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Pseudogap phenomena in ultracold atomic Fermi gases

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Abstract

The pairing and superfluid phenomena in a two-component ultracold atomic Fermi gas is an analogue of Cooper pairing and superconductivity in an electron system, in particular, the high T c superconductors. Owing to the various tunable parameters that have been made accessible experimentally in recent years, atomic Fermi gases can be explored as a prototype or quantum simulator of superconductors. It is hoped that, utilizing such an analogy, the study of atomic Fermi gases may shed light to the mysteries of high T c superconductivity. One obstacle to the ultimate understanding of high T c superconductivity, from day one of its discovery, is the anomalous yet widespread pseudogap phenomena, for which a consensus is yet to be reached within the physics community, after over 27 years of intensive research efforts. In this article, we shall review the progress in the study of pseudogap phenomena in atomic Fermi gases in terms of both theoretical understanding and experimental observations. We show that there is strong, unambiguous evidence for the existence of a pseudogap in strongly interacting Fermi gases. In this context, we shall present a pairing fluctuation theory of the pseudogap physics and show that it is indeed a strong candidate theory for high T c superconductivity.

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References and notes

  1. Q. J. Chen, J. Stajic, S. N. Tan, and K. Levin, BCS-BEC crossover: From high temperature superconductors to ultracold superfluids, Phys. Rep., 2005, 412(1): 1

    ADS  Google Scholar 

  2. I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys., 2008, 80: 885

    ADS  Google Scholar 

  3. J. M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys., 1998, 2: 231, see also: arXiv: hep-th/9711200v3

    MathSciNet  MATH  ADS  Google Scholar 

  4. E. Witten, Anti De Sitter space and holography, Adv. Theor. Math. Phys., 1998, 2: 253

    MathSciNet  MATH  ADS  Google Scholar 

  5. O. Aharony, S. S. Gubser, J. Maldacena, H. Ooguri, and Y. Oz, Large N field theories, string theory and gravity, Phys. Rep., 2000, 323(3–4): 183

    MathSciNet  ADS  Google Scholar 

  6. M. Čubrović, J. Zaanen, and K. Schalm, String theory, quantum phase transitions, and the emergent Fermi liquid, Science, 2009, 325(5939): 439

    MathSciNet  ADS  Google Scholar 

  7. T. Timusk and B. Statt, The pseudogap in high-temperature superconductors: An experimental survey, Rep. Prog. Phys., 1999, 62(1): 61

    ADS  Google Scholar 

  8. J. R. Schrieffer, Theory of Supercondutivity, 3rd Ed., Perseus Books, Reading, MA, 1983

    Google Scholar 

  9. S. N. Bose, Plancks gesetz und lichtquantenhypothese, Z. Phys., 1924, 26(1): 178

    MATH  ADS  Google Scholar 

  10. A. Einstein, Quantentheorie des einatomigen idealen gases (II), Sitzungsberichte der Preussischen Akademie der Wissenschaften, 1925, 1: 3

    Google Scholar 

  11. L. Pitaevskii and S. Stringari, Bose-Einstein Condensation, New York: Oxford, 2003

    MATH  Google Scholar 

  12. C. J. Pethik and H. Smith, Bose-Einstein Condensation in Dilute Gases, Cambridge: Cambridge University Press, 2002

    Google Scholar 

  13. D. M. Eagles, Possible pairing without superconductivity at low carrier concentrations in bulk and thin-film superconducting semiconductors, Phys. Rev., 1969, 186(2): 456

    ADS  Google Scholar 

  14. A. J. Leggett, Diatomic molecules and cooper pairs, in: Modern Trends in the Theory of Condensed Matter, Berlin: Springer-Verlag, 1980, pp. 13–27

    Google Scholar 

  15. P. Nozières and S. Schmitt-Rink, Bose condensation in an attractive fermion gas: From weak to strong coupling superconductivity, J. Low Temp. Phys., 1985, 59(3–4): 195

    ADS  Google Scholar 

  16. R. Friedberg and T. D. Lee, Boson-Fermion model of superconductivity, Phys. Lett. A, 1989, 138(8): 423

    ADS  Google Scholar 

  17. T. Friedberg and T. D. Lee, Gap energy and long-range order in the boson-fermion model of superconductivity, Phys. Rev. B, 1989, 40: 6745

    ADS  Google Scholar 

  18. C. A. R. Sá de Melo, M. Randeria, and J. R. Engelbrecht, Crossover from BCS to Bose superconductivity: Transition temperature and time-dependent Ginzburg-Landau theory, Phys. Rev. Lett., 1993, 71: 3202

    ADS  Google Scholar 

  19. M. Randeria, Crossover from BCS theory to Bose-Einstein Condensation, in: Bose-Einstein Condensation, edited by A. Griffin, D. Snoke, and S. Stringari, Cambridge: Cambridge University Press, 1995, pp. 355–392

    Google Scholar 

  20. B. Jankó, J. Maly, and K. Levin, Pseudogap effects induced by resonant pair scattering, Phys. Rev. B, 1997, 56(18): R11407(R)

    ADS  Google Scholar 

  21. J. Maly, B. Jankó, and K. Levin, Numerical studies of the s-wave pseudogap state and related T c: The “pairing approximation” theory, Physica C, 1999, 321(1–2): 113

