Precision spectroscopy of Rydberg Positronium

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Hydrogen is the testing ground for quantum physics and has been the subject of intense experimentation, providing very stringent tests of QED theory. Spectroscopy of this fundamental system is so advanced that it is now limited by our incomplete knowledge of the structure of the proton, which is not governed by QED and cannot be calculated with sufficient accuracy. In order to try and improve measurements of the proton structure some remarkable experiments were conducted using muonic hydrogen: this is a system in which the electron in a hydrogen atom is replaced with a muon. Although muons are intrinsically unstable and decay in a few microseconds, they can act as excellent probes of the charge radius of the proton because they are over 200 times more massive than electrons. These experiments [see R. Pohl, et al. "The size of the proton", Nature, 466 213 (2010)] have been very successful, providing a highly accurate measurement of the proton size. However, this improved precision has revealed a discrepancy with previous hydrogen spectroscopy and electron-proton scattering measurements that has not yet been explained, and is known as the "proton radius puzzle". This project aims to address the problem from a different perspective: instead of replacing the hydrogenic electron with a heavy muon, and thereby increasing the effect of the proton size, we will completely eliminate the effect by replacing the proton with a positron. This positron-electron bound state is known as positronium and, even though it is intrinsically unstable and prone to self-annihilation, it can be studied via microwave and optical spectroscopy. In order to do this with sufficient precision we will need to use lasers to put the Ps atoms into highly-excited Rydberg states which prevents self-annihilation, significantly extending their lifetimes. Moreover, the motion of excited Rydberg states can be controlled via external electric fields owing to their large dipole moments, making it possible to generate a slow, long-lived, and focused Ps atom beam. With a beam of atoms that live for a long time we can directly measure how they fall in the gravitational field of the earth. This will help answer the question: does antimatter fall differently to matter? If the answer is not "no" there will be profound implications for our existing physical theories. Similarly, if the proton radius puzzle does not have a simple explanation it too may be a sign of exciting new physics. Whatever the answers to these questions are, this project will address them using cutting edge methods covering several areas of atomic and positronium physics, and will also require the development of many new techniques along the way.