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The European Physical Journal D

Two-qubit entanglement in an antiferromagnetic environment

Xiao-Zhong Yuan, Ka‐Di Zhu, Zhuo-Jie Wu

Published Feb 8, 2005• 11 citations
Publisher
DOI
10.1140/epjd/e2005-00023-y

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We revisit the quantum features of an anti-ferromagnetic (AF) spin environment at finite temperature with gap in its frequency spectrum, on the dynamics quantum correlations of a coupled central two qubits system with Dzyaloshinskii-Moriya (DM) interaction, prepared in two entangled Bell states. Using entanglement and quantum discord as quantum meters of decoherence, the prepared entangled states are classified as robust or fragile relative to the degree of information leakage to the AF environment. By tailoring the size of the frequency gap, anisotropy field strength and induced field, due to system AF spin environment coupling, size of the AF environment and DM interaction parameter, a decoherence-free sub-space can be accessed for efficient execution of quantum protocols encoded in the entangled states.
We discuss two central spin models coupled, respectively, to a quantum Heisenberg XY spin star environment [1] and to an antiferromagnetic environment [2]. In the first model [1], the exact quantum dynamics of the reduced density matrix of two coupled spin qubits in a quantum Heisenberg XY spin star environment in the thermodynamic limit at arbitrarily finite temperatures is obtained using a novel operator technique. In this approach, the transformed Hamiltonian becomes effectively Jaynes-Cumming like and thus the analysis is also relevant to cavity quantum electrodynamics. This special operator technique is mathematically simple and physically clear, and allows us to treat systems and environments that could all be strongly coupled mutually and internally. To study their entanglement evolution, the concurrence of the reduced density matrix of the two coupled central spins is also obtained exactly. It is shown that the dynamics of the entanglement depends on the initial state of the system and the coupling strength between the two coupled central spins, the thermal temperature of the spin environment and the interaction between the constituents of the spin environment. We also investigate the effect of detuning which in our model can be controlled by the strength of a locally applied external magnetic field. It is found that the detuning has a significant effect on the entanglement generation between the two spin qubits.
Using the spin-wave approximation, we study the geometric phase (GP) of a central spin (signal qubit) coupled to an antiferromagnetic (AF) environment under the application of an external global magnetic field. The external magnetic field affects the GP of the qubit directly and also indirectly through its effect on the AF environment. We find that when the applied magnetic field is increased to the critical magnetic field point, the AF environment undergoes a spin-flop transition, a first-order phase transition, and at the same time the GP of the qubit changes abruptly to zero. This sensitive change of the GP of a signal qubit to the parameter change of a many-body environment near its critical point may serve as another efficient tool or witness to study the many-body phase transition. The influences of the AF environment temperature and crystal anisotropy field on the GP are also investigated.