Quantum Entanglement in the system of two spin-1/2 particles with Heinsenberg exchange interaction in the presence of a single-mode vacuum field

The nonclassical properties of two spin-1/2 particles with Heisenberg exchange interaction in a single-mode vacuum field are investigated. By using the quantum reduced entropy, we demonstrate that the ratio k a between Heisenberg exchange interaction constant difference (J - J_z) and the spin-field coupling constant Ω can affect the feature of the entanglement significantly. It is found that the entanglement of the system evolves periodically with time, the evolvement period of the entanglement between two spin-1/2 particles and the field increases with the increasing k_a, which is true for the single spin-field entanglement, but that is contrary for the entanglement between the two spin particles. Our results show that three entangled states of two spins-field, spin-spin, and spin-field can be prepared via two spin-1/2 particles interacting with a single-mode vacuum field. We also characterize the field state by using Mandel's Q parameter, it is proved that the nonclassical properties of the field state will get weaker with the increasing k_a and are dramatically different from those in the case of selective measurement for spin.