Effects of initial states on the quantum correlation in Bose-Hubbard model

Abstract

Quantum correlation is an important resource in quantum information, quantum computation, and quantum metrology. Quantum entanglement, Einstein-Podolsky-Rosen (EPR) quantum steering and Bell nonlocality are the major quantum correlations. For quantum entanglement and Bell nonlocality, two subsystems play the same significant roles. EPR quantum steering is stronger than entanglement and weaker than Bell nonlocality. It represents the ability of one subsystem to nonlocally affect another subsystem's states through local measurements. In this paper, the dynamic quantum correlation between the modes in the two-site Bose-Hubbard model is investigated. According to Hillery-Zubairy entanglement criterion and based on maximum mean quantum Fisher information, the influences of initial states on the quantum entanglement evolutions are explored. If the coupling between the modes is much greater than that of the particles at the same site, and the initial states are symmetric or anti-symmetric SU(2) coherent states, the quantum correlations show simple periodic evolutions. The oscillation amplitudes of the evolutions increase with the interaction between the particles at the same site. The oscillation period decreases with the coupling strength between the modes. The dependence of the period on the interaction of the particles at the same site is related to the initial states. In other words, the time evolutions of quantum correlation are closely related to the symmetry of the initial states. In the case of symmetric (anti-symmetric) SU(2) coherent state and repulsive (attractive) interaction of the particles at the same site, the system presents two-way quantum steering. When the subsystem exchange symmetry of the initial states is broken, the collapse and revival of quantum correlation appear, moreover one-way quantum steering emerges in the infancy. One-way quantum steering is asymmetric for two subsystems. So exchange asymmetry of the initial state is necessary condition of one-way quantum steering when the Hamiltonian of the system is symmetric for two subsystems.