    ADS  Google Scholar 

  22. J. Maly, B. Jankó, and K. Levin, Superconductivity from a pseudogapped normal state: A mode-coupling approach to precursor superconductivity, Phys. Rev. B, 1999, 59: 1354

    ADS  Google Scholar 

  23. Q. J. Chen, I. Kosztin, B. Jankó, and K. Levin, Pairing fluctuation theory of superconducting properties in underdoped to overdoped cuprates, Phys. Rev. Lett., 1998, 81: 4708

    ADS  Google Scholar 

  24. Q. J. Chen, I. Kosztin, B. Jankó, and K. Levin, Superconducting transitions from the pseudogap state: d-wave symmetry, lattice, and low-dimensional effects, Phys. Rev. B, 1999, 59: 7083

    ADS  Google Scholar 

  25. I. Kosztin, Q. J. Chen, B. Jankó, and K. Levin, Relationship between the pseudo- and superconducting gaps: Effects of residual pairing correlations below T c, Phys. Rev. B, 1998, 58: R5936(R)

    ADS  Google Scholar 

  26. R. Micnas, J. Ranninger, and S. Robaszkiewicz, Superconductivity in narrow-band systems with local nonretarded attractive interactions, Rev. Mod. Phys., 1990, 62: 113

    ADS  Google Scholar 

  27. R. Micnas and S. Robaszkiewicz, Superconductivity in systems with local attractive interactions, Cond. Matt. Phys. (Lviv), 1998, 13: 89

    Google Scholar 

  28. R. Micnas, M. H. Pedersen, S. Schafroth, T. Schneider, J. J. Rodríguez-Núñez, and H. Beck, Excitation spectrum of the attractive Hubbard model, Phys. Rev. B, 1995, 52: 16223

    ADS  Google Scholar 

  29. J. Ranninger and J. M. Robin, Manifestations of the pseudogap in the boson-fermion model for Bose-Einsteincondensation-driven superconductivity, Phys. Rev. B, 1996, 53: R11961(R)

    ADS  Google Scholar 

  30. M. Drechsler and W. Zwerger, Crossover from BCSsuperconductivity to Bose-condensation, Ann. Phys., 1992, 1: 15

    Google Scholar 

  31. R. Haussmann, Crossover from BCS superconductivity to Bose-Einstein condensation: A self-consistent theory, Z. Phys. B, 1993, 91(3): 291

    ADS  Google Scholar 

  32. R. Haussmann, Properties of a Fermi liquid at the superfluid transition in the crossover region between BCS superconductivity and Bose-Einstein condensation, Phys. Rev. B, 1994, 49: 12975

    ADS  Google Scholar 

  33. O. Tchernyshyov, Noninteracting Cooper pairs inside a pseudogap, Phys. Rev. B, 1997, 56: 3372

    ADS  Google Scholar 

  34. E. V. Gorbar, V. M. Loktev, and S. G. Sharapov, Crossover from BCS to composite-boson (local-pair) superconductivity in quasi-2D systems, Physica C, 1996, 257(3–4): 355

    ADS  Google Scholar 

  35. V. P. Gusynin, V. M. Loktev, and S. G. Sharapov, Phase diagram of a 2D metal system with a variable number of carriers, JETP Lett., 1997, 65(2): 182

    ADS  Google Scholar 

  36. M. Marini, F. Pistolesi, and G. C. Strinati, Evolution from BCS superconductivity to Bose condensation: Analytic results for the crossover in three dimensions, Eur. Phys. J. B, 1998, 1(2): 151

    ADS  Google Scholar 

  37. B. DeMarco and D. S. Jin, Onset of Fermi degeneracy in a trapped atomic gas, Science, 1999, 285(5434): 1703

    Google Scholar 

  38. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Observation of Bose-Einstein condensation in a dilute atomic vapor, Science, 1995, 269(5221): 198

    ADS  Google Scholar 

  39. C. C. Bradley, C. A. Sackett, J. J. Tollett, and R. G. Hulet, Evidence of Bose-Einstein condensation in an atomic gas with attractive interactions, Phys. Rev. Lett., 1995, 75: 1687

    ADS  Google Scholar 

  40. C. C. Bradley, C. A. Sackett, J. J. Tollett, and R. G. Hulet, Evidence of Bose-Einstein condensation in an atomic gas with attractive interactions [Phys. Rev. Lett. 75, 1687 (1995)], Phys. Rev. Lett., 1997, 79: 1170

    ADS  Google Scholar 

  41. K. B. Davis, M. Mewes, M. R. Andrews, D. S. Durfee, D. M. Kurn, W. Ketterle, and W. Ketterle, Bose-Einstein condensation in a gas of sodium atoms, Phys. Rev. Lett., 1995, 75(22): 3969

    ADS  Google Scholar 

  42. M. Greiner, C. A. Regal, and D. S. Jin, Emergence of a molecular Bose-Einstein condensate from a Fermi gas, Nature, 2003, 426(6966): 537

    ADS  Google Scholar 

  43. S. Jochim, M. Bartenstein, A. Altmeyer, G. Hendl, S. Riedl, C. Chin, J. H. Denschlag, and R. Grimm, Bose-Einstein condensation of molecules, Science, 2003, 302(5653): 2101

    ADS  Google Scholar 

  44. M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. Raupach, S. Gupta, Z. Hadzibabic, and W. Ketterle, Observation of Bose-Einstein condensation of molecules, Phys. Rev. Lett., 2003, 91(25): 250401

