Investigation of Nonlinear Dispersion for Quantum Optics by Experiments with Cavity Polaritons in Polymers with Nonlinear Response

Parametric down conversion and four wave mixing are cornerstones of quantum optics that are independently well understood. However, a theory that properly handles nonlinear dispersion and its effects on many photon state evolution remains elusive. We develop a path toward a fully dispersive theory of nonlinear quantum optics, explore the consequences of simultaneously supporting parametric down conversion and four wave mixing with nonlinear dispersion, and discuss its applications to exotic photon state preparation, beam manipulation, and uses in metrology. Simulations of multiphoton state evolution are designed -- inspired by the work of Sipe et al. -- to include nonlinear dispersion ad hoc. We explore a variety of methods for including nonlinear dispersion and test their validity by replicating the simulation experimentally. Our experiments involve scattering cavity polaritons in stratified nonlinear polymers and microring resonators, and measuring correlations to determine the generation of time-frequency, path, and polarization entanglement for multiphoton systems beyond the biphoton regime. The experiments and simulation inform the development of a proper quantization of Maxwell's equations in nonlinear media.