The European Physical Journal Special Topics

, Volume 224, Issue 3, pp 483–496 | Cite as

The interspersed spin boson lattice model

  • A. Kurcz
  • J. J. García-Ripoll
  • A. Bermudez
Regular Article
Part of the following topical collections:
  1. Novel Quantum Phases and Mesoscopic Physics in Quantum Gases


We describe a family of lattice models that support a new class of quantum magnetism characterized by correlated spin and bosonic ordering [Phys. Rev. Lett. 112, 180405 (2014)]. We explore the full phase diagram of the model using Matrix-Product-State methods. Guided by these numerical results, we describe a modified variational ansatz to improve our analytic description of the groundstate at low boson frequencies. Additionally, we introduce an experimental protocol capable of inferring the low-energy excitations of the system by means of Fano scattering spectroscopy. Finally, we discuss the implementation and characterization of this model with current circuit-QED technology.


European Physical Journal Special Topic Ising Model Quantum Phase Transition Fano Resonance Infrared Divergence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    See I. Bloch, J. Dalibard, S. Nascimbéne, Nat. Phys. 8, 267 (2012), and references therein CrossRefGoogle Scholar
  2. 2.
    See R. Blatt, C.F. Roos, Nat. Phys. 8, 277 (2012), and references therein CrossRefGoogle Scholar
  3. 3.
    See A.A. Houck, H.E. Türeci, J. Koch, Nat. Phys. 8, 264 (2012), and references therein CrossRefGoogle Scholar
  4. 4.
    See P. Barthelemy, L.M.K. Vandersypen, Ann. Phys. 525, 808 (2013), and references therein CrossRefMathSciNetGoogle Scholar
  5. 5.
    R.P. Feynman, Int. J. Theo. Phys. 21, 467 (1982)CrossRefMathSciNetGoogle Scholar
  6. 6.
    J.I. Cirac, P. Zoller, Nat. Phys. 8, 264 (2012)CrossRefGoogle Scholar
  7. 7.
    J. Simon, W.S. Bakr, R. Ma, M.E. Tai, P.M. Preiss, M. Greiner, Nature 472, 307 (2011)CrossRefADSGoogle Scholar
  8. 8.
    A. Friedenauer, H. Schmitz, J.T. Glueckert, D. Porras, T. Schaetz, Nat. Phys. 4, 757 (2008)CrossRefGoogle Scholar
  9. 9.
    K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E.E. Edwards, J.K. Freericks, G.-D. Lin, L.-M. Duan, C. Monroe, Nature 465, 590 (2010)CrossRefADSGoogle Scholar
  10. 10.
    J.W. Britton, B.C. Sawyer, A.C. Keith, C.-C.J. Wang, J.K. Freericks, H. Uys, M.J. Biercuk, J.J. Bollinger, Nature 484, 489 (2012)CrossRefADSGoogle Scholar
  11. 11.
    R. Islam, C. Senko, W.C. Campbell, S. Korenblit, J. Smith, A. Lee, E.E. Edwards, C.-C.J. Wang, J.K. Freericks, C. Monroe, Science 340, 583 (2013)CrossRefADSGoogle Scholar
  12. 12.
    P. Richerme, Z.-X. Gong, A. Lee, C. Senko, J. Smith, M. Foss-Feig, S. Michalakis, A.V. Gorshkov, C. Monroe, Nature 511, 198 (2014)CrossRefADSGoogle Scholar
  13. 13.
    P. Jurcevic, B.P. Lanyon, P. Hauke, C. Hempel, P. Zoller, R. Blatt, C.F. Roos, Nature 511, 202 (2014)CrossRefADSGoogle Scholar
  14. 14.
    S. Trotzky, P. Cheinet, S. Fölling, M. Feld, U. Schnorrberger, A.M. Rey, A. Polkovnikov, E.A. Demler, M.D. Lukin, I. Bloch, Science 319, 295 (2008)CrossRefADSGoogle Scholar
  15. 15.
    T. Fukuhara, P. Schau, M. Endres, S. Hild, M. Cheneau, I. Bloch, C. Gross, Nature 502, 76 (2013)CrossRefADSGoogle Scholar
  16. 16.
    D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, T. Esslinger, Science 340, 1307 (2013)CrossRefADSGoogle Scholar