    ADS  Google Scholar 

  45. C. A. Regal, M. Greiner, and D. S. Jin, Observation of resonance condensation of fermionic atom pairs, Phys. Rev. Lett., 2004, 92(4): 040403

    ADS  Google Scholar 

  46. M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, C. Chin, J. H. Denschlag, and R. Grimm, Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas, Phys. Rev. Lett., 2004, 92(12): 120401

    ADS  Google Scholar 

  47. C. Chin, M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, J. H. Denschlag, and R. Grimm, Observation of the pairing gap in a strongly interacting Fermi gas, Science, 2004, 305(5687): 1128

    ADS  Google Scholar 

  48. M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. Raupach, A. J. Kerman, and W. Ketterle, Condensation of pairs of fermionic atoms near a Feshbach resonance, Phys. Rev. Lett., 2004, 92(12): 120403

    ADS  Google Scholar 

  49. J. Kinast, A. Turlapov, J. E. Thomas, Q. J. Chen, J. Stajic, and K. Levin, Heat capacity of a strongly interacting Fermi gas, Science, 2005, 307(5713): 1296

    ADS  Google Scholar 

  50. M. W. Zwierlein, J. R. Abo-Shaeer, and A. Schirotzek, and W. Ketterle, Vortices and superfluidity in a strongly interacting Fermi gas, Nature, 2005, 435: 1047

    ADS  Google Scholar 

  51. M. W. Zwierlein, A. Schirotzek, C. H. Schunck, and W. Ketterle, Fermionic super-fluidity with imbalanced spin populations, Science, 2006, 311(5760): 492

    ADS  Google Scholar 

  52. G. B. Partridge, W. Li, R. I. Kamar, Y. A. Liao, and R. G. Hulet, Pairing and phase separation in a polarized Fermi gas, Science, 2006, 311(5760): 503

    ADS  Google Scholar 

  53. P. Fulde and R. A. Ferrell, Superconductivity in a strong spin-exchange field, Phys. Rev., 1964, 135(3A): A550

    ADS  Google Scholar 

  54. A. I. Larkin and Yu. N. Ovchinnikov, Neodnorodnoe sostoyanie sverkhprovodnikov, Zh. Eksp. Teor. Fiz., 1964, 47: 1136

    Google Scholar 

  55. I. Larkin and Yu. N. Ovhinnikov, Nonuniform state of superconductors, Sov. Phys. JETP, 1965, 20: 762

    Google Scholar 

  56. Q. J. Chen, Generalization of BCS theory to short coherence length superconductors: A BCS-Bose-Einstein crossover scenario, Ph.D. thesis, University of Chiago, 2000, available in the ProQuest Dissertations & Theses Database online.

    Google Scholar 

  57. Q. J. Chen, J. Stajic, and K. Levin, Applying BCS-BEC crossover theory to high temperature superconductors and ultracold atomic Fermi gases, Low Temp. Phys., 2006, 32(4): 406; Fiz. Nizk. Temp., 2006, 32: 538

    ADS  Google Scholar 

  58. S. Giorgini, L. P. Pitaevskii, and S. Stringari, Theory of ultracold atomic Fermi gases, Rev. Mod. Phys., 2008, 80(4): 1215

    ADS  Google Scholar 

  59. C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Feshbach resonances in ultracold gases, Rev. Mod. Phys., 2010, 82(2): 1225

    ADS  Google Scholar 

  60. M. Inguscio, W. Ketterle, and C. Salomon (Eds.), Ultracold Fermi gases, Proceedings of the International School of Physics “Enrico Fermi”, Vol. CLXIV, Varenna, 2006, Società Italiana di Fisca Bologna, Italy (ISO press, Amsterdam, 2008)

    Google Scholar 

  61. H. Ding, T. Yokoya, J. C. Campuzano, T. Takahashi, M. Randeria, M. R. Norman, T. Mochiku, K. Hadowaki, and J. Giapintzakis, Spectroscopic evidence for a pseudogap in the normal state of underdoped high-T c superconductors, Nature, 1996, 382(6586): 51

    ADS  Google Scholar 

  62. Ch. Renner, B. Revaz, K. Kadowaki, I. Maggio-Aprile, and O. Fischer, Observation of the low temperature pseudogap in the vortex cores of Bi2Sr2CaCu2O8+δ , Phys. Rev. Lett., 1998, 80(16): 3606

    ADS  Google Scholar 

  63. Ch. Renner, B. Revaz, J. Y. Genoud, K. Kadowaki, and O. Fischer, Pseudogap precursor of the superconducting gap in under- and overdoped Bi2Sr2CaCu2O8+δ , Phys. Rev. Lett., 1998, 80(1): 149

    ADS  Google Scholar 

  64. V. M. Krasnov, A. Yurgens, D. Winkler, P. Delsing, and T. Claeson, Evidence for coexistence of the superconducting gap and the pseudogap in Bi-2212 from intrinsic tunneling spectroscopy, Phys. Rev. Lett., 2000, 84: 5860

    ADS  Google Scholar 

  65. M. Kugler, O. Fischer, Ch. Renner, S. Ono, and Y. Ando, Scanning tunneling spectroscopy of Bi2Sr2CuO6+δ : New evidence for the common origin of the pseudogap and superconductivity, Phys. Rev. Lett., 2001, 86(21): 4911

