The European Physical Journal D

, Volume 44, Issue 2, pp 389–400 | Cite as

Thermal entanglement of two interacting qubits in a static magnetic field

Quantum Optics and Quantum Information


We study systematically the entanglement of a two-qubit Heisenberg XY model in thermal equilibrium in the presence of an external arbitrarily-directed static magnetic field, thereby generalizing our prior work [G. Lagmago Kamta, A.F. Starace, Phys. Rev. Lett. 88, 107901 (2002)]. We show that a magnetic field having a component in the xy-plane containing the spin-spin interaction components produces different entanglement for ferromagnetic (FM) and antiferromagnetic (AFM) couplings. In particular, quantum phase transitions induced by the magnetic field-driven level crossings always occur for the AFM-coupled qubits, but only occur in FM-coupled qubits when the coupling is of Ising type or when the magnetic field has a component perpendicular to the xy-plane. When the magnetic field has a component in the xy-plane, the cut-off temperature above which the entanglement of both the FM- and AFM-coupled qubits vanishes can always be controlled using the magnetic field for any value of the XY coupling anisotropy parameter. Thus, by adjusting the magnetic field, an entangled state of two spins can be produced at any finite temperature. Finally, we find that a higher level of entanglement is achieved when the in-plane component of the magnetic field is parallel to the direction in which the XY exchange coupling is smaller.


03.65.Ud Entanglement and quantum nonlocality 03.67.-a Quantum information 03.67.Mn Entanglement production, characterization, and manipulation 75.10.Jm Quantized spin models 


03.40.+t Thermal/mixed state entanglement 04.10.+s Entanglement in spin models 04.30.+p Entanglement in quantum phase transitions 


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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • G. Lagmago Kamta
    • 1
  • A. Y. Istomin
    • 2
  • A. F. Starace
    • 2
  1. 1.Laboratoire de Chimie Théorique, Faculté des Sciences, Université de SherbrookeQuebecCanada
  2. 2.Department of Physics and AstronomyThe University of Nebraska, 116 Brace LaboratoryLincolnUSA

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