Skip to main content

Prethermalization in one-dimensional Bose gases: Description by a stochastic Ornstein-Uhlenbeck process

Abstract

We experimentally study the relaxation dynamics of a coherently split one-dimensional Bose gas using matterwave interference. Measuring the full probability distributions of interference contrast reveals the prethermalization of the system to a non-thermal steady state. To describe the evolution of noise and correlations we develop a semiclassical effective description that allows us to model the dynamics as a stochastic Ornstein-Uhlenbeck process.

This is a preview of subscription content, access via your institution.

References

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

    ADS  Article  Google Scholar 

  2. J. Berges, S. Borsányi, C. Wetterich, Phys. Rev. Lett. 93, 142002 (2004)

    ADS  Article  Google Scholar 

  3. M. Eckstein, M. Kollar, P. Werner, Phys. Rev. Lett. 103, 056403 (2009)

    ADS  Article  Google Scholar 

  4. M. Moeckel, S. Kehrein, New J. Phys. 12, 055016 (2010)

    ADS  Article  Google Scholar 

  5. C. Kollath, A.M. Läuchli, E. Altman, Phys. Rev. Lett. 98, 180601 (2007)

    ADS  Article  Google Scholar 

  6. L. Mathey, A. Polkovnikov, Phys. Rev. A 81, 033605 (2010)

    ADS  Article  Google Scholar 

  7. R. Barnett, A. Polkovnikov, M. Vengalattore, Phys. Rev. A 84, 023606 (2011)

    ADS  Article  Google Scholar 

  8. J. Marino, A. Silva, Phys. Rev. B 86, 060408(R) (2012)

    ADS  Article  Google Scholar 

  9. J.M. Deutsch, Phys. Rev. A 43, 2046 (1991)

    MathSciNet  ADS  Article  Google Scholar 

  10. M. Srednicki, Phys. Rev. E 50, 888 (1994)

    ADS  Article  Google Scholar 

  11. M. Rigol, V. Dunjko, M. Olshanii, Nature 452, 854 (2009)

    ADS  Article  Google Scholar 

  12. M. Gring, M. Kuhnert, T. Langen, T. Kitagawa, B. Rauer, M. Schreitl, I. Mazets, D. Adu Smith, E. Demler, J. Schmiedmayer, Science 337, 1318 (2012)

    ADS  Article  Google Scholar 

  13. T. Kitagawa, S. Pielawa, A. Imambekov, J. Schmiedmayer, V. Gritsev, E. Demler, Phys. Rev. Lett. 104, 255302 (2010)

    ADS  Article  Google Scholar 

  14. T. Kitagawa, A. Imambekov, J. Schmiedmayer, E. Demler, New J. Phys. 13, 073018 (2011)

    ADS  Article  Google Scholar 

  15. G.E. Uhlenbeck, L.S. Ornstein, Phys. Rev. 36, 823 (1930)

    ADS  MATH  Article  Google Scholar 

  16. D.S. Petrov, G.V. Shlyapnikov, J.T.M. Walraven, Phys. Rev. Lett. 85, 3745 (2000)

    ADS  Article  Google Scholar 

  17. J. Esteve, J.-B. Trebbia, T. Schumm, A. Aspect, C.I. Westbrook, I. Bouchoule, Phys. Rev. Lett. 96, 130403 (2006)

    ADS  Article  Google Scholar 

  18. R. Bistritzer, E. Altman, Proc. Natl. Acad. Sci. USA 104, 9955 (2007)

    ADS  Article  Google Scholar 

  19. A.A. Burkov, M.D. Lukin, E. Demler, Phys. Rev. Lett. 98, 200404 (2007)

    ADS  Article  Google Scholar 

  20. I.E. Mazets, T. Schumm, J. Schmiedmayer, Phys. Rev. Lett. 100, 210403 (2008)

    ADS  Article  Google Scholar 

  21. I.E. Mazets, J. Schmiedmayer, New J. Phys. 12, 055023 (2010)

    ADS  Article  Google Scholar 

  22. S. Tan, M. Pustilnik, L.I. Glazman, Phys. Rev. Lett. 105, 090404 (2010)

    ADS  Article  Google Scholar 

  23. T. Schumm, S. Hofferberth, L.M. Anderson, S. Wildermuth, S. Groth, I. Bar-Joeseph, J. Schmiedmayer, P. Krüger, Nature Phys. 1, 57 (2005)

    ADS  Article  Google Scholar 

  24. S. Hofferberth, I. Lesanovsky, T. Schumm, J. Schmiedmayer, A. Imambekov, V. Gritsev, E. Demler, Nature Phys. 4, 489 (2008)