    ADS  Google Scholar 

  66. J. W. Loram, K. Mirza, J. Cooper, W. Liang, and J. Wade, Electronic specific heat of YBa2Cu3O6+x from 1.8 to 300 K, J. Superondutivity, 1994, 7(1): 243

    ADS  Google Scholar 

  67. G. V. M. Williams, E. M. Haines, and J. L. Tallon, Pair breaking in the presence of a normal-state pseudogap in high-T c cuprates, Phys. Rev. B, 1998, 57: 146

    ADS  Google Scholar 

  68. D. Walker, A. P. Mackenzie, and J. R. Cooper, Transport properties of zinc-doped YBa2Cu3O7−δ thin films, Phys. Rev. B, 1995, 51: 15653(R)

    ADS  Google Scholar 

  69. T. Graf, J. M. Lawrene, M. F. Hundley, J. D. Thompson, A. Lacerda, E. Haanappel, M. S. Torikahili, Z. Fisk, and P. C. Canfield, Resistivity, magnetization, and specific heat of YbAgCu4 in high magnetic fields, Phys. Rev. B, 1995, 51: 15053

    ADS  Google Scholar 

  70. Y. F. Yan, P. Matl, J. M. Harris, and N. P. Ong, Negative magnetoresistance in the c-axis resistivity of Bi2Sr2CaCu2O8+δ and YBa2Cu3O6+x , Phys. Rev. B, 1995, 52: R751(R)

    ADS  Google Scholar 

  71. G. Williams, J. L. Tallon, R. Dupree, and R. Michalak, Transport and NMR studies of the effect of Ni substitution on superconductivity and the normal-state pseudogap in YBa2Cu4O8, Phys. Rev. B, 1996, 54: 9532

    ADS  Google Scholar 

  72. G. Williams, J. L. Tallon, E. M. Haines, R. Michalak, and R. Dupree, NMR evidence for a d-wave normal-state pseudogap, Phys. Rev. Lett., 1997, 78: 721

    ADS  Google Scholar 

  73. K. Magishi, Y. Kituoka, G.-Q. Zheng, K. Asayama, T. Kondo, Y. Shimakawa, T. Manako, and Y. Kubo, Spin-gap behavior in underdoped TlSr2(Lu0.7Ca0.3)Cu2Oy: 63Cu and 205Tl NMR studies, Phys. Rev. B, 1996, 54: 3070

    ADS  Google Scholar 

  74. A. Goto, H. Yasuoka, K. Otzschi, and Y. Ueda, Phase diagram for the spin pseudogap in LaBa2Cu3Oy studied by NMR, Phys. Rev. B, 1997, 55: 12736

    ADS  Google Scholar 

  75. J. Bobroff, H. Alloul, P. Mendels, V. Viallet, J.-F. Marucco, and D. Colson, 17O NMR evidence for a pseudogap in the monolayer HgBa2CuO4+δ , Phys. Rev. Lett., 1997, 78: 3757

    ADS  Google Scholar 

  76. K. Ishida, K. Yoshida, T. Mito, Y. Tokumaga, Y. Kitaoka, K. Asayama, Y. Nakayama, J. Shimoyama, and K. Kishio, Pseudogap behavior in single-crystal Bi2Sr2CaCu2O8+δ probed by Cu NMR, Phys. Rev. B, 1998, 58: R5960(R)

    ADS  Google Scholar 

  77. A. V. Puchkov, D. N. Basov, and T. Timusk, The pseudogap state in high-T c superconductors: An infrared study, J. Phys.: Condens. Matter, 1996, 8(48): 10049

    ADS  Google Scholar 

  78. D. N. Basov, R. Liang, B. Dabrowski, D. A. Bonn, W. N. Hardy, and T. Timusk, Pseudogap and charge dynamics in CuO2 planes in YBCO, Phys. Rev. Lett., 1996, 77: 4090

    ADS  Google Scholar 

  79. D. Basov, C. Homes, E. Singley, M. Strongin, T. Timusk, G. Blumberg, and D. van der Marel, Unconventional energetics of the pseudogap state and superconducting state in high-T c cuprates, Phys. Rev. B, 2001, 63: 134514

    ADS  Google Scholar 

  80. J. M. Tranquada, P. M. Gehring, G. Shirane, S. Shamoto, and M. Sato, Neutron-scattering study of the dynamical spin susceptibility in YBa2Cu3O6.6, Phys. Rev. B, 1992, 46: 5561

    ADS  Google Scholar 

  81. P. C. Dai, H. A. Mook, S. M. Hayden, and F. Dogan, Resonance as a measure of pairing correlations in the high-T c superconductor YBa2Cu3O6.6, Nature, 2000, 406: 965

    ADS  Google Scholar 

  82. B. Lake, G. Aeppli, T. E. Mason, A. Schroeder, D. F. Mc- Morrow, K. Lefmann, M. Isshiki, M. Nohara, H. Takagi, and S. M. Hayden, Spin gap and magnetic coherence in a clean high-temperature superconductor, Nature, 1999, 400: 43

    ADS  Google Scholar 

  83. G. Ruani and P. Ricci, Transitions at T > T c in underdoped crystals of YBa2Cu3O7−x observed by resonant Raman scattering, Phys. Rev. B, 1997, 55: 93

    ADS  Google Scholar 

  84. X. K. Chen, J. G. Nacini, K. C. Hewitt, J. C. Irwin, R. Liang, and W. N. Hardy, Electronic Raman scattering in underdoped YBa2Cu3O6.5, Phys. Rev. B, 1997, 56: R513(R)

