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The progressive solutions for the Dicke Hamiltonian

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Abstract

A progressive diagonalization scheme for the Dicke Hamiltonian, which describes the interaction of N two-level atoms with a single-mode radiation field via a dipole interaction, is proposed. It is shown that the ground state of the Dicke Hamiltonian with a finite number of atoms can be solved almost exactly by using a progressive diagonalization scheme that involves a one-variable equation at each step. The scheme is efficient for the lower part of the spectrum. Calculated results for ground-state energies, photon numbers, atomic inversions, fluctuations in the latter two quantities, entanglement measures, and Shanon information entropies at resonance points for some finite j cases as functions of the coupling parameter are given. These outcomes show significant changes in the photon number, atomic inversion, and their fluctuations near the critical point where the entanglement measure reaches its maximum value.

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References

  1. R. Dicke, Phys. Rev. 93, 99 (1954)

    Article  MATH  ADS  Google Scholar 

  2. K. Furuya, M.C. Nemes, G.Q. Pellegrino, Phys. Rev. Lett. 80, 5524 (1998)

    Article  ADS  Google Scholar 

  3. R.M. Angelo, K. Furuya, M.C. Nemes, G.Q. Pellegrino, Phys. Rev. A 64, 043801 (2001)

    Article  ADS  Google Scholar 

  4. X.-W. Hou, B. Hu, Phys. Rev. A 69, 042110 (2004)

    Article  ADS  Google Scholar 

  5. V. Bužek, M. Orszag, M. Roško, Phys. Rev. Lett. 94, 163601 (2005)

    Article  ADS  Google Scholar 

  6. K. Baumann, C. Guerlin, F. Brennecke, T. Esslinger, Nature 464, 1301 (2010)

    Article  ADS  Google Scholar 

  7. C. Leonardi, F. Persico, G. Vetri, Riv. Nuovo Cimento 9, 1 (1986)

    Article  MathSciNet  Google Scholar 

  8. B.W. Shore, P.L. Knight, J. Mod. Opt. 40, 1195 (1993)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. G. Ramon, C. Brif, A. Mann, Phys. Rev. A 58, 2506 (1998)

    Article  ADS  Google Scholar 

  10. K. Hepp, E. Lieb, Ann. Phys. (N.Y.) 76, 360 (1973)

    Article  MathSciNet  ADS  Google Scholar 

  11. C. Emary, T. Brandes, Phys. Rev. Lett. 90, 044101 (2003)

    Article  ADS  Google Scholar 

  12. C. Emary, T. Brandes, Phys. Rev. E 67, 066203 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  13. M. Kús, Phys. Rev. Lett. 54, 1343 (1983)

    Article  ADS  Google Scholar 

  14. R. Graham, M. Hönerbach, Phys. Rev. Lett. 57, 1378 (1986)

    Article  ADS  Google Scholar 

  15. L. Müler, J. Stolze, H. Leschke, P. Nagel, Phys. Rev. A 44, 1022 (1991)

    Article  ADS  Google Scholar 

  16. G.A. Finney, J. Gea-Banacloche, Phys. Rev. E 54, 1449 (1996)

    Article  ADS  Google Scholar 

  17. K. Baumann, R. Mottl, F. Brennecke, T. Esslinger, Phys. Rev. Lett. 107, 140402 (2011)

    Article  ADS  Google Scholar 

  18. J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93, 050403 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  19. F. Pan, T. Wang, J. Pan, Y.-F. Li, J.P. Draayer, Phys. Lett. A 341, 94 (2005)

    Article  MATH  ADS  Google Scholar 

  20. T. Skrypnyk, J. Phys. A: Math. Theor. 41, 475202 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  21. T. Skrypnyk, J. Math. Phys. 50, 103523 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  22. D. Braak, J. Phys. B: At. Mol. Opt. Phys. 46, 224007 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  23. N. Lambert, C. Emary, T. Brandes, Phys. Rev. Lett. 92, 073602 (2004)

    Article  ADS  Google Scholar 

  24. N. Lambert, C. Emary, T. Brandes, Phys. Rev. A 71, 053804 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  25. G. Liberti, F. Plastina, F. Piperno, Phys. Rev. A 74, 022324 (2006)

    Article  ADS  Google Scholar 

  26. J. Vidal, S. Dusuel, Europhys. Lett. 74, 817 (2006)

    Article  ADS  Google Scholar 

  27. J. Reslen, L. Quiroga, N.F. Johnson, Europhys. Lett. 69, 8 (2005)

    Article  ADS  Google Scholar 

  28. D. Braak, Phys. Rev. Lett. 107, 100401 (2011)

    Article  ADS  Google Scholar 

  29. Q.-H. Chen, Y.-Y. Zhang, T. Liu, K.-L. Wang, Phys. Rev. A 78, 051801 (2008)

    Article  ADS  Google Scholar 

  30. F. Pan, M.X. Xie, X. Guan, L.-R. Dai, J.P. Draayer, Phys. Rev. C 80, 044306 (2009)

    Article  ADS  Google Scholar 

  31. F. Pan, X. Guan, Y. Wang, J.P. Draayer, J. Phys. B: At. Mol. Opt. Phys. 43, 175501 (2010)

    Article  ADS  Google Scholar 

  32. M.A. Bastarrachea-Magnani, J.G. Hirsch, Rev. Mex. Fis. S 57, 69 (2011)

    Google Scholar 

  33. J.G. Hirsch, M.A. Bastarrachea-Magnani, Phys. Scr. T160, 014005 (2014)

    Article  ADS  Google Scholar 

  34. J.G. Hirsch, M.A. Bastarrachea-Magnani, Phys. Scr. T160, 014018 (2014)

    Article  ADS  Google Scholar 

  35. M.A. Bastarrachea-Magnani, S. Lerma-Hernández, J.G. Hirsch, Phys. Rev. A 89, 032101 (2014)

    Article  ADS  Google Scholar 

  36. M.A. Bastarrachea-Magnani, S. Lerma-Hernández, J.G. Hirsch, Phys. Rev. A 89, 032102 (2014)

    Article  ADS  Google Scholar 

  37. N. Schuch, F. Verstraete, J.I. Cirac, Phys. Rev. A 70, 042310 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  38. F. Benatti, R. Floreanini, U. Marzolino, Ann. Phys. 327, 1304 (2012)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  39. F. Benatti, R. Floreanini, U. Marzolino, Phys. Rev. A 89, 032326 (2014)

    Article  ADS  Google Scholar 

  40. I. Bose, E. Chattopadhyay, Phys. Rev. A 66, 062320 (2002)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Liaoning Normal University, 116029, Dalian, P. R. China

    Lina Bao, Feng Pan, Xiaotong Li & Xiao Liang

  2. Department of Physics and Astronomy, Louisiana State University, 70803-4001, Baton Rouge, Louisiana, USA

    Feng Pan & J. P. Draayer

Authors
  1. Lina Bao
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  2. Feng Pan
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  3. Xiaotong Li
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  4. Xiao Liang
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  5. J. P. Draayer
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Correspondence to Feng Pan.

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Bao, L., Pan, F., Li, X. et al. The progressive solutions for the Dicke Hamiltonian. Eur. Phys. J. Plus 130, 126 (2015). https://doi.org/10.1140/epjp/i2015-15126-1

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  • DOI: https://doi.org/10.1140/epjp/i2015-15126-1

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