Resolution of Gauge Ambiguities in Molecular Cavity Quantum Electrodynamics*

We'll present our recent work on molecular cavity quantum electrodynamics by resolving the gauge ambiguities between the Coulomb gauge and the dipole gauge Hamiltonians under the electronic state truncation [1]. We conjecture that such ambiguity arises because not all operators are consistently constrained in the same truncated electronic subspace for both gauges. We resolve this ambiguity by constructing a unitary transformation operator that properly constrains all light-matter interaction terms in the same subspace. We further derive an equivalent and yet convenient expression for the Coulomb gauge Hamiltonian under the truncated subspace. We finally provide the analytical and numerical results of a model molecular system coupled to the cavity to demonstrate the validity of our theory. 

We will further discuss the situartion of few-mode cavity quantum electrodynamics and resolve the gauge ambiguities [2]. We first propose a general framework to resolve

ambiguities for an arbitrary truncation in a given gauge. 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.

[1] M. A. D. Taylor, A. Mandal, W. Zhou, P. Huo Phys. Rev. Lett. 125, 123602 (2020)

[2] M. A. D. Taylor, A. Mandal, P. Huo Optics Lett. 47, 1446 (2022)