Vacuum-Field Squeezing by Molecules in Optical Cavities: An Exact Bound and Linear-Response Theory

Abstract

The ground state of a molecule coupled to an optical cavity contains virtual photons, and squeezing of the photonic field has been found in exactly solvable models, perturbation theory, and numerical calculations. Here, two exact sum rules for the field quadratures show that, within the dipole approximation, the vector-potential fluctuations of a linearly polarized mode never exceed their vacuum value in the ground state of any molecule at any coupling strength. Consequently, the field is squeezed whenever the mode couples to a dipole-allowed transition from a nondegenerate ground state, and the cavity-induced ground-state energy shift cannot increase with the cavity frequency at a fixed coupling vector, which is an exact constraint on approximate methods. Moreover, the incoherent photon statistics, which exclude the coherent part of the field, are never sub-Poissonian. At weak coupling, an exact resolvent expression reduces the squeezing and the ratio of the anomalous to the normal photon moment to linear-response properties of the isolated molecule, with the ratio set by a mean excitation energy. Time-dependent density functional theory with CAM-B3LYP and PBE0 reproduces exact and QED coupled-cluster references for both quantities to within 5% at 45 benchmark points. A survey of 29 molecules gives mean excitation energies of 9.5-21 eV at a cavity frequency of 2 eV and shows that the most polarizable molecules squeeze the field the most.