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The emerging hybrid cavity optomagnonic system is a very promising quantuminformation processing platform for its strong or ultrastrong photon-magnoninteraction on the scale of micrometers in the experiment. In this paper, thesuperfluid-Mott insulator quantum phase transition in a two-dimensional cavityoptomagnonic array system has been studied based on this characteristic. Theanalytical solution of the critical hopping rate is obtained by the mean fieldapproach, second perturbation theory and Landau second order phase transitiontheory. The numerical results show that the increasing coupling strength andthe positive detunings of the photon and the magnon favor the coherence andthen the stable areas of Mott lobes are compressed correspondingly. Moreover,the analytical results agree with the numerical ones when the total excitationnumber is lower. Finally, an effective repulsive potential is constructed toexhibit the corresponding mechanism. The results obtained here provide anexperimentally feasible scheme for characterizing the quantum phase transitionsin a cavity optomagnonic array system, which will offer valuable insight forquantum simulations.

Superfluid-Mott insulator quantum phase transition in a cavity optomagnonic system