Two-body bound and edge states in the extended SSH Bose-Hubbard model

Abstract

We study the bosonic two-body problem in a Su-Schrieffer-Heeger dimerized chain with on-site and nearest-neighbor interactions. We find two classes of bound states. The first, similar to the one induced by on-site interactions, has its center of mass on the strong link, whereas the second, existing only thanks to nearest-neighbor interactions, is centered on the weak link. We identify energy crossings between these states and analyse them using exact diagonalization and perturbation theory. In the presence of open boundary conditions, novel strongly-localized edge-bound states appear in the spectrum as a consequence of the interplay between lattice geometry, on-site and nearest-neighbor interactions. Contrary to the case of purely on-site interactions, such EBS persist even in the strongly interacting regime.

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References

  1. 1.

    D.C. Mattis. Rev. Mod. Phys. 58, 361 (1986)

    ADS  Article  Google Scholar 

  2. 2.

    K. Winkler, G. Thalhammer, F. Lang, R. Grimm, J. Hecker Denschlag, A.J. Daley, A. Kantian, H.P. Büchler, P. Zoller, Nature 441, 853 (2006)

    ADS  Article  Google Scholar 

  3. 3.

    J.H. Denschlag, A.J. Daley, Proceedings of the international school of physics, Enrico Fermi, Course CLXIV, Ultra-Cold Fermi Gases (2006)

  4. 4.

    M. Valiente, D. Petrosyan, J. Phys. B: At. Mol. Opt. Phys. 42, 121001 (2009)

    ADS  Article  Google Scholar 

  5. 5.

    M. Valiente. Phys. Rev. A 81, 042102 (2010)

    ADS  Article  Google Scholar 

  6. 6.

    M. Valiente, K. Mølmer. Phys. Rev. A 84, 053628 (2011)

    ADS  Article  Google Scholar 

  7. 7.

    C. Menotti, F. Minganti, A. Recati, Phys. Rev. A 93, 033602 (2016)

    ADS  Article  Google Scholar 

  8. 8.

    V. Alba, K. Saha, M. Haque, J. Stat. Mech. P10018 (2013)

  9. 9.

    M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010)

    ADS  Article  Google Scholar 

  10. 10.

    R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983)

    ADS  Article  Google Scholar 

  11. 11.

    C.-K. Chiu, J.C.Y. Teo, A.P. Schnyder, S. Ryu, Rev. Mod. Phys. 88, 035005 (2016)

    ADS  Article  Google Scholar 

  12. 12.

    M. Di Liberto, A. Recati, I. Carusotto, C. Menotti, Phys. Rev. A 94, 062704 (2016)

    ADS  Article  Google Scholar 

  13. 13.

    M.A. Gorlach, A.N. Poddubny, arXiv:1608.02093

  14. 14.

    M.A. Gorlach, A.N. Poddubny, Phys. Rev. A 95, 033831 (2017)

    ADS  Article  Google Scholar 

  15. 15.

    M. Bello, C.E. Creffield, G. Platero, Scientific Rep. 6, 22562 (2016)

    ADS  Article  Google Scholar 

  16. 16.

    M. Bello, C.E. Creffield, G. Platero, Phys. Rev. B 95, 094303 (2017)

    ADS  Article  Google Scholar 

  17. 17.

    A.M. Marques, R.G. Dias, Phys. Rev. B 95, 115443 (2017)

    ADS  Article  Google Scholar 

  18. 18.

    X. Qin, F. Mei, F. Ke, L. Zhang, C. Lee, arXiv:1611.00205 (2016)

  19. 19.

    M. Eric Tai, A. Lukin, M. Rispoli, R. Schittko, T. Menke, D. Borgnia, P.M. Preiss, F. Grusdt, A.M. Kaufman, M. Greiner, arXiv:1612.05631

  20. 20.

    I. Tamm, Z. Sowjetunion, Physics 1, 733 (1932)

    Google Scholar 

  21. 21.

    W. Shockley, Phys. Rev. 56, 317 (1939)

    ADS  Article  Google Scholar 

  22. 22.

    S. Longhi, Opt. Lett. 36, 3248 (2011)

    ADS  Article  Google Scholar 

  23. 23.

    G. Corrielli, A. Crespi, G. Della Valle, S. Longhi, R. Osellame, Nat. Commun. 4, 1555 (2013)

    Article  Google Scholar 

  24. 24.

    A. Schreiber, A. Gábris, P.P. Rohde, K. Laiho, M. Štefaňák, V. Potoček, C. Hamilton, I. Jex, C. Silberhorn, Science 336, 55 (2012)

    ADS  Article  Google Scholar 

  25. 25.

    S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Öhberg, E. Andersson, R.R. Thomson, N. J. Phys. 17 115002 (2015)

    Article  Google Scholar 

  26. 26.

    S. Mukherjee, M. Valiente, N. Goldman, A. Spracklen, E. Andersson, P. Öhberg, R.R. Thomson, Phys. Rev. A 94, 053853 (2016)

    ADS  Article  Google Scholar 

  27. 27.

    S. Baier, M.J. Mark, D. Petter, K. Aikawa, L. Chomaz, Z. Cai, M. Baranov, P. Zoller, F. Ferlaino, Science 352, 201 (2015)

    ADS  Article  Google Scholar 

  28. 28.

    W.P. Su, J.R. Schrieffer, A.J. Heeger, Phys. Rev. Lett. 42, 1698 (1979)

    ADS  Article  Google Scholar 

  29. 29.

    M. Valiente, M. Küster, A. Saenz, Europhys. Lett. 92, 10001 (2010)

    ADS  Article  Google Scholar 

  30. 30.

    C. Cohen-Tannoudji, J. Dupont-Roc, G.G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (John Wiley & Sons, Inc., 1998)

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Di Liberto, M., Recati, A., Carusotto, I. et al. Two-body bound and edge states in the extended SSH Bose-Hubbard model. Eur. Phys. J. Spec. Top. 226, 2751–2762 (2017). https://doi.org/10.1140/epjst/e2016-60388-y

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