Band Structure, Phase transitions and Semiconductor Analogs in One-Dimensional Solid Light Systems

The conjunction of atom-cavity physics and photonic structures (``solid light'' systems) offers new opportunities in terms of more device functionality and the probing of designed emulators of condensed matter systems. By analogy to the canonical one-electron approximation of solid state physics, we propose a one-polariton approximation to study these systems. Using this approximation we apply Bloch states to the uniformly tuned Jaynes-Cummings-Hubbard model to analytically determine the energy band structure. By analyzing the response of the band structure to local atom-cavity control we explore its application as a quantum simulator and show phase transition features absent in mean field theory. Using this novel approach for solid light systems we extend the analysis to include detuning impurities to show the solid light analogy of the semiconductor. This investigation also shows new features with no semiconductor analog.