Advertisement

The European Physical Journal B

, Volume 84, Issue 3, pp 467–474 | Cite as

Non-equilibrium entangled steady state of two independent two-level systems

  • S. Camalet
Regular Article Mesoscopic and Nanoscale Systems

Abstract

We determine and study the steady state of two independent two-level systems weakly coupled to a stationary non-equilibrium environment. Whereas this bipartite state is necessarily uncorrelated if the splitting energies of the two-level systems are different from each other, it can be entangled if they are equal. For identical two-level systems interacting with two bosonic heat baths at different temperatures, we discuss the influence of the baths temperatures and coupling parameters on their entanglement. Geometric properties, such as the baths dimensionalities and the distance between the two-level systems, are relevant. A regime is found where the steady state is a statistical mixture of the product ground state and of the entangled singlet state with respective weights 2/3 and 1/3.

Keywords

Entangle State Coupling Parameter Bell State Heat Bath Splitting Energy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R.F. Werner, Phys. Rev. A 40, 4277 (1989) CrossRefADSGoogle Scholar
  2. 2.
    J.S. Bell, Physics (Long Island City, NY) 1, 195 (1964)Google Scholar
  3. 3.
    K. Zyczkowski, P. Horodecki, A. Sanpera, M. Lewenstein, Phys. Rev. A 58, 883 (1998)CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    M.O. Terra Cunha, New J. Phys. 9, 237 (2007)CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    T. Yu, J.H. Eberly, Phys. Rev. Lett. 93, 140404 (2004) CrossRefADSGoogle Scholar
  6. 6.
    L. Jacóbczyk, A. Jamróz, Phys. Lett. A 333, 35 (2004)CrossRefADSGoogle Scholar
  7. 7.
    T. Yu, J.H. Eberly, Phys. Rev. B 66, 193306 (2002) CrossRefADSGoogle Scholar
  8. 8.
    P.J. Dodd, J.J. Halliwell, Phys. Rev. A 69, 052105 (2004) CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    D. Braun, Phys. Rev. Lett. 89, 277901 (2002) CrossRefADSGoogle Scholar
  10. 10.
    L. Jakóbczyk, J. Phys. A: Math. Gen. 35, 6383 (2002) CrossRefMATHADSGoogle Scholar
  11. 11.
    F. Benatti, R. Floreanini, M. Piani, Phys. Rev. Lett. 91, 070402 (2003) CrossRefADSGoogle Scholar
  12. 12.
    D.P.S. McCutcheon, A. Nazir, S. Bose, A.J. Fisher, Phys. Rev. A 80, 022337 (2009) CrossRefADSGoogle Scholar
  13. 13.
    P. Zanardi, M. Rasetti, Phys. Rev. Lett. 79, 3306 (1997) CrossRefADSGoogle Scholar
  14. 14.
    L. Hartmann, W. Dür, H.-J. Briegel, Phys. Rev. A 74, 052304 (2006) CrossRefADSGoogle Scholar
  15. 15.
    L.D. Contreras-Pulido, R. Aguado, Phys. Rev. B 77, 155420 (2008) CrossRefADSGoogle Scholar
  16. 16.
    M.B. Plenio, S.F. Huelga, Phys. Rev. Lett. 88, 197901 (2002) CrossRefADSGoogle Scholar
  17. 17.
    F. Kheirandish, S.J. Akhtarshenas, H. Mohammadi, Eur. Phys. J. D 57, 129 (2010)CrossRefADSGoogle Scholar
  18. 18.
    Ö. Çakir, A.A. Klyachko, A.S. Shumovsky, Phys. Rev. A 71, 034303 (2005) CrossRefADSGoogle Scholar
  19. 19.
    U. Weiss, Quantum dissipative systems (World Scientific, Singapore, 1993)Google Scholar
  20. 20.
    C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Processus d’interaction entre photons et atomes (CNRS Editions, Paris, 1988)Google Scholar
  21. 21.
    S. Camalet, Eur. Phys. J. B 61, 193 (2008)CrossRefADSGoogle Scholar
  22. 22.
    R.H. Lehmberg, Phys. Rev. A 2, 883 (1970)CrossRefADSGoogle Scholar
  23. 23.
    A.J. Leggett,S. Chakravarty,A.T. Dorsey,M.P.A Fisher, A. Garg, W. Zwerger, Rev. Mod. Phys. 59, 1 (1987)CrossRefADSGoogle Scholar
  24. 24.
    A. Peres, Phys. Rev. Lett. 77, 1413 (1996) CrossRefMATHADSMathSciNetGoogle Scholar
  25. 25.
    M. Horodecki, P. Horodecki, R. Horodecki, Phys. Lett. A 223, 1 (1996)CrossRefMATHADSMathSciNetGoogle Scholar
  26. 26.
    G. Vidal, R.F. Werner, Phys. Rev. A 65, 032314 (2002) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Laboratoire de Physique Théorique de la Matière Condensée, UMR 7600Université Pierre et Marie CurieParisFrance

Personalised recommendations