Quantum Electrodynamics and Fundamental Physics

Missouri University Of Science And Technology, Rolla MO

Investigators

Abstract

This project includes theoretical investigations to challenge and support ongoing high-precision experiments with atomic hydrogen, the simplest chemical element, and with closely related hydrogen-like atoms, also called Rydberg atoms, which have one electron orbiting a closed-shell ion core. Because of their simplicity, hydrogen and its Rydberg cousins have long been used to make precise tests of QED (quantum electrodynamics), the most precise theory in all of physics. The spectrum of hydrogen can be calculated to better than one part in 100 trillions, and properties of its bound electron (such as its response to external magnetic fields) can be calculated to extreme accuracy. Reaching this level of accuracy is possible because quantum mechanics is stable under small perturbations, so it is possible to iteratively correct the theory. However, pushing such calculations to even greater accuracy, as required to advance recent experimental observations, poses numerous challenges, some of which are to be addressed in this project. This high-risk work will attempt to overcome the predictive limits of perturbative QED using novel and untried techniques. If successful, the efforts will be used to improve measurements of the Rydberg constant (a measure of the wavelengths of light emitted by the atom), which in turn, may help resolve the puzzle of the proton radius. The project will explore new pathways for high-precision spectroscopy and the determination of fundamental constants, both by advancing the fundamental theory and by working in close collaboration with experimental groups. New pathways for the two-photon excitation of bound Rydberg states through an unbound intermediate state will be explored. This will allow for very precise measurements of transition frequencies among Rydberg states of hydrogen, thereby conclusively addressing any remaining questions surrounding the so-called proton radius puzzle. Another aspect of the project concerns numerical calculations of quantum electrodynamic corrections to the spectrum of hydrogen-like systems, and to the g factor of bound electrons, which use ultra-precise numerical analysis to advance understanding of the bound states and to look for tiny deviations of theoretical predictions and experimental results, with concomitant discovery potential for New Physics. The project will also address the predictive limits of quantum field theory and the "diminishing returns" that are incurred when calculations of so-called Feynman diagrams become infeasible in view of computational limitations in higher orders of perturbation theory. Through an enhanced understanding of the nature of the perturbative expansion, pathways for overcoming the predictive limits of quantum field theory will be explored using a combination of path-integral methods, dispersion relations and a saddle-point expansion, which identify the asymptotic form of the perturbative expansions for very large orders of perturbation theory. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.