The non-relativistic Pauli-Fierz Hamiltonian ĤPF has been widely applied to study light-matter hybrid systems. A widely used approximation to the Pauli-Fierz Hamiltonian for many molecules in the weak-to-strong coupling regime is the Tavis-Cummings (TC) Hamiltonian ĤTC . The TC Hamiltonian simultaneously drops the dipole-self energy (DSE) and introduces the rotating wave approximation (RWA). The TC Hamiltonian can be written as,