Precision Spectroscopy of Positronium Using a Pulsed Slow Positron Beam

Abstract

Positronium is the lightest known atom and comprises a structureless point-like electron and its anti-particle, the positron. As such, it is purely leptonic and can be described to very high precision by bound-state QED without the inherent complications given by the finite size and quark substructure of protonic atoms. Furthermore, being a true onium atom, recoil effects are strongly enhanced and its quantum numbers sum to zero, making it an ideal candidate to test fundamental symmetries like CPT-invariance. However, positronium is also a very challenging system for precision measurements due to its ephemeral nature. Being a bound state of anti-particles it tends to self-annihilate quickly and due to its lightness it exhibits much larger velocities than other atoms. Nevertheless, being a precision test-bench for QED with many unique features, it represents a particularly interesting system for spectroscopic measurements. This thesis presents the efforts towards precise determinations of the $\text{1}^\text{3}\text{S}_\text{1} \to \text{2}^\text{3}\text{S}_\text{1}$ transition and both the hyperfine and fine structure of positronium in the $n=2$ state. The pulsed slow positron beamline at ETH Zurich, being a key prerequisite for these measurements, was optimized and a new beam transport and bunching system was developed. It was found that the efficiencies were comparable to similar beamlines and several further possible improvements were identified. This thesis includes a measurement of the $\text{1}^\text{3}\text{S}_\text{1} \to \text{2}^\text{3}\text{S}_\text{1}$ transition by Doppler-free two-photon laser spectroscopy of $1\,233\,607\,210.5\:\mathrm{MHz} \pm 49.6\:\mathrm{MHz}$, which paves the way towards a new precision determination of this interval. Improvements by roughly two orders of magnitude on this result are suggested and discussed. The design of an experiment to measure the hyperfine transition in the first excited state is presented. A microwave system supporting more than $100\,\mathrm{kW}$ of circulating power was developed and tested. Extensive simulations of the excitation and detection show the expected sensitivity to be $9.9 \, \mathrm{ppm}$ (statistical) and $2.8 \, \mathrm{ppm}$ (systematic) and further envisioned improvements are presented. This measurement will constitute the first measurement of this transition and the first determination of a hyperfine interval of positronium in vacuum altogether. It was found that the experimental setup directly supports a determination of the $\text{2}^\text{3}\text{S}_\text{1} \to \text{2}^\text{3}\text{P}_\text{0}$ interval. Minor changes allow also for the measurement of the $\text{2}^\text{3}\text{S}_\text{1} \to \text{2}^\text{3}\text{P}_\text{1}$ and $\text{2}^\text{3}\text{S}_\text{1} \to \text{2}^\text{3}\text{P}_\text{2}$ transitions. Simulations show the expected sensitivities to be approximately $7 \, \mathrm{ppm}$ (statistical) and $0.5 \, \mathrm{ppm}$ (systematic), which will allow to shed light on a $4.5\sigma$ discrepancy of the most precise fine structure measurement in positronium with theory calculations.