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Acta Physica Sinica

Effects of Dzyaloshinskii-Moriya interacton and decoherence on entanglement dynamics in Heisenberg spin chain system with different initial states

Mei-Yan Cong, Yang Jing, Huang Yan-Xia

Published Jan 1, 2016• 1 citation
Publisher

Abstract

With considering the intrinsic decoherence, the dynamic behaviors of quantum entanglement in a three-qubit XXZ Heisenberg system with Dzyaloshinskii-Moriya (DM) interaction and anisotropy for different initial states are investigated. The research result shows that the anisotropy parameter does not affect the system entanglement, however, the intrinsic decoherence has obvious inhibitory effect on entanglement. When the initial state of system is an entangled state, we can obtain the stable value of entanglement by adjusting DM interaction parameters appropriately. As the system initial state is a separation state, entanglement oscillates, and the amplitude of oscillation decays with time periodically, and there will appear the death phenomenon after each oscillation, and with time going on, its concurrence will be zero. When the initial state is entangled, by choosing the proper DM parameter, the three pairs of entanglements oscillate with time and eventually approach to a steady value. The increase of accelerates the decay of concurrence. When the initial state is separated, entanglement oscillates, and the amplitude of oscillation decays with time periodically, and there will appear the death phenomenon after each oscillation, with time going on, its concurrence will be zero. Therefore, the proper initial state and DM interaction parameters can control the concurrence effectively under the intrinsic decoherence, thereby obtaining the preferable entanglement resource.

DOI
10.7498/aps.65.170301

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With considering the intrinsic decoherence, the dynamic behaviors of quantum entanglement in a three-qubit XXZ Heisenberg system with Dzyaloshinskii-Moriya (DM) interaction and anisotropy for different initial states are investigated. The research result shows that the anisotropy parameter does not affect the system entanglement, however, the intrinsic decoherence has obvious inhibitory effect on entanglement. When the initial state of system is an entangled state, we can obtain the stable value of entanglement by adjusting DM interaction parameters appropriately. As the system initial state is a separation state, entanglement oscillates, and the amplitude of oscillation decays with time periodically, and there will appear the death phenomenon after each oscillation, and with time going on, its concurrence will be zero. When the initial state is entangled, by choosing the proper DM parameter, the three pairs of entanglements oscillate with time and eventually approach to a steady value. The increase of accelerates the decay of concurrence. When the initial state is separated, entanglement oscillates, and the amplitude of oscillation decays with time periodically, and there will appear the death phenomenon after each oscillation, with time going on, its concurrence will be zero. Therefore, the proper initial state and DM interaction parameters can control the concurrence effectively under the intrinsic decoherence, thereby obtaining the preferable entanglement resource.
Taking the intrinsic decoherence effect into account, the entanglement of a two-qubit anisotropic Heisenberg XYZ chain in the presence of the Dzyaloshinski–Moriya (DM) anisotropic antisymetric interaction is investigated in this paper. Concurrence, the measurement of entanglement, is calculated. Compared with the anisotropic in XY plane, the DM interaction is another kind of anisotropic antisymmetric exchange interaction. It is shown that the intrinsic decoherence obviously suppresses the time evolution of the entanglement. The DM interaction only acts on the time evolution of the entanglement when the initial state is |ψ(0)⟩ = cosα|01⟩ + sinα|10⟩ and weakens the degree of entanglement. The anisotropic in XY plane merely impacts on the time evolution of the entanglement when the system is initially in a state |ψ(0)⟩ = cosα|00⟩ +sinα|11⟩. The sufficiently weak anisotropic in XY plane can effectively enhance the degree of entanglement.
Taking the intrinsic decoherence effect into account,the entanglement of a two-qubit anisotropic Heisenberg XYZ chain in the presence of the Dzyaloshinski-Moriya(DM)anisotropic antisymetric interaction is investigated in this paper.Concurrence,the measurement of entanglement,is calculated.Compared with the anisotropic in XY plane,the DM interaction is another kind of anisotropic antisymmetric exchange interaction.It is shown that the intrinsic decoherence obviously suppresses the time evolution of the entanglement.The DM interaction only acts on the time evolution of the entanglement when the initial state is |(?)(0)=cosα|01+sinα|10 and weakens the degree of entanglement.The anisotropic in XY plane merely impacts on the time evolution of the entanglement when the system is initially in a state |(?)(0)=cosα|00+sinα|11.The sufficiently weak anisotropic in XY plane can effectively enhance the degree of entanglement.
In this paper, we study the improvement and manipulation of pairwise thermal entanglement in one-dimentional three-qubit Heisenberg model, where Dzyaloshinskii-Moriya (DM) interaction is considered and concurrence is calculated to research this entanglements property. The results show that for XXX model, DM interaction can induce entanglement in the antiferromagnetic and ferromagnetic spin chains although the required critical values are different for these cases. For XXZ model, by introducing DM interaction D, antiferromagnetic spin chain has entanglement which is absent when D=0, and in addition, for antiferromagnetic and ferromagnetic cases, DM interaction D and the anisotropy parameter Δ have different effects on entanglement. As a result, the entanglement can be controlled and enhanced by choosing appropriate DM interaction and anisotropy parameter. Furthermore, we find that at the same temperature, no matter for antiferromagnetic or ferromagnetic spin chains, the critical DM interaction inducing entanglement should be greater in a three-qubit XXZ model than that in a two-qubit XXZ model.
This paper investigates the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of Dzyaloshinskii–Moriya interaction. The time evolution of the concurrence is studied for the initial pure entangled states cos θ |00⟩ + sin θ |11⟩ and cos φ |01⟩ + sin φ |10⟩ at zero temperature. The influences of Dzyaloshinskii–Moriya interaction D , anisotropic parameter Δ and environment coupling strength γ on entanglement evolution are analysed in detail. It is found that the effect of noisy environment obviously suppresses the entanglement evolution, and the Dzyaloshinskii–Moriya interaction D acts on the time evolution of entanglement only when the initial state is cos φ |01⟩ + sin φ |10⟩. Finally, a formula of steady state concurrence is obtained, and it is shown that the stable concurrence, which is independent of different initial states and Dzyaloshinskii–Moriya interaction D , depends on the anisotropic parameter Δ and the environment coupling strength γ.
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 and , respectively. It is found that if the system is initially in the state , the entanglement can obtain its maximum when the DM interaction vector D is in the plane of XOZ and magnetic field B = B y with the infinite time t, moreover the entanglement is independent of B y and t when B y is perpendicular to D . In addition, we obtain similar results when the system is initially in the states or . However, we find that if the system is initially in the state , 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 B is perpendicular to D for the initial state ρ 4 (0), the negativity oscillates with time t and reaches a stable value, the larger the value of 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.
We investigate the exact entanglement dynamics of a two-qubit Heisenberg XXZ chain with Dzyaloshinskii-Moriya (DM) interactions, interacting with an anisotropic spin bath in thermal equi- librium at a temperature T, driven by an external magnetic field B along the z-axis. We establish that, for an initially entangled qubit pair, the DM interactions generate entanglement and enhance the entanglement in the revival region. The effects of the DM interaction are also seen to be very important at high temperatures and for weak coupling between the two qubits where it is seen to preserve entanglement. These effects are weakened when the magnetic field B and the Heisenberg coupling are switched on. If the two-qubits are prepared in an initially separable state, the DM in- teraction instead has a negative effect on their entanglement. On a whole entanglement can better be preserve in the spin chain even at high temperatures by increases the external magnetic field B and the Heisenberg couplings, and by tuning the strength of the DM interaction.