Long-Range Quantum Coherence and Quantum Phase Transition in Atom-Microcavity Coupled System

In this study, the quantum simulation of the Heisenberg spin XY model is realized by obtaining the effective Hamiltonian of the atom-microcavity coupled systems via adiabatic approximation. Further, the quantum coherence between any two-body quantum systems is analyzed based on the criterion of relative entropy to obtain quantum resources. The long-range quantum coherence decreases exponentially with increasing the two-body spacing. Furthermore, when the system parameters arc varied, it is found that there is a numerical mutation in the long-range quantum coherence near the quantum critical point, which provides a possible order parameter for characterizing the quantum phase transition. After considering the influence of external light-field noise on the quantum coherence, it is found that the quantum coherence decays with time and gradually disappears.