Quantum entanglement in the system of two spin-1/2 particles with Heisenberg 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 Omega 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 ka and are dramatically different from those in the case of selective measurement for spin.