Advertisement

Crossovers in Unitary Fermi Systems

  • Henning HeiselbergEmail author
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 836)

Abstract

Universality and crossover is described for attractive and repulsive interactions where, respectively, the BCS–BEC and crossover takes place and a ferromagnetic phase transition is claimed. Crossovers are also described for optical lattices and multicomponent systems. The crossovers, universal parameters and phase transitions are described within the Leggett and NSR models and calculated in detail within the Jastrow-Slater approximation. The physics of ultracold Fermi atoms is applied to neutron, nuclear and quark matter, nuclei and electrons in solids whenever possible. Specifically, the differences between optical lattices and cuprates is discussed w.r.t. antiferromagnetic, d-wave superfluid phases and phase separation.

Keywords

Hubbard Model Optical Lattice Feshbach Resonance Unitarity Limit Fermi Atom 
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.

References

  1. 1.
    Bishop, R.F., Gernoth, K.A., Walet, N.R., Xian, Y. (Eds.): Proc. of 10th Conf. on Recent Progress in Many-Body Theories, World Sci. (1999)Google Scholar
  2. 2.
    Baker, G.A.: Int. J. Mod. Phys. B 15, 1314 (2001)Google Scholar
  3. 3.
    Heiselberg, H.: Phys. Rev. A 63, 043606 (2001)CrossRefGoogle Scholar
  4. 4.
    O’Hara, K.M., Hemmer, S.L., Gehm, M.E., Granade, S.R., Thomas, J.E.: Science 298, 2179 (2002)ADSCrossRefGoogle Scholar
  5. 5.
    Jochim, S., et al.: Phys. Rev. Lett. 91, 240402 (2003)Google Scholar
  6. 6.
    Bartenstein, M., et al.: ibid. 92, 120401 (2004)Google Scholar
  7. 7.
    Ottenstein, T.B., Lompe, T., Kohnen, M., Wenz, A.N., Jochim, S.: Phys. Rev. Lett 101, 203202 (2008)Google Scholar
  8. 8.
    Kitagawa, M. et al.: Phys. Rev. A 77, 012719 (2008)ADSCrossRefGoogle Scholar
  9. 9.
    Spiegelhalder, F.M., et al.: arXiv:0908.1101Google Scholar
  10. 10.
    Wille, E., et al.: Phys. Rev. Lett. 100, 053201 (2008)Google Scholar
  11. 11.
    Alford, M.G., Rajagopal, K., Schaefer, T., Schmitt, A.: Rev. Mod. Phys 80, 1455 (2008)ADSCrossRefGoogle Scholar
  12. 12.
    Eagles, D.M.: Phys. Rev. 186, 456 (1969)ADSCrossRefGoogle Scholar
  13. 13.
    Leggett A.J.: (1980) in Modern Trends in the Theory of Condensed Matter, Pekalski A., Przystawa R., (ed.) Lect. Notes in Physics 115, (Springer-Verlag) 13Google Scholar
  14. 14.
    Nozières, P., Schmidt-Rink, S., Low, J.: Temp. Phys. 59, 195 (1982)Google Scholar
  15. 15.
    Sá de Melo, C.A.R., Randeria, M., Engelbrecht, J.R.: Phys. Rev. Lett. 71, 3202 (1993)Google Scholar
  16. 16.
    Ho, T.-L.: Phys. Rev. Lett. 92, 090402 (2004)ADSCrossRefGoogle Scholar
  17. 17.
    Jo, G-B. et al.: Science 325, 1521–1524 (2009)ADSCrossRefGoogle Scholar
  18. 18.
    Cowell, S., Heiselberg, H., Mazets, I.E., Morales, J., Pandharipande, V.R., Pethick, C.J.: Phys. Rev. Lett. 88, 210403 (2002)ADSCrossRefGoogle Scholar
  19. 19.
