-2S interval of hydrogen or the Lamb Shift in muonic hydrogen to theory.
Neither of these atoms are governed purely by quantum electrodynamics (QED) alone as nuclear structure has a role to play. The ratio of the masses of the orbiting particle m to that of the nucleus M is a coefficient in a number of a QED corrections to the energy levels of hydrogen (m/M = 1/1836) and muonic hydrogen (m/M = 207/1836) and reveals the importance of performing a complementary spectroscopic measurement in Ps, where m/M = 1.
The last measurement of the 1S-2S interval was carried out by Fee, Chu, Mills, et al. in 1993 to a precision of 3.2 ppb. The state-of-the-art measurement on hydrogen is now at an uncertainty of 4.2 × 10^−15. While the simplicity of Ps causes it to be appealing to test bound-state QED, its antiparticle-particle nature makes it difficult to work with: the ground state lifetime of the triplet state is 142 ns, and whereas the 2S lifetime in Ps is 1.14 µs, the 2S lifetime in hydrogen is 10^5x longer.
We have designed and constructed an apparatus and experiment to measure the 1S-2S interval in Ps at precision levels that we expect to immediately improve upon the previous measurements by factor of 2x and pave the way for ultimate comparison to the hydrogenic measurements. The apparatus also opens the doors to a new frontier in high-precision spectroscopy: the sub-µs regime.