Supersolid Of Extended Jaynes-Cummings-Hubbard Model On The Triangular And One Dimensional Lattices

This thesis uses the mean field(MF)method and the density matrix renormalization group(DMRG)method to study the extended Jaynes-Cummings-Hubbard(JCH)model on the hard-core(maximum photon occupation number equals to 1)and the soft-core(maximum photon occupation number equals to 2)models.JCH model is composed of coupled Jaynes-Cumming(JC)cavities in quantum optics,this will help to understand the regulating effect of light field on quantum many-body states.By using the MF method,this thesis demonstrates the ground state phase diagrams of the extended JCH model on hard-core and soft-core models,and indicates the detailed diagrams with the DMRG method,which,in addition,suggests the supersolids of the phase diagrams are stable.By utilizing the MF method to study hard-core extended JCH model on triangular cavity lattice,two types of solid phases with excitonic density equals to 1/3 and 2/3 are seized.Unlike the previous supersolids found in the extended Bose Hubbard model,the supersolids can be formed with the situation of none repulsion between photons,and thesupersolid exists between the two solid phases.Besides,the hole-excitation supersolid phase is found below the 1/3 solid phase.Both hard-core and soft-core models on the one dimensional lattices,the supersolids phase emerge below the 1/2 solid phase.Moreover,the supersolids are also verified to exist in the thermodynamic limit.Beats emerge within the SS phase for the density-density correlation in both hard-core and soft-core models.The primary substance of this thesis is arranged as follows:In the first chapter,it introduces the concepts and the application of Bose-Einstein condensation of ultracold atoms,the optical lattices and the optical cavity lattices,the superfluid phase,the solid phase and the supersolid phase.And then points out the concepts and the Hamiltonians of normal and extended Bose-Hubbard model,the Jaynes-Cummings model,the Jaynes-Cummings-Hubbard model and the extended Jaynes-Cummings-Hubbard model.According to the second chapter,Mean Field method which contains the single site mean field method and the Cluster mean field method,and the density matrix renormalization group method are mentioned.In the third chapter,exhibiting and analysing results of the extended JCH model on the triangular,one dimensional hard-core and soft-core lattices by using mean field method and the density matrix renormalization group method are proposed.Finally,Chapter IV mainly presents the conclusion and expectation.