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Study of Loschmidt Echo for a qubit coupled to an XY-spin chain environment

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Abstract

We study the temporal evolution of a central spin-1/2 (qubit) coupled to the environment which is chosen to be a spin-1/2 transverse XY spin chain. We explore the entire phase diagram of the spin-Hamiltonian and investigate the behavior of Loschmidt echo(LE) close to critical and multicritical point(MCP). To achieve this, the qubit is coupled to the spin chain through the anisotropy term as well as one of the interaction terms. Our study reveals that the echo has a faster decay with the system size (in the short time limit) close to a MCP and also the scaling obeyed by the quasiperiod of the collapse and revival of the LE is different in comparison to that close to a QCP. We also show that even when approached along the gapless critical line, the scaling of the LE is determined by the MCP where the energy gap shows a faster decay with the system size. This claim is verified by studying the short-time and also the collapse and revival behavior of the LE at a quasicritical point on the ferromagnetic side of the MCP. We also connect our observation to the decoherence of the central spin.

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References

  1. M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000)

  2. V. Vedral, Introduction to Quantum Information Science (Oxford University Press, Oxford, UK, 2007)

  3. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, England, 1999)

  4. B.K. Chakrabarti, A. Dutta, P. Sen, Quantum Ising Phases and transitions in transverse Ising Models, m41 (Springer, Heidelberg, 1996)

  5. M.A. Continentino, Quantum Scaling in Many-Body Systems (World Scientific, 2001)

  6. A. Osterloh, L. Amico, G. Falci, R. Fazio, Nature 416, 608 (2002)

    Article  ADS  Google Scholar 

  7. T.J. Osborne, M.A. Nielsen, Phys. Rev. A 66, 032110 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  8. L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. A. Peres, Phys. Rev. Lett. 77, 1413 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. G. Vidal, R.F. Werner, Phys. Rev. A 65, 032314 (2002)

    Article  ADS  Google Scholar 

  11. P. Zanardi, N. Paunkovic, Phys. Rev. E 74, 031123 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  12. H.-Q. Zhou, J.P. Barjaktarevic, J. Phys. A Math. Theor. 41, 412001 (2008)

    Article  MathSciNet  Google Scholar 

  13. S.J. Gu, Int. J. Mod. Phys. B 24, 4371 (2010)

    Article  ADS  MATH  Google Scholar 

  14. V. Gritsev, A. Polkovnikov, in Developments in Quantum Phase Transitions, edited by L.D. Carr (Taylor and Francis, Boca Raton, 2010)

  15. M. Rams, B. Damski, Phys. Rev. Lett. 106, 055701 (2010)

    Article  ADS  Google Scholar 

  16. M.S. Sarandy, Phys. Rev. A 80, 022108 (2009)

    Article  ADS  Google Scholar 

  17. R. Dillenschneider, Phys. Rev. B 78, 224413 (2008)

    Article  ADS  Google Scholar 

  18. A. Dutta, U. Divakaran, D. Sen, B.K. Chakrabarti, T.F. Rosenbaum, G. Aeppli (2010), arXiv:1012.0653

  19. A. Polkovnikov, K. Sengupta, A. Silva, M. Vengalattore, Rev. Mod. Phys. 83, 863 (2011)

    Article  ADS  Google Scholar 

  20. W.H. Zurek, Phys. Today 44, 36 (1991)

    Article  Google Scholar 

  21. S. Haroche, Phys. Today 51, 36 (1998)

    Article  Google Scholar 

  22. W.H. Zurek, Rev. Mod. Phys. 75, 715 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. E. Joos, H.D. Zeh, C. Keifer, D. Giulliani, J. Kupsch, I.-O. Statatescu, Decoherence and appearance of a classical world in a quantum theory (Springer Press, Berlin, 2003)