    ADS  Google Scholar 

  85. R. Nemetschek, M. Opel, C. Hoffmann, P. F. Muller, R. Hackl, H. Berger, L. Forro, A. Er, and E. Walker, Pseudogap and superconducting gap in the electronic Raman spectra of underdoped cuprates, Phys. Rev. Lett., 1997, 78: 4837

    ADS  Google Scholar 

  86. J. W. Quilty, H. J. Trodahl, and D. M. Pooke, Electronic Raman scattering from Bi2Sr2CaCu2O8+δ : Doping dependence of the pseudogap and anomalous 600 cm−1 peak, Phys. Rev. B, 1998, 57: R11097

    ADS  Google Scholar 

  87. Z. A. Xu, N. Ong, Y. Want, T. Kakeshita, and S. Uchida, Vortex-like excitations and the onset of superconducting phase fluctuation in underdoped La2−x SrxCuO4, Nature, 2000, 406: 486

    ADS  Google Scholar 

  88. Y. Wang, Z. A. Xu, T. Kakeshita, S. Uchida, and N. P. Ong, Onset of the vortexlike Nernst signal above T c in La2−x SrxCuO4 and Bi2Sr2−y LayCuO6, Phys. Rev. B, 2001, 64: 224519

    ADS  Google Scholar 

  89. Y. Y. Wang, N. P. Ong, Z. A. Xu, T. Kakeshita, S. Uchida, D. Bonn, R. Liang, and W. Hardy, High field phase diagram of cuprates derived from the Nernst effect, Phys. Rev. Lett., 2002, 88: 257003

    ADS  Google Scholar 

  90. S. Tan and K. Levin, Nernst effect and anomalous transport in cuprates: A preformed-pair alternative to the vortex scenario, Phys. Rev. B, 2004, 69(6): 064510

    ADS  Google Scholar 

  91. A. G. Loeser, Z. X. Shen, D. S. Dessau, D. S. Marshall, C. H. Park, P. Fournier, and A. Kapitulnik, Excitation gap in the normal state of underdoped Bi2Sr2CaCu2O8+δ , Science, 1996, 273(5273): 325

    ADS  Google Scholar 

  92. A. Kanigel, U. Chatterjee, M. Randeria, M. R. Norman, G. Koren, K. Kadowaki, and J. C. Campuzano, Evidence for pairing above the transition temperature of cuprate superconductors from the electronic dispersion in the pseudogap phase, Phys. Rev. Lett., 2008, 101(13): 137002

    ADS  Google Scholar 

  93. For simplicity, here we do not discuss electron doping, which is rather similar. Further information can be found in Ref. [7].

  94. S. Chakravarty, R. B. Laughlin, D. K. Morr, and C. Nayak, Hidden order in the cuprates, Phys. Rev. B, 2001, 63(9): 094503

    ADS  Google Scholar 

  95. P. A. Lee, High T c superconductors as doped Mott insulators: Fluctuating current and spin chirality, Physica C, 2000, 341–348: 63

    Google Scholar 

  96. P. A. Lee and X.-G. Wen, Vortex structure in underdoped cuprates, Phys. Rev. B, 2001, 63(22): 224517

    ADS  Google Scholar 

  97. C. Honerkamp and P. A. Lee, Staggered flux fluctuations and the quasiparticle scattering rate in the SU(2) gauge theory of the t-J model, Phys. Rev. Lett., 2003, 90(24): 246402

    ADS  Google Scholar 

  98. C. M. Varma, Non-Fermi-liquid states and pairing instability of a general model of copper oxide metals, Phys. Rev. B, 1997, 55(21): 14554

    ADS  Google Scholar 

  99. C. M. Varma, Theory of the pseudogap state of the cuprates, Phys. Rev. B, 2006, 73(15): 155113

    ADS  Google Scholar 

  100. J. W. Loram, K. A. Mirza, J. R. Cooper, and J. L. Tallon, Specific heat evidence on the normal state pseudogap, J. Phys. Chem. Solids, 1998, 59(10–12): 2091

    ADS  Google Scholar 

  101. J. L. Tallon and J. W. Loram, The doping dependence of T* — What is the real high-T c phase diagram? Physica C, 2001, 349(1–2): 53

    ADS  Google Scholar 

  102. Q. J. Chen, K. Levin, and I. Kosztin, Superconducting phase coherence in the presence of a pseudogap: Relation to specific heat, tunneling, and vortex core spectroscopies, Phys. Rev. B, 2001, 63(18): 184519

    ADS  Google Scholar 

  103. P. W. Anderson, The resonating valence bond state in La2CuO4 and superconductivity, Science, 1987, 235(4793): 1196

    ADS  Google Scholar 

  104. P. W. Anderson, P. A. Lee, M. Randeria, T. M. Rie, N. Trivedi, and F. C. Zhang, The physics behind high-temperature superconducting cuprates: The “plain vanilla” version of RVB, J. Phys.: Condens. Matter, 2004, 16(24): R755

    ADS  Google Scholar 

  105. N. Nagaosa and P. A. Lee, Ginzburg-Landau theory of the spin-charge-separated system, Phys. Rev. B, 1992, 45: 966

    ADS  Google Scholar 

  106. For a review of spin-harge separation, see: P. A. Lee, Pseudogaps in underdoped cuprates, Physica C, 1999, 317–318: 194