    Carlson, J., Chang, S-Y., Pandharipande, V.R., Schmidt, K.E.: Phys. Rev. Lett. 91, 50401 (2003)Google Scholar
  20. 20.
    Chang, S-Y., et al.: Phys. Rev. A 70, 043602 (2004)Google Scholar
  21. 21.
    Chang, S-Y., et al.: Nucl. Phys. A 746, 215 (2004)Google Scholar
  22. 22.
    Astrakharchik, G.E., Boronat, J., Casulleras, J., Giorgini, S.: Phys. Rev. Lett. 93, 200 (2004)Google Scholar
  23. 23.
    Hadzibabic, Z., Gupta, S., Stan, C.A., Schunck, C.H., Zwierlein, M.W., Dieckmann, K., Ketterle, W.: Phys. Rev. Lett. 91, 160401 (2003)Google Scholar
  24. 24.
    Zwierlein, M.W., et al.: Phys. Rev. Lett. 91, 250401 (2003)Google Scholar
  25. 25.
    Zwierlein, M.W., et al.: ibid. 92, 120403 (2004)Google Scholar
  26. 26.
    Gupta, S., et al.: Science 300, 47 (2003)Google Scholar
  27. 27.
    Chin, J.K., et al.: Nature 443, 961 (2006)Google Scholar
  28. 28.
    Bourdel, T., et al.: Phys. Rev. Lett. 91, 020402 (2003); cond-mat/0403091Google Scholar
  29. 29.
    Cubizolles, J., et al.: cond-mat/0308018Google Scholar
  30. 30.
    Regal, C.A., Jin, D.S.: Phys. Rev. Lett. 90, 230404 (2003)Google Scholar
  31. 31.
    Regal, C.A., Ticknor, C., Bohn, J.L., Jin, D.S.: cond-mat/0305028Google Scholar
  32. 32.
    Chin, C., Bartenstein, M., Altmeyer, A., Riedl, S., Jochim, S., Hecker Denschlag, J., Grimm, R.: Science 305, 1128 (2004)Google Scholar
  33. 33.
    Bartenstein, M., et al.: Phys. Rev. Lett. 92, 203201 (2004)Google Scholar
  34. 34.
    Nascimbene, S., Navon, N., Jiang, K.J., Cevy, F., Salomon, C.: Nature 463, 1057 (2011)Google Scholar
  35. 35.
    Strecker, K.E., Partridge, G.B., Hulet, R.G.: Phys. Rev. Lett. 91, 080406 (2003)Google Scholar
  36. 36.
    Partridge, G.B., et al.: Phys. Rev. Lett. 95, 020404 (2005)Google Scholar
  37. 37.
    Werner, F., Tarruell, L., Castin, Y.: Eur. Phys. J. B68, 401 (2009)ADSGoogle Scholar
  38. 38.
    Heiselberg, H.: J. Phys. B: At. Mol. Opt. Phys. 37, 1–13 (2004)CrossRefGoogle Scholar
  39. 39.
    Holland, M.J., DeMarco, B., Jin, D.S.: Science, 285, 1703 (1999)Google Scholar
  40. 40.
    DeMarco, B., Papp, S.B., Jin, D.S.: Phys. Rev. Lett. 86, 5409 (2001)Google Scholar
  41. 41.
    Truscott, S.G., et al.: Science 291, 2570 (2001)Google Scholar
  42. 42.
    Schreck, F., et al.: Phys. Rev. A 64, 011402 (2001)Google Scholar
  43. 43.
    O’Hara, K.M., et al.: Phys. Rev. Lett. 85, 2092 (2000)Google Scholar
  44. 44.
    Lee, T.D., Yang, C.N.: Phys. Rev. 105, 1119 (1957)Google Scholar
  45. 45.
    Belyakov, V.A.: Sov. Phys. JETP 13, 850 (1961)Google Scholar
  46. 46.
    Petrov, D.S., Salomon, C., Shlyapnikov, G.: Phys. Rev. Lett. 93, 090404 (2004)ADSCrossRefGoogle Scholar
  47. 47.
