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Effective spin model for interband transport in a Wannier-Stark lattice system

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Abstract

We show that the interband dynamics in a tilted two-band Bose-Hubbard model can be reduced to an analytically accessible spin model in the case of resonant interband oscillations. This allows us to predict the revival time of these oscillations which decay and revive due to inter-particle interactions. The presented mapping onto the spin model and the so achieved reduction of complexity has interesting perspectives for future studies of many-body systems.

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References

  1. O. Morsch, M. Oberthaler, Rev. Mod. Phys. 78, 179 (2006)

    Article  ADS  Google Scholar 

  2. J. Fortágh, C. Zimmermann, Rev. Mod. Phys. 79, 235 (2007)

    Article  ADS  Google Scholar 

  3. I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)

    Article  ADS  Google Scholar 

  4. S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 80, 1215 (2008)

    Article  ADS  Google Scholar 

  5. C. Chin, R. Grimm, P. Julienne, E. Tiesinga, Rev. Mod. Phys. 82, 1225 (2010)

    Article  ADS  Google Scholar 

  6. A. Sorensen, L. Duan, J. Cirac, P. Zoller, Nature 409, 63 (2001)

    Article  ADS  Google Scholar 

  7. S. Diehl et al., Nature Phys. 4, 878 (2008)

    Article  ADS  Google Scholar 

  8. M. Singh, Opt. Express 17, 2600 (2009)

    Article  ADS  Google Scholar 

  9. F. Verstraete et al., Nature Phys. 5, 633 (2009)

    Article  ADS  Google Scholar 

  10. C. Gross, T. Zibold, E. Nicklas, J. Estéve, M.K. Oberthaler, Nature 464, 1165 (2010)

    Article  ADS  Google Scholar 

  11. J. Estève, C. Gross, A. Weller, S. Giovanazzi, M.K. Oberthaler, Nature 455, 1216 (2008)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. C. Sias, A. Zenesini, H. Lignier, S. Wimberger, D. Ciampini, O. Morsch, E. Arimondo, Phys. Rev. Lett. 98, 120403 (2007)

    Article  ADS  Google Scholar 

  14. A. Zenesini, H. Lignier, G. Tayebirad, J. Radogostowicz, D. Ciampini, R. Mannella, S. Wimberger, O. Morsch, E. Arimondo, Phys. Rev. Lett. 103, 090403 (2009)

    Article  ADS  Google Scholar 

  15. D. Cano, B. Kasch, H. Hattermann, R. Kleiner, C. Zimmermann, D. Koelle, J. Fortágh, Phys. Rev. Lett. 101, 183006 (2008)

    Article  ADS  Google Scholar 

  16. D. Hunger, S. Camerer, T.W. Hänsch, D. König, J.P. Kotthaus, J. Reichel, P. Treutlein, Phys. Rev. Lett. 104, 143002 (2010)

    Article  ADS  Google Scholar 

  17. M. Glück, A.R. Kolovsky, H.J. Korsch, Phys. Rep. 366, 103 (2002)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  18. A. Tomadin, R. Mannella, S. Wimberger, Phys. Rev. A 77, 013606 (2008)

    Article  ADS  Google Scholar 

  19. A. Tomadin, Master’s thesis, Università di Pisa, 2006

  20. A.R. Kolovsky, A. Buchleitner, Phys. Rev. E 68, 056213 (2003)

    Article  ADS  Google Scholar 

  21. P. Plötz, J. Madroñero, S. Wimberger, J. Phys. B 43, 081001 (2010)

    Article  ADS  Google Scholar 

  22. H. Fukuyama, R.A. Bari, H.C. Fogedby, Phys. Rev. B 8, 5579 (1973)

    Article  ADS  Google Scholar 

  23. P. Plötz, Ph.D. thesis, Universität Heidelberg, 2010

  24. J. Hausinger, M. Grifoni, Phys. Rev. A 81, 022117 (2010)

    Article  ADS  Google Scholar 

  25. M. Girardeau, J. Math. Phys. 1, 516 (1960)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  26. M. Rigol, A. Muramatsu, Phys. Rev. A 70, 031603 (2004)

    Article  ADS  Google Scholar 

  27. F. Schmitt, M. Hild, R. Roth, J. Phys. B: At. Mol. Opt. Phys. 40, 371 (2007)

    Article  ADS  Google Scholar 

  28. S.R. Clark, D. Jaksch, New J. Phys. 8, 160 (2006)

    Article  ADS  Google Scholar 

  29. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 2001), Chap. 4.2

  30. P. Jordan, E. Wigner, Z. Phys. 47, 631 (1928)

    Article  ADS  Google Scholar 

  31. A. Tomadin, R. Mannella, S. Wimberger, Phys. Rev. Lett. 98, 130402 (2007)

    Article  ADS  Google Scholar 

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Plötz, P., Schlagheck, P. & Wimberger, S. Effective spin model for interband transport in a Wannier-Stark lattice system. Eur. Phys. J. D 63, 47–53 (2011). https://doi.org/10.1140/epjd/e2010-10554-7

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  • DOI: https://doi.org/10.1140/epjd/e2010-10554-7

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