  17. 17.
    R.A. Hart, P.M. Duarte, T.-L. Yang, X. Liu, T. Paiva, E. Khatami, R.T. Scalettar, N. Trivedi, D.A. Huse, R.G. Hulet [arXiv:1407.5932] (2014)
  18. 18.
    D. Porras, J.I. Cirac, Phys. Rev. Lett. 92, 207901 (2004)CrossRefADSGoogle Scholar
  19. 19.
    A. Bermudez, M.A. Martin-Delgado, D. Porras, New J. Phys. 12, 123016 (2010)CrossRefADSGoogle Scholar
  20. 20.
    G. Zhu, S. Schmidt, J. Koch, New J. Phys. 15, 115002 (2013)CrossRefADSGoogle Scholar
  21. 21.
    C. Cormick, A. Bermudez, S.F. Huelga, M.B. Plenio, New J. Phys. 15, 073027 (2013)CrossRefADSGoogle Scholar
  22. 22.
    A. Kurcz, A. Bermudez, J.J. Garcia-Ripoll, Phys. Rev. Lett. 112, 180405 (2014)CrossRefADSGoogle Scholar
  23. 23.
    A. Leggett, S. Chakravarty, A. Dorsey, M. Fisher, A. Garg, W. Zwerger, Rev. Mod. Phys. 59, 1 (1987)CrossRefADSGoogle Scholar
  24. 24.
    A.D. Greentree, C. Tahan, J.H. Cole, L.C.L. Hollenberg, Nat. Phys. 2, 856 (2006)CrossRefGoogle Scholar
  25. 25.
    M.J. Hartmann, F.G.S.L. Brandao, M.B. Plenio, Nat. Phys. 2, 849 (2006)CrossRefGoogle Scholar
  26. 26.
    M. Schiró, M. Bordyuh, B. Öztop, H.E. Türeci, Phys. Rev. Lett. 109, 053601 (2012)CrossRefADSGoogle Scholar
  27. 27.
    M. Schiró, M. Bordyuh, B. Öztop, H.E. Türeci, J. Phys. B 46, 224021 (2013)CrossRefADSGoogle Scholar
  28. 28.
    P.A. Ivanov, S.S. Ivanov, N.V. Vitanov, A. Mering, M. Fleischhauer, K. Singer, Phys. Rev. A 80, 060301(R) (2009)CrossRefADSGoogle Scholar
  29. 29.
    P. Nevado, D. Porras, Eur. Phys. J. Special Topics 217, 29 (2013)CrossRefADSGoogle Scholar
  30. 30.
    J. Jünemann, A. Cadarso, D. Pérez-García, A. Bermudez, J.J. García-Ripoll, Phys. Rev. Lett. 111, 230404 (2013)CrossRefGoogle Scholar
  31. 31.
    D. Porras, P.A. Ivanov, F. Schmidt-Kaler, Phys. Rev. Lett. 108, 235701 (2012)CrossRefADSGoogle Scholar
  32. 32.
    A. Dutta, J.K. Bhattacharjee, Phys. Rev. B 64, 184106 (2001)CrossRefADSGoogle Scholar
  33. 33.
    P. Pfeuty, Ann. Phys. 57, 79 (1970)CrossRefADSGoogle Scholar
  34. 34.
    I.G. Lang, Y.A. Firsov, Zh. Eksp. Teor. Fiz. 43, 1843 (1962), (see also Y.A. Firsov, Small Polarons: Transport Phenomena, in Polarons in Advanced Materials, edited by A.S. Alexandrov (Springer Verlag, Bristol, 2007)Google Scholar
  35. 35.
    P. Jordan, E. Wigner, Z. Physik 47, 631 (1928)CrossRefMATHADSGoogle Scholar
  36. 36.
    N.N. Bogoliubov, Sov. Phys. JETP 7, 41 (1958)MathSciNetGoogle Scholar
  37. 37.
    (English translation Il Nuovo Cim. 6, 794 (1958))Google Scholar
  38. 38.
    R. Orus, G. Vidal, Phys. Rev. B 78, 155117 (2008)CrossRefADSGoogle Scholar
  39. 39.
    J.J. García-Ripoll, New J. Phys. 8, 305 (2006)CrossRefGoogle Scholar
  40. 40.
    F. Verstraete, V. Murg, J. Cirac, Adv. Phys. 57, 143 (2008)CrossRefADSGoogle Scholar
  41. 41.
    V.J. Emery, A. Luther, Phys. Rev. Lett. 26, 1547 (1971)CrossRefADSGoogle Scholar
  42. 42.
    R. Silbey, R.A. Harris, J. Chem. Phys. 80, 2615 (1984)CrossRefADSGoogle Scholar
  43. 43.
    R.A. Harris, R. Silbey, J. Chem. Phys. 83, 1069 (1985)CrossRefADSGoogle Scholar
  44. 44.
    S. Bera, S. Florens, H.U. Baranger, N. Roch, A. Nazir, A.W. Chin, Phys. Rev. B 89, 121108(R) (2014)CrossRefADSGoogle Scholar
  45. 45.
    S. Bera, A. Nazir, A.W. Chin, H.U. Baranger, S. Florens [arXiv:1406.4983] (2014)
  46. 46.