  24. W.H. Zurek, J.P. Paz, Phys. Rev. Lett. 72, 2508 (1994)

    Article  ADS  Google Scholar 

  25. A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic Publishers, Dordrecht)

  26. R.A. Jalabert, H.M. Pastawski, Phys. Rev. Lett. 86, 246 (2001)

    Article  Google Scholar 

  27. Z.P. Karkuszewski, C. Jarzynski, W.H. Zurek, Phys. Rev. Lett. 89, 170405 (2002)

    Article  ADS  Google Scholar 

  28. F.M. Cucchietti, D.A.R. Dalvit, J.P. Paz, W.H. Zurek, Phys. Rev. A 95, 105701 (2003)

    Google Scholar 

  29. H.T. Quan, Z. Song, X.F. Liu, P. Zanardi, C.P. Sun, Phys. Rev. Lett. 96, 140604 (2006)

    Article  ADS  Google Scholar 

  30. Z.G. Yuan, P. Zhang, S.S. Li, Phys. Rev. A 75, 012102 (2007)

    Article  ADS  Google Scholar 

  31. Y.-C. Ou, H. Fan, J. Phys. A Math. Theor. 40, 2455 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. D. Rossini, T. Calarco, V. Giovannetti, S. Montangero, R. Fazio, Phys. Rev. A 75, 032333 (2007)

    Article  ADS  Google Scholar 

  33. J. Zhang, F.M. Cucchietti, C.M. Chandrasekhar, M. Laforest, C.A. Ryan, M. Ditty, A. Hubbard, J.K. Gamble, R. Laflamme, Phys. Rev. A 79, 012305 (2009)

    Article  ADS  Google Scholar 

  34. F.M. Cucchietti, S. Fernandez-Vidal, J.P. Paz, Phys. Rev. A 75, 032337 (2007)

    Article  ADS  Google Scholar 

  35. C. Cormick, J.P. Paz, Phys. Rev. A 77, 022317 (2008)

    Article  ADS  Google Scholar 

  36. B. Damski, H.T. Quan, W.H. Zurek, Phys. Rev. A 83, 062104 (2011)

    Article  ADS  Google Scholar 

  37. E. Lieb, T. Schultz, D. Mattis, Ann. Phys. 16, 37004 (1961)

    MathSciNet  Google Scholar 

  38. E. Barouch, B.M. McCoy, M. Dresden, Phys. Rev. A 2, 1075 (1970)

    Article  ADS  Google Scholar 

  39. E. Barouch, B.M. McCoy, Phys. Rev. A 3, 786 (1971)

    Article  ADS  Google Scholar 

  40. J.B. Kogut, Rev. Mod. Phys. 51, 659 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  41. J.E. Bunder, R.H. McKenzie, Phys. Rev. B 60, 344 (1999)

    Article  ADS  Google Scholar 

  42. U. Divakaran, A. Dutta, Diptiman Sen, Phys. Rev. B 78, 144301 (2008)

    Google Scholar 

  43. S. Deng, G. Ortiz, L. Viola, Europhys. Lett. 84, 67008 (2008)

    Article  ADS  Google Scholar 

  44. S. Deng, G. Ortiz, L. Viola, Phys. Rev. B 80, 241109(R) (2009)

    ADS  Google Scholar 

  45. V. Mukherjee, U. Divakaran, A. Dutta, D. Sen, Phys. Rev. B 76, 174303 (2007)

    Article  ADS  Google Scholar 

  46. U. Divakaran, V. Mukherjee, A. Dutta, D. Sen, J. Stat. Mech. P02007 (2009)

  47. V. Mukherjee, A. Dutta, Europhys. Lett. 92, 37004 (2010)

    Article  ADS  Google Scholar 

  48. V. Mukherjee, A. Polkovnikov, A. Dutta, Phys. Rev. B 83, 075118 (2011)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Indian Institute of Technology Kanpur, 208016, Kanpur, India

    S. Sharma & A. Dutta

  2. Institut de Physique Théorique, CEA Saclay, 91191, Gif-sur-Yvette Cedex, France

    V. Mukherjee

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  1. S. Sharma
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  2. V. Mukherjee
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  3. A. Dutta
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Correspondence to S. Sharma.

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Sharma, S., Mukherjee, V. & Dutta, A. Study of Loschmidt Echo for a qubit coupled to an XY-spin chain environment. Eur. Phys. J. B 85, 143 (2012). https://doi.org/10.1140/epjb/e2012-21022-7

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  • DOI: https://doi.org/10.1140/epjb/e2012-21022-7

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