Taylor Michael A D, Mandal Arkajit, Huo Pengfei
Opt Lett. 2022 Mar 15;47(6):1446-1449. doi: 10.1364/OL.450228.
This work provides the fundamental theoretical framework for few-mode cavity quantum electrodynamics by resolving the gauge ambiguities between the Coulomb gauge and the dipole gauge Hamiltonians under the photonic mode truncation. We first propose a general framework to resolve ambiguities for an arbitrary truncation in a given gauge. Then, we specifically consider the case of mode truncation, deriving gauge invariant expressions for both the Coulomb and dipole gauge Hamiltonians that naturally reduce to the commonly used single-mode Hamiltonians when considering a single-mode truncation. We finally provide the analytical and numerical results of both atomic and molecular model systems coupled to the cavity to demonstrate the validity of our theory.
这项工作通过解决光子模式截断下库仑规范和偶极规范哈密顿量之间的规范模糊性，为少模腔量子电动力学提供了基本的理论框架。我们首先提出一个通用框架，以解决给定规范中任意截断的模糊性。然后，我们具体考虑模式截断的情况，推导出库仑规范和偶极规范哈密顿量的规范不变表达式，当考虑单模截断时，这些表达式自然会简化为常用的单模哈密顿量。我们最终给出了与腔耦合的原子和分子模型系统的解析和数值结果，以证明我们理论的有效性。