    Google Scholar 

  107. Y. J. Uemura, G. M. Luke, B. J. Sternlieb, J. H. Brewer, J. F. Carolan, et al., Universal Correlations between T c and n s/m* (carrier density over effective mass) in high-T c cuprate superconductors, Phys. Rev. Lett., 1989, 62: 2317

    ADS  Google Scholar 

  108. Y. J. Uemura, Bose-Einstein to BCS crossover picture for high-T c cuprates, Physica C, 1997, 282–287: 194

    Google Scholar 

  109. V. Mishra, U. Chatterjee, J. C. Campuzano, and M. R. Norman, Effect of the pseudogap on the transition temperature in the cuprates and implications for its origin, Nat. Phys., 2014, 10(5): 357

    Google Scholar 

  110. V. J. Emery and S. A. Kivelson, Importance of phase fluctuations in superconductors with small superfluid density, Nature, 1995, 374: 434

    ADS  Google Scholar 

  111. M. Franz, Z. B. Tesanovic, and O. Vafek, QED3 theory of pairing pseudogap in cuprates: From d-wave superconductor to antiferromagnet via “algebraic” Fermi liquid, Phys. Rev. B, 2002, 66: 054535

    ADS  Google Scholar 

  112. I. Ussishkin, S. L. Sondhi, and D. A. Huse, Gaussian superconducting fluctuations, thermal transport, and the Nernst effect, Phys. Rev. Lett., 2002, 89(28): 287001

    ADS  Google Scholar 

  113. J. N. Milstein, S. J. J. M. F. Kokkelmans, and M. J. Holland, Resonance theory of the crossover from Bardeen-Cooper-Schrieffer superfluidity to Bose-Einstein condensation in a dilute Fermi gas, Phys. Rev. A, 2002, 66(4): 043604

    ADS  Google Scholar 

  114. Y. Ohashi and A. Griffin, BCS-BEC crossover in a gas of Fermi atoms with a Feshbach resonance, Phys. Rev. Lett., 2002, 89(13): 130402

    ADS  Google Scholar 

  115. N. Andrenacci, P. Pieri, and G. C. Strinati, Evolution from BCS superconductivity to Bose-Einstein condensation: Current correlation function in the broken-symmetry phase, Phys. Rev. B, 2003, 68: 144507

    ADS  Google Scholar 

  116. A. Perali, P. Pieri, L. Pisani, and G. C. Strinati, BCS-BEC crossover at finite temperature for superfluid trapped Fermi atoms, Phys. Rev. Lett., 2004, 92(22): 220404

    ADS  Google Scholar 

  117. H. Hu, P. D. Drummond, and X. J. Liu, Universal thermodynamics of strongly interacting Fermi gases, Nat. Phys., 2007, 3(7): 469

    Google Scholar 

  118. K. Levin, Q. J. Chen, Y. He, and C.-C. Chien, Comparison of different pairing fluctuation approaches to BCS-BEC crossover, Ann. Phys., 2010, 325(2): 233

    MATH  ADS  Google Scholar 

  119. N. E. Bickers, D. J. Scalapino, and S. R. White, Conserving approximations for strongly correlated electron systems: Bethe-Salpeter equation and dynamics for the two-dimensional hubbard model, Phys. Rev. Lett., 1989, 62: 961

    ADS  Google Scholar 

  120. N. E. Bickers and D. J. Scalapino, Conserving approximations for strongly fluctuating electron systems (I): Formalism and calculational approach, Ann. Phys., 1989, 193: 206

    ADS  Google Scholar 

  121. R. Haussmann, W. Rantner, S. Cerrito, and W. Zwerger, Thermodynamics of the BCS-BEC crossover, Phys. Rev. A, 2007, 75(2): 023610

    ADS  Google Scholar 

  122. Y. O. R. Watanabe and S. Tsuchiya, Superfluid density of states and pseudogap phenomenon in the BCS-BEC crossover regime of a superfluid Fermi gas, Phys. Rev. A, 2010, 82: 043630

    ADS  Google Scholar 

  123. P. Magierski, G. Wlazöwski, A. Bulgac, and J. E. Drut, Finite-temperature pairing gap of a unitary Fermi gas by quantum Monte Carlo calculations, Phys. Rev. Lett., 2009, 103(21): 210403

    ADS  Google Scholar 

  124. P. Pieri, A. Perali, G. C. Strinati, S. Riedl, M. J. Wright, A. Altmeyer, C. Kohstall, E. R. S. Guajardo, J. H. Denschlag, and R. Grimm, Pairing-gap, pseudogap, and no-gap phases in the radio-frequency spectra of a trapped unitary 6Li gas, Phys. Rev. A, 2011, 84: 011608(R)

    ADS  Google Scholar 

  125. L. P. Kadanoff and P. C. Martin, Theory of many-particle systems (II): Superconductivity, Phys. Rev., 1961, 124(3): 670

    MathSciNet  MATH  ADS  Google Scholar 

  126. J. Stajic, J. N. Milstein, Q. J. Chen, M. L. Chiofalo, M. J. Holland, and K. Levin, Nature of superfluidity in ultracold Fermi gases near Feshbach resonances, Phys. Rev. A, 2004, 69(6): 063610

    ADS  Google Scholar 

  127. While a general interaction V (kk′) may not be separable, it can however be de composed into different channels as V(kk′) = Σ l φ l k Σ l φ l k , where φ lk represents s-, p-, d-wave channels, etc. In most cases, only one channel dominates the superfluid order so that we may neglect other channels. In this way, the use of a separable potential is justified.

