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Chinese Physics B

Entanglement sudden death induced by the Dzialoshinskii–Moriya interaction

Zeng Hong-Fang, Shao Bin, Linguang Yang, Jian Li, Zou Jian

Published Jul 31, 2009• 15 citations
Publisher

Abstract

In this paper, we study the entanglement dynamics of two-spin Heisenberg XYZ model with the Dzialoshinskii–Moriya (DM) interaction. The system is initially prepared in the Werner state. The effects of purity of the initial state and DM coupling parameter on the evolution of entanglement are investigated. The necessary and sufficient condition for the appearance of the entanglement sudden death (ESD) phenomenon has been deduced. The result shows that the ESD always occurs if the initial state is sufficiently impure for the given coupling parameter or the DM interaction is sufficiently strong for the given initial state. Moreover, the critical values of them are calculated.

DOI
10.1088/1674-1056/18/8/029

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In this paper, we study the entanglement dynamics of two-spin Heisenberg XYZ model with the Dzialoshinskii–Moriya (DM) interaction. The system is initially prepared in the Werner state. The effects of purity of the initial state and DM coupling parameter on the evolution of entanglement are investigated. The necessary and sufficient condition for the appearance of the entanglement sudden death (ESD) phenomenon has been deduced. The result shows that the ESD always occurs if the initial state is sufficiently impure for the given coupling parameter or the DM interaction is sufficiently strong for the given initial state. Moreover, the critical values of them are calculated.
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.
In this article, we present the entanglement dynamics in a qubit-qutrit system. Here, we consider a closed system as a pair of qubit-qutrit and an external qubit which interacts with the qutrit of the closed system via y-component of the Dzyaloshinskii-Moriya (DM) interaction. We find that the state of external qubit do not affect the entanglement in two parameter qubit-qutrit states, it is only DM interaction strength which is affecting the entanglement. Further, we investigate the phenomenon of entanglement sudden death and identify the affected and unaffected two parameter qubitqutrit states by DM interaction.
Taking the decoherence effect due to population relaxation into account, we investigate the entanglement properties for two qubits in the Heisenberg XY interaction and subject to an external magnetic Geld. It is found that the phenomenon of entanglement sudden death (ESD) as well as sudden birth (ESB) appear during the evolution process for particular initial states. The influence of the external magnetic Geld and the spin environment on ESD and ESB are addressed in detail. It is shown that the concurrence, a measure of entanglement, can be controlled by tuning the parameters of the spin chain, such as the anisotropic parameter, external magnetic Geld, and the coupling strength with their environment. In particular, we Gnd that a critical anisotropy constant exists, above which ESB vanishes while ESD appears. It is also notable that stable entanglement, which is independent of different initial states of the qubits, occurs even in the presence of decoherence.
In this paper, we investigate the dynamical behaviour of entanglement in terms of concurrence in a bipartite system subjected to an external magnetic field under the action of dissipative environments in the extended Werner-like initial state. The interesting phenomenon of entanglement sudden death as well as sudden birth appears during the evolution process. We analyse in detail the effect of the purity of the initial entangled state of two qubits via Heisenberg XY interaction on the apparition time of entanglement sudden death and entanglement sudden birth. Furthermore, the conditions on the conversion of entanglement sudden death and entanglement sudden birth can be generalized when the initial entangled state is not pure. In particular, a critical purity of the initial mixed entangled state exists, above which entanglement sudden birth vanishes while entanglement sudden death appears. It is also noticed that stable entanglement, which is independent of different initial states of the qubits (pure or mixed state), occurs even in the presence of decoherence. These results arising from the combination of the extended Werner-like initial state and dissipative environments suggest an approach to control and enhance the entanglement even after purity induced sudden birth, death and revival.