Hartree method for molecular polaritons

The formation of the composite photonic-excitonic particle, known as a polariton, is a phenomenon emerging in materials possessing strong coupling to light. The organic-based materials besides the strong light-matter coupling also demonstrate strong interaction of electronic and vibrational degrees of freedom. We study the vibration-assisted polariton wave-function evolution treating both types of interactions as equally strong. Using the multiconfiguration Hartree approach we derive the equations of motion for the polariton wave function, where the vibration degrees of freedom interact with the polariton quantum field through the mean-field Hartree term. For the conventional quadratic polariton Hamiltonian and the Holstein-type vibration Hamiltonian (Tavis-Cummings-Holstein model), the obtained equations are in one-to-one correspondence with the original Schrodinger equation. In the second part of the paper, we show that our theory reproduces the physical properties of the polariton light emission spectrum. In particular, the theory explains experimental observations of the molecular Stokes shift in the polariton fluorescence spectra in the systems with strong light-matter coupling. We also investigate the behavior of the polariton wave function in the vicinity of the anticrossing point and demonstrate that the Hartree term can produce an infinite potential barrier of a dynamical origin, which is responsible for the formation of the mixed upper-lower polariton states. The nonlinear nature of the polariton theory reflects their collective behavior. We expect that the multiconfiguration Hartree approach being applied to polaritons and similar systems will result in a manifestation of new physical phenomena.