    Heiselberg, H.: Phys. Rev. Lett. 93, 040402 (2004)ADSCrossRefGoogle Scholar
  48. 48.
    Heiselberg, H.: Phys. Rev. A 73, 013607 (2006)ADSCrossRefGoogle Scholar
  49. 49.
    Yu, Z., Bruun, G.M., Baym, G.: Phys. Rev. A 80, 023615 (2009)ADSCrossRefGoogle Scholar
  50. 50.
    Griffin, A., Zaremba, E.: Phys. Rev. A 956, 4839 (1997)ADSCrossRefGoogle Scholar
  51. 51.
    Pethick, C.J., Smith, H.: Bose-Einstein Condensation in Dilute Gases. Cambridge University Press, Cambridge (2002)Google Scholar
  52. 52.
    Pandharipande, V.R.: Nucl. Phys. A 174, 641 (1971)Google Scholar
  53. 53.
    Pandharipande, V.R.: Nucl. Phys. A 178, 123 (1971)Google Scholar
  54. 54.
    Pandharipande, V.R., Bethe, H.A.: Phys. Rev. C 7, 1312 (1973)Google Scholar
  55. 55.
    Pandharipande, V.R., Schmidt, K.E.: Phys. Rev. A 15, 2486 (1977)Google Scholar
  56. 56.
    Carlson, J., Heiselberg, H., Pandharipande, V.R.: Phys. Rev. C 63, 017603 (2001)ADSCrossRefGoogle Scholar
  57. 57.
    Heiselberg, H.: Phys. Rev. A 68, 053616 (2003)ADSCrossRefGoogle Scholar
  58. 58.
    Fisher, M.: Phil. Mag. 7, 1731 (1962)ADSCrossRefGoogle Scholar
  59. 59.
    Tan, S.: Ann. Phys. 323, 2971–2986 (2008)Google Scholar
  60. 60.
    Houbiers, M. et al.: Phys. Rev. A 56, 4846 (1997)Google Scholar
  61. 61.
    Pandharipande, V.R.: Private Communication, Nordita (1999)Google Scholar
  62. 62.
    Brueckner, K.A., Levinson, C.A., Mahmoud, H.M.: Phys. Rev. 103, 1353 (1956)Google Scholar
  63. 63.
    Bethe, H.A., Goldstone, J.: Proc. Roy. Soc. (London), A238, 551 (1957)Google Scholar
  64. 64.
    Baym, G., Pethick, C.J.: Ann. Rev. Astr. Astrophys. 17, 415 (1979)Google Scholar
  65. 65.
    Pandharipande, V.R.: Int. J. of Mod. Phys. B13, 543 (1999)Google Scholar
  66. 66.
    Heiselberg, H., Pandharipande, V.R.: Ann. Rev. Nucl. Part. Sci. 50, 481–524 (2000)Google Scholar
  67. 67.
    Heiselberg, H., Hjorth-Jensen, M.: Phys. Rep. 50, 481–524 (2000)Google Scholar
  68. 68.
    Heiselberg, H., Pethick, C.J., Ravenhall, D.G.: Phys. Rev. Letts. 61, 818 (1988)ADSCrossRefGoogle Scholar
  69. 69.
    Efimov, V.: Phys. Lett. B 33, 563 (1970)ADSCrossRefGoogle Scholar
  70. 70.
    Braaten, E., et al.: Phys. Rev. Lett. 87, 160407 (2001)Google Scholar
  71. 71.
    Braaten, E., et al.: Phys. Rev. A 63, 063609 (2001)Google Scholar
  72. 72.
    Jonsell, S., Heiselberg, H., Pethick, C.J.: Phys. Rev. Lett. 88, 50401 (2002)CrossRefGoogle Scholar
  73. 73.
    Stoner, E.: Phil. Mag. 15, 1018 (1933)Google Scholar
  74. 74.
