Interaction-induced Lipkin-Meshkov-Glick model in a Bose-Einstein condensate inside an optical cavity

In this paper we present an experimentally feasible scheme to simulate a generalized Lipkin-Meskov-Glick model in a Bose-Einstein condensate coupled dispersively with an ultrahigh-finesse optical cavity. This obtained Hamiltonian has a unique advantage in that all parameters can be controlled independently by using Feshbach resonance technique, a pump laser along cavity axis and an external driving laser. By the proper choice of parameters, the macroscopic quantum coherent effect with a large amplitude can be successfully achieved. Comparing with the exist schemes, our proposal has a cleaner, perhaps significantly improved to observe this whole coherent effect. Finally, we predict a novel interaction-induced topological transition, which is an abrupt variation from pi to zero of the Berry phase.