Dynamics Of Entanglement In Spin Chain Systems

Entanglement is a nonlocal correlation between quantum systems that do not exist classically. Quantum entanglement has been recognized as a crucial resource in various fields of quantum information, such as quantum cryptography, teleportation, and computation. Many physical systems have been proposed in the quantum information processing, spin chain system is such a solid system that easy to be extended and integrated, and it can be used as quantum wire. In this paper, we focus on the study of entanglement dynamics in spin chains, and the preparation and preservation of quantum entanglement are discussed.The effect of three-body interactions on the dynamics of entanglement is studied for the first time in this paper. With the development of experimental technique, effective three-spin interactions have been realized in cold polar molecules and atoms in optical lattices, and it can also be simulated by the combination of two spin interactions and RF pulses in NMR. The entanglement dynamics of isotropic Heisenberg chains and Ising chains are simulated for two types of initial states. For closed Ising chains, it is found that three-body interactions will have great effects on the generation and preservation of entanglement. A large remote entanglement can be obtained through free evolution from an initial separable state when three-body interactions are involved. For an initially maximal pair-entangled state, the entanglement will decrease more slowly with time upon consideration of three-body interactions. Effects of three-body interactions on the dynamics of entanglement in an open Ising chain are similar to that in a closed Ising chain. Under the same spin couplings, a slightly larger entanglement can be obtained in the open chain comparing with the closed chain from a separable initial state. For an isotropic Heisenberg chain, the effect of three-body interaction on the dynamics of entanglement is different from that for the Ising chain. For a separable initial state, the three-body interactions are not in favour of preparing entanglement in a Heisenberg chain. For an initially maximal pair-entangled state, the concurrences fluctuate with relatively small amplitudes when the three-body interactions are concerned. In a word, three-body interactions will give rise to great influence on the dynamics of entanglement in spin chains, and it is unfavorable for the preparing and preservation of entanglement in the Heisenberg chain.Secondly, we discuss the dynamics of thermal entanglement in a driven XY spin chain, in which the spin coupling can be controlled externally. Effects of driving frequency, chain's length, temperature, and anisotropic parameterγon the evolution of concurrence between two ends spins are studied. We find that the concurrence approaches unity when the driven frequency satisfiesωd =2B at zero temperature. With the increase of temperature, the maximum value of concurrence between the ends spins C1 mNax will decrease to zero at a critical temperature Tc , and Tc will decrease with the increase of the chain's length. For a given temperature, C1 mNaxdecreases with the increase of the chain's length. Furthermore, with the increasing of the anisotropic parameter, the maximal concurrence will decrease to zero. In the isotropic XY spin chain, the resonance of entanglement can not be observed.In summary, Effects of three-body interactions on the preparation and preservation of quantum entanglement dynamically in spin chains are investigated for the first time. It is found that the effects of three-body interactions on the evolution of entanglement in the Ising chain and in the Heisenberg chain are different. Entanglement resonance in a driven XY spin chain at a finite temperature is investigated in the second part of this paper, and the effects of chain's length, temperature, and anisotropic parameter on the thermal entanglement is obtained. We hope our study can shed light on the control of the thermal entanglement in spin chain systems, and it is significant in the field of quantum controlling.