Quantum phase transitions in the multiphoton Jaynes-Cummings-Hubbard model

Abstract: We explore quantum phase transitions in the multiphoton Jaynes-Cummings-Hubbard model (JCHM). Using the mean-field approximation, we show that multiphoton JCHM reveals quantum phase transitions between the Mott insulator (MI), superfluid and Bose-Einstein condensation (BEC) phases. The multiphoton JCHM MI phases are classified according to a conserved quantity associated with the total number of excited atoms and photons. If this conserved quantity diverges to infinity, this system is in the BEC phase. Exploring this system we observe the MI, BEC, and superfluid phases in both the single- and two-photon JCHMs although the two-photon JCHM MI phases are restricted to the small conserved quantity subspace. Contrastingly, only the superfluid and BEC phases arise in the three- and four-photon JCHMs (the MI phase is not observed).