Intracavity photon statistics from correlated molecular electronic structure

Quantum optics characterizes light through photon correlations, motivating their connection to correlated ab initio molecular electronic structure. In this study, intracavity photon statistics of cavity-coupled molecules are computed from QED coupled-cluster (QED-CCSD-22) densities and validated against exact diagonalization of the Pauli-Fierz Hamiltonian. A change of coordinate origin or dipole convention displaces the ground state coherently, so second-order and higher cumulants of the cavity field are independent of these conventions even for molecular ions. The photon subsystem of QED Hartree-Fock is exactly coherent, so the invariant statistics describe fluctuations beyond this electron-photon product reference. The field fluctuations are super-Poissonian, and their degree of second-order coherence depends primarily on cavity frequency in the tested weak-coupling regime, falling from 18.5 to 4.9 for H2 as the cavity is detuned from 5 to 20 eV. The third cumulant identifies non-Gaussian fluctuations and changes sign under reversal of the coupling direction.