Superfluid-Mott Insulator Quantum Phase Transition In A Cavity Optomagnonic System

The superfluid-Mott insulator quantum phase transition is one of the paradigm examples of a quantum phase transition.The quantum phase transition of bosons has been proposed in the Bose-Hubbard model theoretically,and it's been realized experimentally in Bose-Einstein condensate.Hereafter,this quantum phase transition of light has been investigated in the Jaynes-Cummings Hubbard model,and many extended Jaynes-Cummings Hubbard models have been studied in recent years theoretically.Based on the basic characteristics of the cavity optomagnonic system of the emerging hybrid quantum system,this paper carries out theoretical research on the superfluid-Mott insulator quantum phase transition in the cavity optomagnonic array system.The hybrid quantum system has attracted much attentions in recent years,one of its unique advantages is that it can achieve strong(even ultrastrong)coupling between cavity photons and magnons,which leads this system to become a very promising quantum information processing platform.In this paper,the superfluid-Mott insulator quantum phase transition in a two-dimensional cavity optomagnonic array system has been studied based on this characteristic.The analytical solutions of superfluid order parameter and the critical hopping rate are obtained by the mean-field approach,second perturbation theory,and Landau phase transition theory.The numerical results show that the increasing coupling strength and the positive detunings of the photon and the magnon favor the coherence and then the stable areas of Mott lobes are compressed correspondingly.Moreover,the analytical results agree with the numerical ones when the total excitation number is lower.Finally,an effective repulsive potential is constructed to exhibit the corresponding mechanism.In addition,the influence of the magnon Kerr nonlinear effect and the photon Kerr nonlinear effect on the superfluid-Mott insulator quantum phase transition are discussed.The results exhibit that when the magnon Kerr nonlinear coefficient is positive,the system is more favorable to the Mott insulator phase with the increasing of the magnon Kerr nonlinear coefficient,and the Mott insulator phase region in the phase diagram increase obviously when the coupling strength between photon and magnon increases.Inversely,it is not conducive to the Mott lobe with the high excitation number when the magnon Kerr nonlinear coefficient is negative and large.Both the superfluid phase region and the Mott insulator phase region are compressed by the unreliable region,and the Mott lobe is destroyed when the coupling strength is large.Moreover,the photon Kerr nonlinear effect is not an advantage to the coherence of the system.Finally,it is found that when both kinds of Kerr nonlinear effects exist in the system,the influence of the magnon(photon)Kerr nonlinear effect on the phase transition is enhanced.The results obtained here provide an experimentally feasible scheme for characterizing the quantum phase transitions and a new possibility in a cavity optomagnonic array system.