Resolution of Gauge Ambiguities in Molecular Cavity Quantum Electrodynamics

TL;DR

This paper resolves gauge ambiguities in molecular cavity QED by developing a theoretical framework that constrains operators in truncated electronic subspaces, ensuring consistent Hamiltonian descriptions.

Contribution

It introduces a unitary transformation to properly constrain operators in truncated electronic subspaces, clarifying gauge equivalence in molecular cavity QED.

Findings

Analytical and numerical validation on a model molecular system.

Demonstration of gauge ambiguity resolution.

Consistent Hamiltonian formulation under electronic truncation.

Abstract

This work provides the fundamental theoretical framework for the molecular cavity Quantum Electrodynamics by resolving the gauge ambiguities between the Coulomb gauge and the dipole gauge Hamiltonian under the electronic state truncation. Our conjecture for the arising of such gauge ambiguity is that not all operators are properly constrained in the truncated electronic subspace. Based upon this conjecture, we construct a unitary transformation that properly constrains all operators in the subspace, and 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.