    Conduit, G.J., Simons, B.D.: arXiv: 0907.372Google Scholar
  75. 75.
    Zhai, H.: arXiv: 0909.4917Google Scholar
  76. 76.
    Pieri, P., Pisani, L., Strinati, G.C.: Phys. Rev. B 70, 094508 (2004)ADSCrossRefGoogle Scholar
  77. 77.
    Bloch, I., Dalibard, J., Zwerger, W.: Rev. Mod. Phys. 80, 885 (2008)ADSCrossRefGoogle Scholar
  78. 78.
    Bardeen, J., Cooper, L.N., Schrieffer, J.R.: Phys. Rev. 108, 1175 (1957)MathSciNetADSzbMATHCrossRefGoogle Scholar
  79. 79.
    Bogoliubov, N.N.: Sov. Phys. JETP 7, 41 (1958)MathSciNetGoogle Scholar
  80. 80.
    van Hove, L.: Phys. 25, 849 (1959)Google Scholar
  81. 81.
    Emery, V.J.: Nucl. Phys. 19, 154 (1960)Google Scholar
  82. 82.
    Gorkov, L.P., Melik-Barkhudarov, T.K.: JETP 13, 1018 (1961)Google Scholar
  83. 83.
    Heiselberg, H., Pethick, C.J., Smith, H., Viverit, L.: Phys. Rev. Letts. 85, 2418 (2000)ADSCrossRefGoogle Scholar
  84. 84.
    Martikainen, J.-P., Kinnunen, J., Törma, P., Pethick, C.J.: Phys. Rev. Lett. 103, 260403 (2009)ADSCrossRefGoogle Scholar
  85. 85.
    Kim, D.-H., Törma, P., Martikainen, J.-P.: Phys. Rev. Lett. 102, 245301 (2009)Google Scholar
  86. 86.
    Heiselberg, H.: arXiv:0905.2107Google Scholar
  87. 87.
    Burovski, E., Prokofev, N., Svistunov, B., Troyer, M.: Phys. Rev. Lett. 96, 160402 (2006)Google Scholar
  88. 88.
    Burovski, E., Kozik, E., Prokof’ev, N., Svistunov, B., Troyer, M.: Phys. Rev. Lett. 101, 090402 (2008)Google Scholar
  89. 89.
    Schirotzek, A., Shin, Y., Schunck, C.H., Ketterle, W.: arXiv:0808.0026Google Scholar
  90. 90.
    Haussmann, R., Rantner, W., Cerrito, S., Zwerger, W.: Phys. Rev. A 75, 023610 (2007)ADSCrossRefGoogle Scholar
  91. 91.
    Bohr, A., Mottelson, B.R.: Nuclear Structure I+II. Benjamin, New York (1969)Google Scholar
  92. 92.
    Cozzini, M., Stringari, S.: Phys. Rev. A 67, 041602(R) (2003)ADSGoogle Scholar
  93. 93.
    Riedl S., et al.: arXiv:0907.3814Google Scholar
  94. 94.
    Clancy, B., Luo, L., Thomas, J.E.: arXiv:0705.2782Google Scholar
  95. 95.
    Heiselberg H., Mottelson B.R.: Phys. Rev. Lett. 88, 190401 (2002)Google Scholar
  96. 96.
    Bruun, G.M., Heiselberg, H.: Phys. Rev. A 65, 053407 (2002)Google Scholar
  97. 97.
    Bohr, A., Mottelson, B.R., Pines, D.: Phys. Rev. 110, 936 (1958)ADSCrossRefGoogle Scholar
  98. 98.
    Audi, G., Wapstra, A.H.: Nucl. Phys. A595, 409 (1995)Google Scholar
  99. 99.
    Dobaczewski, J., et al.: Phys. Rev. C63, 024308 (2001)Google Scholar
  100. 100.
    Dobaczewski, J. et al.: Phys.Rev. C 63, 024308 (2001)ADSCrossRefGoogle Scholar
  101. 101.
