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Chinese Physics

Thermal entanglement in 1D optical lattice chains with nonlinear coupling

Zhou Ling, Yi Xue-Xi, He‐Shan Song, Yanqing Guo

Published May 3, 2005• 19 citations
Publisher

Abstract

The thermal entanglement of spin-1 atoms with nonlinear coupling in an optical lattice chain is investigated for two-particle and multi-particle systems. It is found that the relation between linear coupling and nonlinear coupling is the key to determine thermal entanglement, which shows in what kinds of atoms thermal entanglement exists. This result is true both for two-particle and multi-particle systems. For multi-particle systems, the thermal entanglement does not decrease greatly and the critical temperature decreases only slightly.

DOI
10.1088/1009-1963/14/6/019

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The thermal entanglement of spin-1 atoms with nonlinear coupling in an optical lattice chain is investigated for two-particle and multi-particle systems. It is found that the relation between linear coupling and nonlinear coupling is the key to determine thermal entanglement, which shows in what kinds of atoms thermal entanglement exists. This result is true both for two-particle and multi-particle systems. For multi-particle systems, the thermal entanglement does not decrease greatly and the critical temperature decreases only slightly.
The thermal entanglement of two spin-1 atoms with nonlinear couplings in optical lattices is investigated in this paper. It is found that the nonlinear couplings favor the thermal entanglement creating. The dependence of the thermal entanglement in this system on the linear coupling, the nonlinear coupling, the magnetic field and temperature is also presented. The results show that the nonlinear couplings really change the feature of the thermal entanglement in the system, increasing the nonlinear coupling constant increases the critical magnetic field and the threshold temperature.
Thermal entanglement of spins are investigated in the several Heisenberg models by using of various entanglement measures, and we will evaluate the quantity of thermal entanglement with different parameters of the system (such as, magnetic field, temperture, impurity and different components of interaction). In part of proceduring, we will show that entanglement between two spins have a gaussian profile at the low temperature, and we show that there exists a relation between the QPT and the entanglement in three – qubit Heisenberg chain under the effect of impurity. In fact, QPT is the structure change in property of the ground state at the many–body system, which occures at absolute zero temperature and is purely driven by quantum fluctuation. This transitions appear with the change of a physical parameter. Thus we expect that phase transitions and critical behavior of systems can be explained by entanglement. Also, we investigate the entanglement in pure and thermal cluster states and pay attention to entanglement generation from thermal spin states inputed in a beam spliter. Then, thermal entanglement of Bosonic atoms are investigated in an optical lattices with nonlinear couplings and inhomogeneous magnetic field parameters by using of Negativity measure. We understand from the receiving results that nonlinear coupling coefficient support to entanglement can be improve under antiparalel magnetic field. Finally, we investigate quantum Teleportation at the Heisenberg model in presence of system impurity, as the result of quantum entanglement. We will demonstrate that the Fidelity average, as the measure for evaluation quantum Teleportation, can be controled by modulating magnetic field and impurity parameter Keywords: Beam Spliter, Closest Separable State, Concurrence, Entanglement, Fidelity Average, Generation Entanglement, Ground State Entanglement, Heisenberg Model, Impurity, Inhomogenous, Negativity, Nonlinear Coupling, Normal Lattice, Pure Cluster States, Pure state, Quantum Phase Transition, Quantum Teleportation, Thermal Entanglement.
In this paper we study the effect of temperature, magnetic field, and exchange coupling on the thermal entanglement in a spin chain which consist of two qubits and one qutrit.We use negativity as a measure of entanglement in our study.We apply magnetic field, uniform and nonuniform field, on it.The results show that the entanglement decreases with increase in temperature.Also, we have found that under a magnetic field, either uniform or nonuniform, in constant temperature, the entanglement decreases.We have found that increasing exchange coupling of any two particles decreases the entanglement of the other two particles.Finally, we have compared our system with a two-particle system and found that in presence of a magnetic field the increase in number of particles leads to the decrease in the entanglement.
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The entanglement in a general Heisenberg antiferromagnetic chain of arbitrary spin-sss is investigated. The entanglement is witnessed by the thermal energy which equals the minimum energy of any separable state. There is a characteristic temperature below that an entangled thermal state exists. The characteristic temperature for thermal entanglement is increased with spin sss. When the total number of lattice is increased, the characteristic temperature decreases and then approaches a constant. This effect shows that the thermal entanglement can be detected in a real solid state system of larger number of lattices for finite temperature. The comparison of negativity and entanglement witness is obtained from the separability of the unentangled states. It is found that the thermal energy provides a sufficient condition for the existence of the thermal entanglement in a spin-sss antiferromagnetic Heisenberg chain.