The European Physical Journal B

, Volume 68, Issue 3, pp 293–308 | Cite as

Spin 3/2 fermions with attractive interactions in a one-dimensional optical lattice: phase diagrams, entanglement entropy, and the effect of the trap

  • G. RouxEmail author
  • S. Capponi
  • P. Lecheminant
  • P. Azaria


We study spin 3/2 fermionic cold atoms with attractive interactions confined in a one-dimensional optical lattice. Using numerical techniques, we determine the phase diagram for a generic density. For the chosen parameters, one-particle excitations are gapped and the phase diagram is separated into two regions: one where the two-particle excitation gap is zero, and one where it is finite. In the first region, the two-body pairing fluctuations (BCS) compete with the density ones. In the other one, a molecular superfluid (MS) phase, in which bound-states of four particles form, competes with the density fluctuations. The properties of the transition line between these two regions is studied through the behavior of the entanglement entropy. The physical features of the various phases, comprising leading correlations, Friedel oscillations, and excitation spectra, are presented. To make the connection with experiments, the effect of a harmonic trap is taken into account. In particular, we emphasize the conditions under which the appealing MS phase can be realized, and how the phases could be probed by using the density profiles and the associated structure factor. Lastly, the consequences on the flux quantization of the different nature of the pairing in the BCS and MS phases are studied in a situation where the condensate is in a ring geometry.


03.75.Mn Multicomponent condensates; spinor condensates 71.10.Pm Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.) 71.10.Fd Lattice fermion models (Hubbard model, etc.) 