    Baym, G., Heiselberg, H.: Phys.Rev. D 56, 5254–5259 (1997)ADSCrossRefGoogle Scholar
  102. 102.
    Thomas, J.E.: Proc. of Quark Matter 09Google Scholar
  103. 103.
    Gelman, B.A., Shuryak, E.V., Zahed, I.: Phys. Rev. A 72, 043601 (2005)Google Scholar
  104. 104.
    Schaefer, T., Teaney, D.: Rept. Prog. Phys. 72, 126001 (2009)Google Scholar
  105. 105.
    Baym, G.: Acta. Phys. Polon. B29, 1839–1884 (1998)Google Scholar
  106. 106.
    Heiselberg, H.: Phys. Rev. Lett. 82, 2052–2055 (1999)Google Scholar
  107. 107.
    Fölling, S. et al.: Nature 434, 481 (2005)ADSCrossRefGoogle Scholar
  108. 108.
    Spielman, I.B., Phillips, W.D., Porto, J.V.: Phys. Rev. Lett. 98, 080404 (2007)ADSCrossRefGoogle Scholar
  109. 109.
    Rom, T., Best, Th., van Oosten, D., Schneider, U., Fölling, S., Paredes, B., Bloch, I.: Nature 444, 733 (2006)ADSCrossRefGoogle Scholar
  110. 110.
    Micnas, R., Ranninger, J., Robaszkiewicz, S., Tabor, S.: Phys. Rev. B 37, 9410 (1988)Google Scholar
  111. 111.
    Micnas, R., Ranninger, J., Robaszkiewicz, S., Tabor, S.: Rev. Mod. Phys. 67, 117 (1998)Google Scholar
  112. 112.
    Marsiglio, F.: Phys. Rev. B 55, 575 (1997)ADSCrossRefGoogle Scholar
  113. 113.
    Dupuis, N., Phys. Rev. B 70, 134502 (2004). Note that the approximate level density used leads to a gap reduced by a factor \(2/\pi\) in the dilute limit.Google Scholar
  114. 114.
    Nishida, Y., Son, D.T.: Phys. Rev. A 75, 063617 (2007)MathSciNetADSCrossRefGoogle Scholar
  115. 115.
    Tamaki, H., Ohashi, Y., Miyake, K.: arXiv:0803.2084Google Scholar
  116. 116.
    Pruschke, T., Zitzler, R.: J. Phys.: Condens. Matter 15, 7867 (2003)ADSCrossRefGoogle Scholar
  117. 117.
    Lieb, E.H., Wu, F.Y.: Phys. Rev. Lett. 20, 1445 (1968)ADSCrossRefGoogle Scholar
  118. 118.
    van Dongen, P.G.J.: Phys. Rev. Lett. 67, 757 (1991)Google Scholar
  119. 119.
    van Dongen, P.G.J.: Phys. Rev. B 50, 14016 (1994)Google Scholar
  120. 120.
    Staudt, R., Dzierzawa, M., Muramatsu, A.: Eur. Phys. J. B 17, 411 (2000)ADSCrossRefGoogle Scholar
  121. 121.
    Georges, A.: arXiv:cond-mat/0702122Google Scholar
  122. 122.
    Langmann, E., Wallin, M.: cond-mat/0406608Google Scholar
  123. 123.
    Kusko, C., Markiewicz, R.S.: cond-mat/0102440Google Scholar
  124. 124.
    Anderson, P.W.: Sci. 235, 1196 (1987)ADSCrossRefGoogle Scholar
  125. 125.
    Pistolesi, F., Nozieres, Ph.: Phys. Rev. B 66, 054501 (2002)ADSCrossRefGoogle Scholar
  126. 126.
    Heiselberg, H.: Phys. Rev. A 79, 063611 (2009)ADSCrossRefGoogle Scholar
  127. 127.
    Paiva, T., Scalettar, R., Randeria, M., Trivedi, N.: arXiv:0906.2141Google Scholar
  128. 128.