    ADS  Article  Google Scholar 

  25. S. Hofferberth, I. Lesanovsky, B. Fischer, T. Schumm, J. Schmiedmayer, Nature 449, 324 (2007)

    ADS  Article  Google Scholar 

  26. J. Reichel, V. Vuletic (eds.), Atom Chips (Wiley VCH, 2011)

  27. A. Imambekov, I.E. Mazets, D.S. Petrov, V. Gritsev, S. Manz, S. Hofferberth, T. Schumm, E. Demler, J. Schmiedmayer, Phys. Rev. A 80, 033604 (2009)

    ADS  Article  Google Scholar 

  28. S. Manz, R. Bücker, T. Betz, Ch. Koller, S. Hofferberth, I.E. Mazets, A. Imambekov, E. Demler, A. Perrin, J. Schmiedmayer, T. Schumm, Phys. Rev. A 81, 031610(R) (2010)

    ADS  Article  Google Scholar 

  29. D.A. Smith, S. Aigner, S. Hofferberth, M. Gring, M. Andersson, St. Wildermuth, P. Krüger, S. Schneider, T. Schumm, J. Schmiedmayer, Optics Expr. 19, 8471 (2011)

    ADS  Article  Google Scholar 

  30. P. Krüger, S. Hofferberth, I.E. Mazets, I. Lesanovsky, J. Schmiedmayer, Phys. Rev. Lett. 105, 265302 (2010)

    ADS  Article  Google Scholar 

  31. I. Lesanovsky, T. Schumm, S. Hofferberth, L.M. Andersson, P. Krüger, J. Schmiedmayer, Phys. Rev. A 73, 033619 (2006)

    ADS  Article  Google Scholar 

  32. N.K. Whitlock, I. Bouchoule, Phys. Rev. A 68, 053609 (2003)

    ADS  Article  Google Scholar 

  33. T. Betz, S. Manz, R. Bücker, T. Berrada, C. Koller, G. Kazakov, I.E. Mazets, H.-P. Stimming, A. Perrin, T. Schumm, J. Schmiedmayer, Phys. Rev. Lett. 106, 020407 (2011)

    ADS  Article  Google Scholar 

  34. A. Polkovnikov, E. Altman, E. Demler, Proc. Natl. Acad. Sci. USA 103, 6125 (2006)

    ADS  Article  Google Scholar 

  35. V. Gritsev, E. Altman, E. Demler, A. Polkovnikov, Nature Phys. 2, 705 (2006)

    ADS  Article  Google Scholar 

  36. C.S. Gerving, T.M. Hoang, B.J. Land, M. Anquez, C.D. Hamley, M.S. Chapman, Nature Comm. 3, 1169 (2012)

    ADS  Article  Google Scholar 

  37. S. Trotzky, Y.-A. Chen, A. Flesch, I.P. McCulloch, U. Schöllwöck, J. Eisert, I. Bloch, Nature Phys. 8, 325 (2012)

    ADS  Article  Google Scholar 

  38. M. Kuhnert, R. Geiger, T. Langen, M. Gring, B. Rauer, T. Kitagawa, E. Demler, D. Adu Smith, J. Schmiedmayer [arXiv:1211.5323]

  39. C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Springer-Verlag, Berlin, 1985)

  40. H.-P. Stimming, N.J. Mauser, J. Schmiedmayer, I.E. Mazets, Phys. Rev. Lett. 105, 015301 (2010)

    ADS  Article  Google Scholar 

  41. E. Mazets Igor, Phys. Rev. A 86, 055603 (2012)

    Article  Google Scholar 

  42. C. Mora, Y. Castin, Phys. Rev. A 67, 053615 (2003)

    ADS  Article  Google Scholar 

  43. T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, 2004)

  44. A. Polkovnikov, E. Altman, E. Demler, PNAS 103, 6125 (2006)

    ADS  Article  Google Scholar 

  45. M. Cheneau, P. Barmettler, D. Poletti, M. Endres, P. Schauß, T. Fukuhara, C. Gross, I. Bloch, C. Kollath, S. Kuhr, Nature 481, 484 (2012)

    ADS  Article  Google Scholar 

  46. D.T. Gillespie, Physical Rev. E 54, 2084 (1996)

    MathSciNet  ADS  Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jörg Schmiedmayer.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Langen, T., Gring, M., Kuhnert, M. et al. Prethermalization in one-dimensional Bose gases: Description by a stochastic Ornstein-Uhlenbeck process. Eur. Phys. J. Spec. Top. 217, 43–53 (2013). https://doi.org/10.1140/epjst/e2013-01752-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2013-01752-0

Keywords

  • European Physical Journal Special Topic
  • Quantum Phasis
  • Thermal Equilibrium State
  • Atom Chip
  • Mesoscopic Physics