Quantum Vacuum and Atoms: Exploring QED and Atom-Surface Interactions with the Help of Advanced Numerical Methods

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The spectroscopic measurement of transition frequencies in simple atomic systems has significantly contributed to the progress of physics within the last 100 years. The Bohr model of the hydrogen atom was developed on the basis of the quantum-classical correspondence of planetary orbits under the influence of the central electrostatic potential generated by the positively charged proton, with the additional ingredient of the Bohr-Sommerfeld quantization condition. The theory has been refined over decades, with additional input from relativistic physics and quantum field theory. By analyzing the spectrum ever more carefully, one has been able to deduce from the experiments a few subtle properties of the atoms, such as the charge radius of the massive central particle, i.e., the proton. Recently, an experiment has been performed which questions the understanding of the field-theoretical modifications of the Coulomb force law at short distances: The so-called muonic hydrogen experiment at the Paul-Scherrer Institute in Villigen, Switzerland, has been obtaining results for transitions in the bound system of muon and proton, which are in disagreement with other experiments and theoretical calculations performed by the physics community over at least two decades. Within the NSF program, some of the last conceivable explanations for the ensuing proton radius puzzle will be studied from the theoretical side, with the aim of either excluding these explanations, or finding confirmation for necessary modifications of our understanding of the nuclear charge distribution within the proton.Based on the PI's somewhat broad knowledge in field theory, the concepts and ideas originally developed in the analysis of bound-state corrections will be applied to so-called dynamical processes and atom-surface interactions. When an atom is in contact with a dielectric surface, the vacuum modes of the electric field are perturbed in the immediate vicinity of the surface. The quantum fluctuations (the unavoidable 'quiver' due to the Heisenberg uncertainty relation) of the vacuum modes (the 'preferred natural oscillation modes' of the electric field in the vicinity of the metallic surface) change the interaction potential of the atom near the surface, and the 'dragging' of the mirror charge inside the dielectric material induces a friction force. This happens even if the atom is not in physical contact with the surface, and the overlap of the quantum mechanical wave function of the atom with the surface is negligible. These effects are due to be studied within the NSF research program, and compared to the results of ongoing experiments in various laboratories in the world. Finally, all of these effects will be studied for few-electron atoms, for which the energy eigenvalues of the basic quantum mechanical time evolution operator (the 'Hamiltonian' which defines the energy levels) cannot be calculated in analytic form. Ideas to improve approximation methods based on novel basis sets ('quantum mechanical trial wave functions') will be explored. All of the research endeavors sketched above are suited for the education of graduate students. Indeed, both the gain in the knowledge on basic, but also applied physics as well the education in the use of advanced numerical methods contributes to the success of a number of graduate students supervised in the past (and, one may envisage, present and future). This includes the numerical methods used in the study of bound systems as well as other, more mathematically inclined concepts, based on the vacuum fluctuations of the quantum fields, which often find surprising, practically useful applications.There are three major areas of work in this project. The first problem is the puzzle of the muonic hydrogen and proton radius. The muonic hydrogen puzzle continues to intrigue physicists and represents one of the most pressing questions to answer in regard to our understanding of fundamental forces. Namely, measurements in muonic hydrogen have led to a value of the proton charge radius which is in disagreement with both scattering experiments as well as laser-spectroscopic measurements in atomic hydrogen. This project involves the recalculation of one of the last possible theoretical explanations for the disagreement which has not yet been fully covered in the literature. The second problem involves higher order corrections in many-body systems. Beyond the two-body problem, it is impossible to analytically solve bound-state systems even in non-relativistic quantum mechanics. Three aspects of higher-order corrections in helium-like systems which are of prime importance for the description of experiments will be studied. These include so-called relativistic Bethe logarithms in helium, as well as higher-order effects in the bound 'muonic helium' system. The calculations will be important in confronting the muonic hydrogen puzzle with other muonic bound systems, and, potentially, in determining the electron-muon mass ratio. Finally, Casimir effects, dynamic processes and atom-wall interactions will be studied. The atom-wall interaction is a vacuum-mediated interaction between an atom flying by a solid material ('wall') and depends on the functional form of the dielectric response function of the medium. The project includes an investigation, conceivably in collaboration with experimentalists, of the temperature dependence of the atom-wall interaction, which may have already been seen in an experiment, as well as details of the atom-wall interaction potential for the helium-alpha-quartz and helium-gold systems. Theoretical progress on the understanding of the quantum friction force, due to the dragging of the mirror charge inside the wall, also forms part of the current ject. The cross-disciplinary proposal combines atomic theory and quantum-field theory in the low-energy domain to address fundamentally important questions and pressing current experimental-theoretical discrepancies. Advanced numerical methods and the education of graduate students and the development of postdoctoral research associates are cornerstones of the investigations. Potential applications of some of the developed numerical methods, beyond those devised for atomic-physics calculations, are currently being envisaged.