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arXiv:1405.7009

Dzyaloshinskii-Moriya interactions effects on the entanglement dynamics of a two qubit xxz spin system in non-Markovian environment

Georges Collince Fouokeng, Martin Tchoffo, Edwine Tendong, Lukong Cornelius Fai

Published May 27, 2014• 2 citations
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Abstract

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.

DOI
10.48550/arxiv.1405.7009

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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.
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.
Thermal entanglement of a two-qubit Heisenberg XXZ chain in the presence of different Dzyaloshinskii–Moriya (DM) anisotropic antisymmetric interactions and entanglement teleportation using two independent Heisenberg chains as quantum channel are investigated. It is found that the anisotropic coupling coefficient Jz (z-component exchange constant) and DM interactions can excite the entanglement, and x-component DM interaction Dx has a more remarkable influence than the z-axis DM interaction Dz for exchange constant J > 0 (antiferromagnetic) case, which is contrary to coupling coefficient J < 0 (ferromagnetic) case. The output entanglement and fidelity increase with increasing z-axis coupling parameter Jz for both the antiferromagnetic J > 0 case and ferromagnetic J < 0 case. By introducing the different DM interactions, it is superior to teleportate initial state by using the Dz interaction in the model for J > 0 case. But for J < 0 case, the Dx interaction is better, and the output concurrence and fidelity can reach the maximum value 1 with suitable Dx.
The thermal entanglement in a two-qubit anisotropic Heisenberg XXZ system, also XYZ system, with Dzyaloshinskii-Moriya (DM) couplings in an inhomogenous magnetic field, was studied. The effects of these two kinds of anisotropies on the thermal entanglement have been studied in detail in the concept for concurrence, the measure of entanglement. The analytical expressions of concurrence are obtained for this model. It is found that the DM interaction can enhance thermal entanglement and can be efficiently controlled by the DM interaction parameter and ehchange interaction Jx, Jy and Jz. When D is large enough, the entanglement can exist for larger temperatures and strong magnetic field. We also analysed thermodynamic properties of Heisenberg model and the most important results were shown in the paper.
This paper explores thermal quantum memory-assisted entropic uncertainty, Bell-non-locality, and entanglement in a two-qubit Heisenberg XXX chain with x-directional Dzyaloshinskii-Moriya (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions in thermal equilibrium. We find this crucial that the initial degree of nonlocality and entanglement in the two-qubit state entirely depends upon the temperature, orientation, and strength of the DM and KSEA interaction of the magnetic field. Among many other situations, the magnetic field characterized by DM interaction with minimal temperature, exchange coupling strength, and KSEA interaction is the most reliable for generating and maintaining maximal nonlocality and entanglement while completely suppressing entropic uncertainty. On the other hand, repeated revivals and non-Markovian dynamics have been observed when the magnetic field is characterized by exchange coupling constant, DM and KSEA interaction with a higher temperature limit. Except for temperature-based magnetic fields, we show that maximal entanglement and nonlocality are generated and preserved in the two qubits with zero-order entropic uncertainty, which we believe is a better result than previous studies.
Thermal entanglement of a two-qubit Ising chain subjected to an external magnetic field and Dzyaloshinsky—Moriya (DM) interaction is examined. The effect of magnetic field, strength of DM interaction and temperature are analyzed by adopting negativity of partial transpose as the measure of entanglement. It is shown that when the DM interaction along the Ising axis is considerable, thermal entanglement can be sustained for a higher temperature. The usefulness of longitudinal DM interaction over the one that is perpendicular to the Ising axis, in the manipulation and control of entanglement at a feasible temperature, is illustrated.