Effects of Pure Dzyaloshinskii–Moriya Interaction with Magnetic Field on Entanglement in Intrinsic Decoherence

We investigate the effects of pure Dzyaloshinskii–Moriya (DM) interaction with magnetic field on entanglement in intrinsic decoherence, assuming that the system is initially in four Bell states |\phi_\pm\rangle=(|00\rangle\pm|11\rangle)/\sqrt2 and |\psi_\pm\rangle=(|01\rangle\pm|10\rangle)/\sqrt2, respectively. It is found that if the system is initially in the state \rho_1(0)=|\phi_+\rangle\langle\phi_+|, the entanglement can obtain its maximum when the DM interaction vector \boldsymbol D is in the plane of XOZ and magnetic field \boldsymbol B=\boldsymbol B_y with the infinite time t, moreover the entanglement is independent of B_y and t when \boldsymbol B_y is perpendicular to \boldsymbol D. In addition, we obtain similar results when the system is initially in the states \rho_2(0)=|\phi_-\rangle\langle\phi_-| or \rho_3(0)=|\psi_+\rangle\langle\psi_+|. However, we find that if the system is initially in the state \rho_4(0)=|\psi_-\rangle\langle\psi_-|, the entanglement can obtain its maximum for infinite t, when the DM vector is in the plane of YOZ, XOZ, or XOY, with the magnetic field parallel to X, Y, or Z axis, respectively. Moreover, when the axial \boldsymbol B is perpendicular to \boldsymbol D for the initial state \rho_4(0), the negativity oscillates with time t and reaches a stable value, the larger the value of \boldsymbol B is, the greater the stable value is, and the shorter the oscillation time of the negativity is. Thus we can adjust the direction and value of the external magnetic field to obtain the maximal entanglement, and avoid the adverse effects of external environment in some initial state. This is feasible within the current experimental technology.