Title: Polariton Creation in Coupled Cavity Arrays with Spectrally Disordered Emitters

Abstract: Integrated photonics has been a promising platform for analog quantum simulation of condensed matter phenomena in strongly correlated systems. To that end, we explore the implementation of all-photonic quantum simulators in coupled cavity arrays with integrated ensembles of spectrally disordered emitters. Our model is reflective of color center ensembles integrated into photonic crystal cavity arrays. Using the Quantum Master Equation and the Effective Hamiltonian approaches, we study energy band formation and wavefunction properties in the open quantum Tavis-Cummings-Hubbard framework. We find conditions for polariton creation and (de)localization under experimentally relevant values of disorder in emitter frequencies, cavity resonance frequencies, and emitter-cavity coupling rates. To quantify these properties, we introduce two metrics, the polaritonic and nodal participation ratios, that characterize the light-matter hybridization and the node delocalization of the wavefunction, respectively. These new metrics combined with the Effective Hamiltonian approach prove to be a powerful toolbox for cavity quantum electrodynamical engineering of solid-state systems.