  128. S. J. J. M. F. Kokkelmans, J. N. Milstein, M. L. Chiofalo, R. Walser, and M. J. Holland, Resonance superfluidity: Renormalization of resonance scattering theory, Phys. Rev. A, 2002, 65(5): 053617

    ADS  Google Scholar 

  129. Here we will mainly discuss s-wave short range contact potential for atomic Fermi gases. At present, p-wave superfluids are not yet available experimentally in atomic Fermi gases.

  130. H. Guo, C.-C. Chien, Q. J. Chen, Y. He, and K. Levin, Finite-temperature behavior of an interspecies fermionic superfluid with population imbalance, Phys. Rev. A, 2009, 80: 011601(R)

    ADS  Google Scholar 

  131. J. B. Wang, Y. M. Che, L. F. Zhang, and Q. J. Chen, Searching for the elusive exotic Fulde-Ferrell-Larkin-Ovchinnikov states in Fermi-Fermi mixtures of ultracold quantum gases, arXiv: 1404.5696, 2014

    Google Scholar 

  132. C.-C. Chien, Q. J. Chen, Y. He, and K. Levin, Intermediatetemperature superfluidity in an atomic Fermi gas with population imbalance, Phys. Rev. Lett., 2006, 97(9): 090402

    ADS  Google Scholar 

  133. C.-C. Chien, Q. J. Chen, Y. He, and K. Levin, Superfluid phase diagrams of trapped Fermi gases with population imbalance, Phys. Rev. Lett., 2007, 98(11): 110404

    ADS  Google Scholar 

  134. Q. J. Chen, Y. He, C.-C. Chien, and K. Levin, Theory of superfluids with population imbalance: Finite-temperature and BCS-BEC crossover effects, Phys. Rev. B, 2007, 75(1): 014521

    ADS  Google Scholar 

  135. J. B. Wang, H. Guo, and Q. J. Chen, Exotic phase separation and phase diagrams of a Fermi-Fermi mixture in a trap at finite temperature, Phys. Rev. A, 2013, 87: 041601(R)

    ADS  Google Scholar 

  136. K. M. O’Hara, S. L. Hemmer, M. E. Gehm, S. R. Granade, and J. E. Thomas, Observation of a strongly interacting degenerate Fermi gas of atoms, Science, 2002, 298(5601): 2179

    ADS  Google Scholar 

  137. T. Bourdel, L. Khaykovich, J. Cubizolles, J. Zhang, F. Chevy, M. Teichmann, L. Tarruell, S. J. Kokkelmans, and C. Salomon, Experimental study of the BEC-BCS crossover region in lithium 6, Phys. Rev. Lett., 2004, 93(5): 050401

    ADS  Google Scholar 

  138. J. Carlson, S. Y. Chang, V. R. Pandharipande, and K. E. Schmidt, Superfluid Fermi gases with large scattering length, Phys. Rev. Lett., 2003, 91(5): 050401

    ADS  Google Scholar 

  139. I. Kosztin, Q. J. Chen, Y.-J. Kao, and K. Levin, Pair excitations, collective modes, and gauge invariance in the BCS-Bose-Einstein crossover scenario, Phys. Rev. B, 2000, 61(17): 11662

    ADS  Google Scholar 

  140. Q. J. Chen, Y. He, C.-C. Chien, and K. Levin, Stability conditions and phase diagrams for two-component Fermi gases with population imbalance, Phys. Rev. A, 2006, 74(6): 063603

    ADS  Google Scholar 

  141. In fact, the parameter γ can be taken from experiment, as has been done in Ref. [102], where one can find more details.

  142. P. Pieri, L. Pisani, and G. C. Strinati, BCS-BEC crossover at finite temperature in the broken-symmetry phase, Phys. Rev. B, 2004, 70(9): 094508

    ADS  Google Scholar 

  143. N. Fukushima, Y. Ohashi, E. Taylor, and A. Griffin, Superfluid density and condensate fraction in the BCS-BEC crossover regime at finite temperatures, Phys. Rev. A, 2007, 75(3): 033609

    ADS  Google Scholar 

  144. I. Kosztin and A. J. Leggett, Nonlocal effects on the magnetic penetration depth in d-wave superconductors, Phys. Rev. Lett., 1997, 79(1): 135

    ADS  Google Scholar 

  145. S. Hufner, M. A. Hossain, A. Damaselli, and G. Sawatzky, Two gaps make a high-temperature superconductor? Rep. Prog. Phys., 2008, 71(6): 062501

    ADS  Google Scholar 

  146. G. Baskaran, Z. Zou, and P. W. Anderson, The resonating valence bond state and high-T c superconductivity -A mean field theory, Solid State Commun., 1987, 63(11): 973

    ADS  Google Scholar 

  147. N. Miyakawa, J. Zasadzinski, L. Ozyuzer, P. Guptasarma, D. Hinks, C. Kendziora, and K. Gray, Predominantly superconducting origin of large energy gaps in underdoped Bi2Sr2CaCu2O8+δ from tunneling spectroscopy, Phys. Rev. Lett., 1999, 83(5): 1018

    ADS  Google Scholar 

  148. T.-L. Ho, Universal thermodynamics of degenerate quantum gases in the unitarity limit, Phys. Rev. Lett., 2004, 92(9): 090402

