The Jaynes-Cummings-Hubbard (JCH) model is a combination of the Jaynes–Cummings model and the coupled cavities. The one-dimensional JCH model consists of a chain of N-coupled single-mode cavities and each cavity contains a two-level atom as illustrated in the figures. This model was originally proposed in June 2006 in the context of Mott transitions for strongly interacting photons in coupled cavity arrays in Ref. A different interaction scheme has been suggested at the same time, where four level atoms were interacting with external fields and strongly correlated dynamics of polaritons were studied. In Ref. the phase diagram of the JCH using mean field theory has been calculated in which the Mott insulator phase and superfluid phase are identified.