The Control Of Quantum Entanglement In Heisenberg System

In the field of quantum information, there are various quantum properties (quantum entanglement, quantum correlation, quantum decoherence) have relation with the effective implementation of quantum information processing in quantum systems, so it is necessary for the study of complex quantum properties in quantum system. In addition, it is also very important to find the appropriate physical system to implement large-scale quantum information processing, and the physical system must have good scalability and integration for the requirement of the physical law. The extensive researches show that the solid system is the most likely system for the realization of quantum computation.Heisenberg model is a simple model which can be obtained in solid system. Moreover, quantum entanglement shows the unusual nonlocal correlation in quantum system, and is the key resource for all kinds of quantum information processing.In view of the above reasons, this paper focuses on the quantum entanglement in Heisenberg system, the main works of this paper are as follows:1. The effect of the spin of the system on the thermal entanglement is studied for the general Heisenberg in two-site system. It is shown that with increasing spin, the Negativity will increase, and then decrease slowly. In addition, we find that Negativity will approach a constant with the increase of DM interaction, the constant increases with the increase of spin, and both the threshold temperature and critical uniform external magnetic field will increase with the increasing spin. Thus high-spin system can inhibit the influence of the external environment better.2. We investigate the effect of the directions of DM interaction and magnetic field on the thermal entanglement in the pure DM model, which we call it special Heisenberg system. There are two types of Hamiltonian in our paper, one is H1=D·(σ1(?)σ2)+B·σ1 the other is H2=D·(σ1(?)σ2)+B·(σ1+σ2). It is found that when the Hamiltonian is H1 the entanglement can reach its maximum if the directions of the magnetic field and the DM vector are parallel. In addition, when the Hamiltonian is H2, if the directions of the magnetic field and the DM vector are perpendicular in high magnetic field, or their directions are parallel in weak magnetic field, the entanglement can also reach its maximum. So the entanglement can be enhanced by adjusting the direction of the external magnetic field.3. We investigate the effect of the directions of DM interaction and magnetic field on entanglement in intrinsic decoherence for the special Heisenberg system. We assume that the system is initially in four bell states. For the three symmetrical states, there is a special direction of magnetic field that can keep the maximally entangled state when the DM interaction is perpendicular to the magnetic field. Besides, the maximally entangled state is independent of magnetic field and the time of evolution. However, for the antisymmetrical state, we find three special direction of magnetic field that the entanglement decrease to a stable value with time when the DM interaction is perpendicular to the magnetic field. Besides, the stable value will increase with the increasing magnetic field.