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

简单原子系统跃迁频率的光谱测量对近100年来物理学的进步作出了重大贡献。氢原子的玻尔模型是在带正电的质子产生的中心静电势影响下行星轨道的量子-经典对应的基础上，加上玻尔-索默菲尔德量子化条件建立起来的。几十年来，相对论物理学和量子场论对这一理论进行了进一步完善。通过更仔细地分析光谱，人们已经能够从实验中推断出原子的一些微妙特性，比如大质量中心粒子（即质子）的电荷半径。最近，人们进行了一项实验，对短距离库仑力定律的场论修正提出了质疑：瑞士维利根Paul-Scherrer研究所进行的所谓介子氢实验，已经获得了介子和质子结合系统的跃迁结果，这与物理界至少20年来进行的其他实验和理论计算不一致。在美国国家科学基金会的计划中，将从理论方面研究随后的质子半径谜题的一些最后可能的解释，目的是排除这些解释，或者为我们对质子内核电荷分布的理解进行必要的修改找到确认。基于PI在场论方面的广泛知识，最初在束缚态修正分析中发展起来的概念和思想将应用于所谓的动态过程和原子表面相互作用。当原子与介电表面接触时，电场的真空模在该表面附近受到扰动。真空模式（金属表面附近电场的“首选自然振荡模式”）的量子涨落（由于海森堡不确定性关系而不可避免的“抖动”）改变了表面附近原子的相互作用势，并且介电材料内部镜像电荷的“拖拽”引起了摩擦力。即使原子与表面没有物理接触，这种情况也会发生，原子与表面的量子力学波函数的重叠可以忽略不计。这些影响将在美国国家科学基金会的研究项目中进行研究，并与世界上各个实验室正在进行的实验结果进行比较。最后，所有这些效应都将在少数电子原子中进行研究，因为这些原子的基本量子力学时间演化算符（定义能级的“哈密顿算符”）的能量特征值不能以解析形式计算。将探讨基于新颖基集（“量子力学试波函数”）改进近似方法的想法。上述所有的研究努力都适合研究生的教育。事实上，在基础物理学和应用物理学的知识上的获得，以及在使用先进数值方法方面的教育，都有助于许多研究生在过去（人们可以设想，现在和将来）的指导下取得成功。这包括用于研究束缚系统的数值方法，以及基于量子场的真空涨落的其他更倾向于数学的概念，这些方法经常发现令人惊讶的、实际有用的应用。在这个项目中有三个主要的工作领域。第一个问题是介子氢和质子半径的难题。介子氢之谜一直困扰着物理学家，它代表了我们对基本力的理解中最迫切需要回答的问题之一。也就是说，对介子氢的测量得出的质子电荷半径值与散射实验和原子氢的激光光谱测量结果都不一致。这个项目涉及重新计算最后一个可能的理论解释的分歧，尚未完全覆盖在文献中。第二个问题涉及多体系统中的高阶修正。在二体问题之外，即使在非相对论性量子力学中，也不可能解析求解束缚态系统。我们将研究类氦系统中高阶校正的三个方面，这三个方面对实验的描述是至关重要的。这些包括氦中的所谓相对论贝特对数，以及束缚的“介子氦”系统中的高阶效应。这些计算对于解决介子氢与其他介子束缚系统的难题，以及确定电子-介子质量比都很重要。最后，将研究卡西米尔效应、动力学过程和原子-壁相互作用。原子-壁相互作用是由固体材料（“壁”）飞行的原子之间的真空介导的相互作用，取决于介质的介电响应函数的功能形式。该项目包括一项研究，可以想象是与实验学家合作，研究原子-壁相互作用的温度依赖性，这可能已经在实验中看到，以及氦- α -石英和氦-金系统的原子-壁相互作用电位的细节。对量子摩擦力理解的理论进展，由于镜面电荷在壁内的拖拽，也形成了当前物体的一部分。这个跨学科的提议结合了低能领域的原子理论和量子场论，以解决根本性的重要问题和紧迫的当前实验理论差异。先进的数值方法和研究生的教育以及博士后研究人员的发展是这些研究的基石。除了为原子物理计算设计的数值方法之外，目前正在设想一些已开发的数值方法的潜在应用。

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.