We explore quantum phase transitions in the multiphoton Jaynes-Cummings-Hubbard model (JCHM). Using the mean-field approximation, we demonstrate that the multiphoton JCHM exhibits quantum phase transitions between the Mott insulator (MI) phase, the superfluid phase, and an additional phase we refer to as the forbidden phase. The multiphoton JCHM MI phases are classified according to a conserved quantity associated with the total number of excited atoms and photons. When this conserved quantity diverges toward positive infinity, this system enters the forbidden phase. By analyzing the system, we observe MI, superfluid, and forbidden phases in both the single- and two-photon JCHMs, although the MI phases in the two-photon case are confined to subspaces with small values of the conserved quantity. In contrast, only the superfluid and forbidden phases appear in the three- and four-photon JCHMs, with no MI phase observed.
The Jaynes-Cummings-Hubbard model describes a network of interacting atom-cavity systems. In this model the photons can hop between cavities effecting a tunneling interaction, and the Jaynes-Cummings interaction gives rise to an onsite interaction. This model forms a bridge connection between condensed matter physics and quantum optics. Here we review the physics underpinning this model, properties of Jaynes-Cummings-Hubbard systems, the requirements on systems for realizing this model, and some of the progress to date.