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  1. M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A.S. De, U. Sen, Adv. Phys. 56, 243 (2006)Google Scholar
  2. M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, I. Bloch, Nature 415, 39 (2002)Google Scholar
  3. R. Jördens, N. Strohmaier, K. Günter, H. Moritz, T. Esslinger, arXiv:0804.4009 Google Scholar
  4. I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)Google Scholar
  5. S. Giorgini, L.P. Pitaevskii, S. Stringari, to be published in Rev. Mod. Phys, arXiv:0706.3360 Google Scholar
  6. W. Ketterle, M.W. Zwierlein, to appear in “Ultracold Fermi Gases", Proceedings of the International School of Physics “Enrico Fermi", Course CLXIV, Varenna, 20 - 30 June 2006, edited by M. Inguscio, W. Ketterle, C. Salomon (IOS Press, Amsterdam, 2008), arXiv:0801.2500 Google Scholar
  7. D.S. Koltun, Phys. Rev. C 36, 2047 (1987)Google Scholar
  8. P. Schlottmann, J. Phys.: Condens. Matter 6, 1359 (1994)Google Scholar
  9. A.G.K. Modawi, A.J. Leggett, J. Low Temp. Phys. 109, 625 (1997)Google Scholar
  10. T.-L. Ho, S. Yip, Phys. Rev. Lett. 82, 247 (1999)Google Scholar
  11. A.S. Stepanenko, J.M.F. Gunn, arXiv:cond-mat/9901317 Google Scholar
  12. C. Honerkamp, W. Hofstetter, Phys. Rev. Lett. 92, 170403 (2004)Google Scholar
  13. C. Honerkamp, W. Hofstetter, Phys. Rev. B 70, 094521 (2004)Google Scholar
  14. C. Wu, Phys. Rev. Lett. 95, 266404 (2005)Google Scholar
  15. P. Lecheminant, E. Boulat, P. Azaria, Phys. Rev. Lett. 95, 240402 (2005)Google Scholar
  16. H. Kamei, K. Miyake, J. Phys. Soc. Jpn 74, 1911 (2005)Google Scholar
  17. T. Paananen, J.-P. Martikainen, P. Törmä, Phys. Rev. A 73, 053606 (2006)Google Scholar
  18. L. He, M. Jin, P. Zhuang, Phys. Rev. A 74, 033604 (2006)Google Scholar
  19. P.F. Bedaque, J.P. D’Incao, arXiv:cond-mat/0602525 Google Scholar
  20. A. Sedrakian, J.W. Clark, Phys. Rev. C 73, 035803 (2006)Google Scholar
  21. D. Lee, Phys. Rev. Lett. 98, 182501 (2007)Google Scholar
  22. Á. Rapp, G. Zaránd, C. Honerkamp, W. Hofstetter, Phys. Rev. Lett. 98, 160405 (2007)Google Scholar
  23. R.W. Cherng, G. Refael, E. Demler, Phys. Rev. Lett. 99, 130406 (2007)Google Scholar
  24. H. Zhai, Phys. Rev. A 75, 031603 (2007)Google Scholar
  25. T. Fukuhara, Y. Takasu, M. Kumakura, Y. Takahashi, Phys. Rev. Lett. 98, 030401 (2007)Google Scholar
  26. S. Capponi, G. Roux, P. Lecheminant, P. Azaria, E. Boulat, S.R. White, Phys. Rev. A 77, 013624 (2008)Google Scholar
  27. Á. Rapp, W. Hofstetter, G. Zaránd, Phys. Rev. B 77, 144520 (2008)Google Scholar
  28. D. Blume, S.T. Rittenhouse, J. von Stecher, C.H. Greene, Phys. Rev. A 77, 033627 (2008)Google Scholar
  29. X.-J. Liu, H. Hu, P.D. Drummond, Phys. Rev. A 77, 013622 (2008)Google Scholar
  30. X.W. Guan, M.T. Batchelor, C. Lee, H.-Q. Zhou, Phys. Rev. Lett. 100, 200401 (2008)Google Scholar
  31. P. Lecheminant, P. Azaria, E. Boulat, Nucl. Phys. B 798, 443 (2008)Google Scholar
  32. M. Bartenstein, A. Altmeyer, S. Riedl, R. Geursen, S. Jochim, C. Chin, J.H. Denschlag, R. Grimm, A. Simoni, E. Tiesinga, C.J. Williams, P.S. Julienne, Phys. Rev. Lett. 94, 103201 (2005)Google Scholar
  33. T.B. Ottenstein, T. Lompe, M. Kohnen, A.N. Wenz, S. Jochim, arXiv:0806.0587 Google Scholar
  34. B. DeMarco, Ph.D. thesis, University of Colorado, Boulder (2001)Google Scholar
  35. G. Röpke, A. Schnell, P. Schuck, P. Nozières, Phys. Rev. Lett. 80, 3177 (1998)Google Scholar
  36. G. Röpke, P. Schuck, Mod. Phys. Lett. A 21, 2513 (2006)Google Scholar
  37. P. Nozières, D. Saint James, J. Phys. France 43, 1133 (1982)Google Scholar
  38. B. Douçot, J. Vidal, Phys. Rev. Lett. 88, 227005 (2002)Google Scholar
  39. M.-S. Chang, I. Affleck, Phys. Rev. B 76, 054521 (2007)Google Scholar
  40. T.-L. Ho, Phys. Rev. Lett. 81, 742 (1998)Google Scholar
  41. C. Wu, J.-P. Hu, S.-C. Zhang, Phys. Rev. Lett. 91, 186402 (2003)Google Scholar
  42. C. Wu, Mod. Phys. Lett. B 20, 1707 (2006)Google Scholar
  43. S. Capponi, G. Roux, P. Azaria, E. Boulat, P. Lecheminant, Phys. Rev. B 75, 100503(R) (2007)Google Scholar
  44. S.R. White, Phys. Rev. Lett. 69, 2863 (1992)Google Scholar
  45. S.R. White, Phys. Rev. B 48, 10345 (1993)Google Scholar
  46. U. Schollwöck, Rev. Mod. Phys. 77, 259 (2005)Google Scholar
  47. A.W. Sandvik, Phys. Rev. B 59, R14157 (1999)Google Scholar
  48. F. Alet, S. Wessel, M. Troyer, Phys. Rev. E 71, 036706 (2005)Google Scholar