    See e.g., Edegger, B., Muthukumar, V.N., Gros, C.: Advances in Physics 56, 927 (2007), and References thereinGoogle Scholar
  129. 129.
    Laughlin, R.B.: arXiv:cond-mat/0209269Google Scholar
  130. 130.
    Zhang, F.C.: Phys. Rev. Lett. 90, 207002 (2003)Google Scholar
  131. 131.
    Gan, J.Y., Zhang, F.C., Su, Z.B.: Phys. Rev. B 71, 014508 (2005)Google Scholar
  132. 132.
    Schneider, U. et al.: Sci. 322, 1520 (2008)ADSCrossRefGoogle Scholar
  133. 133.
    Tranquada, J.M. et al.: Phys. Rev. B 54, 7489 (1996)ADSCrossRefGoogle Scholar
  134. 134.
    Uemura, Y.J.: Physica C 282, 194 (1997)ADSCrossRefGoogle Scholar
  135. 135.
    Hofstetter, W., Cirac, J.I., Zoller, P., Demler, E., Lukin, M.D.: Phys. Rev. Lett. 89, 220407 (2002)ADSCrossRefGoogle Scholar
  136. 136.
    Chen, Q., et al.: Phys. Rep. 412, 1 (2005)ADSCrossRefGoogle Scholar
  137. 137.
    Zaanen, J., Gunnarsson, O.L.: Phys. Rev. B 40, 7391 (1989)Google Scholar
  138. 138.
    Poilblanc, D., Rice, T.M.: Phys. Rev. B 39, 9749 (1989)Google Scholar
  139. 139.
    Schulz, H.J.: J. Physiq. 50, 2833 (1989)Google Scholar
  140. 140.
    Machida, K.: Physica C 158, 192 (1989)Google Scholar
  141. 141.
    Scalapino, D.J.: Physics Reports 250, 329 (1995); and cond-mat/0610710, to appear as Chapter 13 in “Handbook of High Temperature Superconductivity", Schrieffer, J.R. (ed.) Springer, 2006Google Scholar
  142. 142.
    White, S.R., Scalapino, D.J.: Phys. Rev. Lett. 81, 3227 (1998)Google Scholar
  143. 143.
    Berg, E., Fradkin, E., Kivelson, S.A., Tranquada, J.: New J. Phys. 11, 115004 (2009)Google Scholar
  144. 144.
    Vojta, M., Adv. Phys. 58, 699 (2009)Google Scholar
  145. 145.
    Pethick, C.J., Ravenhall, G.R.: Ann. NY Acad. Sci. 647, 503 (1991)Google Scholar
  146. 146.
    Heiselberg, H., Pethick, C.J., Staubo, E.F.: Phys. Rev. Lett. 70, 1355 (1993)Google Scholar
  147. 147.
    Köhl, M., Moritz, H., Stöferle, T., Gunter, K., Esslinger, T.: Phys. Rev. Lett. 94, 080403 (2005)CrossRefGoogle Scholar
  148. 148.
    Andersen, B.M., Bruun, G.M.: Phys. Rev. A 76, 041602(R) (2007)ADSCrossRefGoogle Scholar
  149. 149.
    Seibold, G., Castellani, C., Di Castro, C., Grilli, M.: cond-mat/9803184Google Scholar
  150. 150.
    Lorenzana, J., Castellani, C., Di Castro, C.: Phys. Rev. B 64, 235128 (2001)Google Scholar
  151. 151.
    Arrigoni, E., Fradkin, E., Kivelson, S.A.: Phys. Rev. B 69, 214519 (2004)ADSCrossRefGoogle Scholar
  152. 152.
    Bogoliubov, N.N.: Sowjetunion 6, 1 (1962)Google Scholar
  153. 153.
    Mermin, N.D., Wagner, H.: Phys. Rev. Lett. 17, 1133 (1966)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Applied Research, DALOBallerupDenmark

Personalised recommendations