where qc = h/2ω c (â † + â) and pc = i hω c /2(â † -â) are photon field operators, â † and â are the photonic creation and annihilation operators, respectively, and ω c is the photon frequency inside the cavity. The light-matter coupling term Ĥenp (electronicnuclear-photonic interactions) under the dipole gauge (and the long wavelength approximation) is expressed as