    We define the following parameters u q = [1 2(1 + Δq/𝜖q)]1/2, v q = i[1 2(1 −Δq/𝜖q)]1/2 in terms of Δq = 2(J cosqd + h t), and 𝜖q = [Δ + (2J sinqd)2]1/2Google Scholar
  47. 47.
    R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957)CrossRefMathSciNetADSGoogle Scholar
  48. 48.
    H. Bruus, K. Flensberg, Many-Body Quantum Theory in Condensed Matter Physics: An Introduction (Oxford University Press, Oxford, 2004)Google Scholar
  49. 49.
    U. Fano, Phys. Rev. 124, 1866 (1961)CrossRefMATHADSGoogle Scholar
  50. 50.
    See A.E. Miroshnichenko, S. Flach, Y.S. Kivshar, Rev. Mod. Phys. 82, 2257 (2010), and references therein CrossRefADSGoogle Scholar
  51. 51.
    J.T. Shen, S. Fan, Opt. Lett. 30, 2001 (2005)CrossRefADSGoogle Scholar
  52. 52.
    A.E. Miroshnichenko, S.F. Mingaleev, S. Flach, Y.S. Kivshar, Phys. Rev. E 71, 036626 (2005)CrossRefMathSciNetADSGoogle Scholar
  53. 53.
    L. Zhou, Z.R. Gong, Y.-X. Liu, C.P. Sun, F. Nori, Phys. Rev. Lett. 101, 100501 (2008)CrossRefADSGoogle Scholar
  54. 54.
    M. Biondi, S. Schmidt, G. Blatter, H.E. Türeci, Phys. Rev. A 89, 025801 (2014)CrossRefADSGoogle Scholar
  55. 55.
    The lowest higher-energy excitations are composed of two-quasiparticles with energies 𝜖(q,q′) = 𝜖(q) + 𝜖(q′). Since the system-probe coupling may connect a low-energy excitation  to these higher-energy ones, we have to impose that the process is highly off-resonant |g p|≪|𝜖(q,q′) − 𝜖(q′′)|,∀,q,q′,q′′, which amounts to the condition in the textGoogle Scholar
  56. 56.
    The multi-level Fano coupling constants are g qα = g pe2|𝜖(q)⟩(u qδα,+ − v qδα,−) × e iqd/√ _N, where ⟨e2| = (0,1)Google Scholar
  57. 57.
    J.T. Shen, S. Fan, Phys. Rev. A 76, 062709 (2007)CrossRefADSGoogle Scholar
  58. 58.
    M.H. Devoret, Quantum fluctuations in electrical circuits (Les Houches, Session LXIII, 1995)Google Scholar
  59. 59.
    B. Yurke, J.S. Denker, Phys. Rev. A 29, 1419 (1984)CrossRefMathSciNetADSGoogle Scholar
  60. 60.
    See the Supplemental Material to [22] for a more detailed account on the microscopic circuit-QED modelGoogle Scholar
  61. 61.
    J. Majer, J.M. Chow, J.M. Gambetta, J. Koch, B.R. Johnson, J.A. Schreier, L. Frunzio, D.I. Schuster, A.A. Houck, A. Wallraff, A. Blais, M.H. Devoret, S.M. Girvin, R.J. Schoelkopf, Nature 449, 443 (2007)CrossRefADSGoogle Scholar
  62. 62.
    H. Paik, D.I. Schuster, L.S. Bishop, G. Kirchmair, G. Catelani, A.P. Sears, B.R. Johnson, M.J. Reagor, L. Frunzio, L.I. Glaz- man, S.M. Girvin, M.H. Devoret, R.J. Schoelkopf, Phys. Rev. Lett. 107, 240501 (2011)CrossRefADSGoogle Scholar
  63. 63.
    C. Rigetti, J.M. Gambetta, S. Poletto, B.L.T. Plourde, J.M. Chow, A.D. Corcoles, J.A. Smolin, S.T. Merkel, J.R. Rozen, G.A. Keefe, M.B. Rothwell, M.B. Ketchen, M. Steffen, Phys. Rev. B 86, 100506(R) (2012)CrossRefADSGoogle Scholar
  64. 64.
    L. Sun, A. Petrenko, Z. Leghtas, B. Vlastakis, G. Kirchmair, K.M. Sliwa, A. Narla, M. Hatridge, S. Shankar, J. Blumoff, L. Frunzio, M. Mirrahimi, M.H. Devoret, R.J. Schoelkopf, Nature 511, 444 (2014)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences and Springer 2015

Authors and Affiliations

  • A. Kurcz
    • 1
  • J. J. García-Ripoll
    • 1
  • A. Bermudez
    • 1
  1. 1.Instituto de Física FundamentalIFF-CSICMadridSpain

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