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arXiv:0807.3208 · Chinese Physics Letters

Sudden Death, Birth and Stable Entanglement in a Two-Qubit Heisenberg XY Spin Chain

Shan Chuan-Jia, Cheng Wei-Wen, Tang-Kun Liu, Jibing Liu, Wei Hua

Published Sep 1, 2008• 20 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/0256-307x/25/9/006

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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.
Taking the decoherence effect into account, the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of inhomogeneous magnetic field is investigated. The time evolution of concurrence is studied for the initial state cos θ |01⟩ +sin θ|10⟩ at zero temperature. The influences of inhomogeneous magnetic field, anisotropic parameter and decoherence on entanglement dynamic are addressed in detail, and a concurrence formula of the steady state is found. It is shown that the entanglement sudden death (ESD) and entanglement sudden birth (ESB) appear with the decoherence effect, and the stable concurrence depends on the uniform magnetic field B , anisotropic parameter Δ and environment coupling strength γ, which is independent of different initial states and nonuniform magnetic field b.
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.
We investigate the entanglement dynamical behavior of two coupled qubits via a Heisenberg XX interaction, which are connected with two independent finite temperature heat baths. By numerical simulations of the quantum master equation, it is found that the interesting phenomena of entanglement sudden death (ESD) as well as sudden birth (ESB) appear during the evolution process for particular initial states. We also show that two critical temperatures T 1 (determining that the quantum state is entangled or separable) and T 2 (where maximal stationary entanglement can be observed) exist, and stationary entanglement exhibits a non-monotonic behavior as a function of the finite temperature noise strength. These results enlarge the domain of the reasonable experimental temperature where stationary entanglement can be observable.
For a three-qubit Heisenberg XX spin chain with the uniform magnetic field and magnetic impurity, dynamic evolution of pairwise entanglement are studied. We show that the phenomenon of entanglement sudden death (ESD) occurs in the evolution of entanglement for some initial states. We also find that magnetic impurity cannot only eliminate the phenomenon of ESD but also induce the ESD effects, which is different from the case of uniform magnetic field where the ESD can be depressed but cannot be eliminated by introducing the uniform magnetic field.
In this paper, we investigate the entanglement dynamics of two entangled two-level atoms with initial X state and dipole-dipole coupling intensity in Tavis-Cummings model. The interesting phenomena of entanglement sudden death as well as sudden birth appear during the evolution process. We analyze in detail the effect of purity of initially entangled state of two atoms, the dipole-dipole coupling intensity between two atoms, and the field in the Fock state on the apparition time of entanglement sudden death and entanglement sudden birth. Furthermore, the conditions for the conversion of entanglement sudden death and entanglement sudden birth can be generalized when the initial entangled state is not pure. The results show that the above system parameters affect the concurrence, entanglement sudden birth and sudden death remarkably, the dipole-dipole coupling intensity affects amplitudes of the concurrence oscillation and leads time interval of the ESD to decrease. With the increasing of the purity, the time of entanglement sudden death and entanglement sudden birth will decrease, it is also notable that invariant and stable entanglement, which can be controlled by different initial states of the atoms, occurs for particular initial X state.