Non-equilibrium cavity pumping of electronic molecular polaritons

Abstract

Strong light-matter coupling in optical cavities offers a non-invasive route to modify molecular properties, and it is usually reached by collectively coupling many molecules to the same mode. Here we consider the photonic counterpart of the collective regime, in which a single molecule interacts with a cavity mode holding many photons, a steady state of the pumped cavity. Since the eigenstates of the Pauli-Fierz Hamiltonian carry no transverse electric field, such a state cannot be described as an excited state of the light-matter system. We therefore constrain the photon number of the strong coupling QED Hartree-Fock wave function with a Lagrange multiplier and self consistently minimize the energy with respect to all parameters. The constrained reference carries the field of a coherent state with an average number of photons, generated by a cavity mode whose effective free-field frequency is lowered by the multiplier. We apply this framework to benzene and a benzene-water complex, where the pumped cavity polarizes the molecules and modifies their interaction as with a static classical field. For hydrogen peroxide, the field can reshape the torsional potential and the far-infrared torsional spectrum. The classical driven field limit thus emerges from a quantized mean field description, and the photon density becomes a control parameter for cavity-modified chemistry.