Variational theory of non-relativistic quantum electrodynamics

TL;DR

This paper develops a variational theoretical framework for non-relativistic quantum electrodynamics, enabling accurate, non-perturbative calculations of ground and excited states in complex light-matter systems, including phenomena like Lamb shifts and Casimir forces.

Contribution

It introduces a novel variational approach with an effective photonic vacuum, providing a new ab initio method for analyzing coupled light-matter systems beyond perturbation theory.

Findings

Achieves less than 1% error in energy calculations across coupling regimes.

Provides a non-perturbative description of Lamb shifts and Casimir-Polder forces.

Suggests new physical concepts like the Casimir energy of a single atom.

Abstract

The ability to achieve ultra-strong coupling between light and matter promises to bring about new means to control material properties, new concepts for manipulating light at the atomic scale, and fundamentally new insights into quantum electrodynamics (QED). Thus, there is a need to develop quantitative theories of QED phenomena in complex electronic and photonic systems. In this Letter, we develop a variational theory of general non-relativistic QED systems of coupled light and matter. Essential to our ansatz is the notion of an effective photonic vacuum whose modes are different than the modes in the absence of light-matter coupling. This variational formulation leads to a set of general equations that can describe the ground state of multi-electron systems coupled to many photonic modes in real space. As a first step towards a new ab initio approach to ground and excited state energies in QED, we apply our ansatz to describe a multi-level emitter coupled to many optical modes, a system with no analytical solution. We find a compact semi-analytical formula which describes ground and excited state energies to less than 1% error in all regimes of coupling parameters allowed by sum rules. Additionally, our formulation provides essentially a non-perturbative theory of Lamb shifts and Casimir-Polder forces, as well as suggesting new physical concepts such as the Casimir energy of a single atom in a cavity. Our method should give rise to highly accurate descriptions of phenomena in general QED systems, such as Casimir forces, Lamb shifts, spontaneous emission, and other fluctuational electrodynamical effects.