  49. F.F. Assaad, Quantum Monte Carlo Methods on Lattices: The Determinantal Approach (John von Neumann Institute for Computing, Jülich, 2002), NIC Vol. 10, p. 99Google Scholar
  50. D. Controzzi, A.M. Tsvelik, Phys. Rev. Lett. 96, 097205 (2006)Google Scholar
  51. A.O. Gogolin, A.A. Nersesyan, A.M. Tsvelik, Bosonization and Strongly Correlated Systems (Cambridge University Press, Cambridge, UK, 1998)Google Scholar
  52. T. Giamarchi, Quantum Physics in one Dimension, International series of monographs on physics (Oxford University Press, Oxford, UK, 2004), Vol. 121Google Scholar
  53. L. Kecke, T. Momoi, A. Furusaki, Phys. Rev. B 76, 060407(R) (2007)Google Scholar
  54. F.D.M. Haldane, Phys. Rev. Lett. 47, 1840 (1981)Google Scholar
  55. M.A. Cazalilla, J. Phys. B 37, S1 (2004)Google Scholar
  56. A.F. Albuquerque et al., J. Magn. Magn. Mater. 310, 1187 (2007)Google Scholar
  57. M. Troyer, B. Ammon, E. Heeb, Lect. Notes Comput. Sci. 1505, 502 (1998)Google Scholar
  58. S. Ejima, F. Gebhard, S. Nishimoto, Europhys. Lett. 70, 492 (2005)Google Scholar
  59. H.-H. Lin, L. Balents, M.P.A. Fisher, Phys. Rev. B 58, 1794 (1998)Google Scholar
  60. T. Giamarchi, B.S. Shastry, Phys. Rev. B 51, 10915 (1995)Google Scholar
  61. E. Orignac, T. Giamarchi, Phys. Rev. B 57, 11713 (1998)Google Scholar
  62. N. Andrei, J.H. Lowenstein, Phys. Lett. B 90, 106 (1980)Google Scholar
  63. G. Xianlong, M. Rizzi, M. Polini, R. Fazio, M.P. Tosi, J.V.L. Campo, K. Capelle, Phys. Rev. Lett. 98, 030404 (2007)Google Scholar
  64. J. Zhao, K. Ueda, X. Wang, Phys. Rev. B 74, 233102 (2006)Google Scholar
  65. J. Zhao, K. Ueda, X. Wang, J. Phys. Soc. Jpn 76, 114711 (2007)Google Scholar
  66. R. Egger, H. Grabert, Phys. Rev. Lett. 75, 3505 (1995)Google Scholar
  67. S.R. White, I. Affleck, D.J. Scalapino, Phys. Rev. B 65, 165122 (2002)Google Scholar
  68. L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008)Google Scholar
  69. N. Laflorencie, E.S. Sorensen, M.S. Chang, I. Affleck, Phys. Rev. Lett. 96, 100603 (2006)Google Scholar
  70. E.S. Sorensen, M.S. Chang, N. Laflorencie, I. Affleck, J. Stat. Mech., P08003 (2007)Google Scholar
  71. O. Legeza, J.Sólyom, L. Tincani, R.M. Noack, Phys. Rev. Lett. 99, 087203 (2007)Google Scholar
  72. M. Rigol, A. Muramatsu, G.G. Batrouni, R.T. Scalettar, Phys. Rev. Lett. 91, 130403 (2003)Google Scholar
  73. R.A. Molina, J. Dukelsky, P. Schmitteckert, Phys. Rev. Lett. 99, 080404 (2007)Google Scholar
  74. A.E. Feiguin, F. Heidrich-Meisner, Phys. Rev. B 76, 220508(R) (2007); M. Tezuka, M. Ueda, Phys. Rev. Lett. 100, 110403 (2008); M. Rizzi, M. Polini, M.A. Cazalilla, M.R. Bakhtiari, M.P. Tosi, Rosario Fazio, Phys. Rev. B 77, 245105 (2008); A. Lüscher, R.M. Noack, A.M. Läuchli, Phys. Rev. A 78, 013637 (2008)Google Scholar
  75. D.S. Petrov, G.V. Shlyapnikov, J.T.M. Walraven, Phys. Rev. Lett. 85, 3745 (2000)Google Scholar
  76. V. Dunjko, V. Lorent, M. Olshanii, Phys. Rev. Lett. 86, 5413 (2001)Google Scholar
  77. I.V. Tokatly, Phys. Rev. Lett. 93, 090405 (2004)Google Scholar
  78. B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling, I. Cirac, G.V. Shlyapnikov, T.W. Hänsch, I. Bloch, Nature 429, 277 (2004)Google Scholar
  79. D.M. Gangardt, G.V. Shlyapnikov, Phys. Rev. Lett. 90, 010401 (2003)Google Scholar
  80. C. Kollath, U. Schollwöck, J. von Delft, W. Zwerger, Phys. Rev. A 69, 031601 (2004)Google Scholar
  81. M. Machida, S. Yamada, Y. Ohashi, H. Matsumoto, Phys. Rev. A 74, 053621 (2006)Google Scholar
  82. G. Xianlong, M. Polini, M.P. Tosi, V.L. Campo, V.L. Jr, K. Capelle, arXiv:cond-mat/0506570 Google Scholar
  83. J.A. Sauer, M.D. Barrett, M.S. Chapman, Phys. Rev. Lett. 87, 270401 (2001)Google Scholar
  84. W.H. Heathcote, E. Nugent, B.T. Sheard, C.J. Foot, New J. Phys. 10, 043012 (2008)Google Scholar
  85. C. Ryu, M.F. Andersen, P. Clade, V. Natarajan, K. Helmerson, W.D. Phillips, arXiv:0709.0012 Google Scholar
  86. T. Wang, J. Javanainen, S.F. Yelin, Phys. Rev. A 76, 011601 (2007)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • G. Roux
    • 1
    Email author
  • S. Capponi
    • 2
  • P. Lecheminant
    • 3
  • P. Azaria
    • 4
  1. 1.Institute for Theoretical Physics C, RWTH Aachen UniversityAachenGermany
  2. 2.Laboratoire de Physique Théorique - IRSAMC, UPS and CNRS, Université de Toulouse 31062 ToulouseToulouseFrance
  3. 3.Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, CNRSCergy-PontoiseFrance
  4. 4.Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, CNRSParisFrance

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