Resolution of Gauge Ambiguities in Molecular Cavity Quantum Electrodynamics

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.