    ADS  Google Scholar 

  149. M. L. Chiofalo, S. J. J. M. F. Kokkelmans, J. N. Milstein, and M. J. Holland, Signatures of resonance superfluidity in a quantum Fermi gas, Phys. Rev. Lett., 2002, 88(9): 090402

    ADS  Google Scholar 

  150. Note here that the definition for n c and n p differ from that in Ref. [156] by a factor of 2.

  151. G. E. Astrakharchik, J. Boronat, J. Casulleras, and S. Giorgini, Momentum distribution and condensate fraction of a fermion gas in the BCS-BEC Crossover, Phys. Rev. Lett., 2005, 95: 230405 (Their result seems to suggest a tendency of decrease in the condensate fraction with an increasing particle number used for simulation.)

    ADS  Google Scholar 

  152. The curves in Fig. 19 were calculated using a two-channel model. Nevertheless, for wide Feshbach resonances such as in 6Li and 40K, the closed-channel fraction is very small [191, 192] so that the quantitative difference in the entropy s(r) between the two-channel and one-channel model is negligible.

  153. Q. J. Chen, J. Stajic, and K. Levin, Thermodynamics of interacting fermions in atomic traps, Phys. Rev. Lett., 2005, 95(26): 260405

    ADS  Google Scholar 

  154. Q. J. Chen, C. A. Regal, M. Greiner, D. S. Jin, and K. Levin, Understanding the superfluid phase diagram in trapped Fermi gases, Phys. Rev. A, 2006, 73: 041601(R)

    ADS  Google Scholar 

  155. Note that the experimental data cannot be measuring N c = N as shown in Fig. 18, since at 1/(k F a) = −1,N c = N is far below the experimental threshold of detection.

  156. J. Stajic, Q. J. Chen, and K. Levin, Density profiles of strongly interacting trapped Fermi gases, Phys. Rev. Lett., 2005, 94: 060401

    ADS  Google Scholar 

  157. While one may argue that the kink, if it exists, may be smoothed out by the ∫ dydz integration, we note that as of the time of this writing, no kink behavior has ever been reported in 3D density profiles obtained via an inverse Abel transformation of experimental data.

  158. Q. J. Chen, C. A. Regal, D. S. Jin, and K. Levin, Finitetemperature momentum distribution of a trapped Fermi gas, Phys. Rev. A, 2006, 74: 011601(R)

    ADS  Google Scholar 

  159. Q. J. Chen, Y. He, C.-C. Chien, and K. Levin, Theory of radio frequency spectroscopy experiments in ultracold Fermi gases and their relation to photoemission in the cuprates, Rep. Prog. Phys., 2009, 72(12): 122501

    ADS  Google Scholar 

  160. C. H. Shunk, Y. Shin, A. Schirotzek, M. W. Zwierlein, and W. Ketterle, Determination of the fermion pair size in a resonantly interacting superfluid, Nature, 2008, 454(7205): 739

    ADS  Google Scholar 

  161. C. H. Schunk, Y. Shin, A. Schirotzek, M. W. Zwierlein, and W. Ketterle, Pairing without superfluidity: The ground state of an imbalanced Fermi mixture, Science, 2007, 316(5826): 867

    ADS  Google Scholar 

  162. Z. Yu and G. Baym, Spin-correlation functions in ultracold paired atomic-fermion systems: Sum rules, self-consistent approximations, and mean fields, Phys. Rev. A, 2006, 73(6): 063601

    ADS  Google Scholar 

  163. G. Baym, C. J. Pethick, Z. H. Yu, and M. W. Zwierlein, Coherence and clock shifts in ultracold Fermi gases with resonant interactions, Phys. Rev. Lett., 2007, 99(19): 190407

    ADS  Google Scholar 

  164. M. Punk and W. Zwerger, Theory of RF-spectroscopy of strongly interacting fermions, Phys. Rev. Lett., 2007, 99(17): 170404

    ADS  Google Scholar 

  165. A. Perali, P. Pieri, and G. C. Strinati, Competition between final-state and pairing-gap effects in the radio-frequency spectra of ultracold Fermi atoms, Phys. Rev. Lett., 2008, 100(1): 010402

    ADS  Google Scholar 

  166. S. Basu and E. J. Müller, Final-state effects in the radio frequency spectrum of strongly interacting fermions, Phys. Rev. Lett., 2008, 101(6): 060405

    ADS  Google Scholar 

  167. Y. He, C. C. Chien, Q. J. Chen, and K. Levin, Temperature and final state effects in radio frequency spectroscopy experiments on atomic Fermi gases, Phys. Rev. Lett., 2009, 102(2): 020402

    ADS  Google Scholar 

  168. M. J. H. Ku, A. T. Sommer, L. W. Cheuk, and M. W. Zwierlein, Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas, arXiv: 1110.3309, 2011

    Google Scholar 

  169. E. Burovski, N. Prokof’ev, B. Svistunov, and M. Troyer, Critical temperature and thermodynamics of attractive fermions at unitarity, Phys. Rev. Lett., 2006, 96(16): 160402

    ADS  Google Scholar 

  170. E. Burovski, E. Kozik, N. Prokof’ev, B. Svistunov, and M. Troyer, Critical temperature curve in BEC-BCS crossover, Phys. Rev. Lett., 2008, 101(9): 090402

    ADS  Google Scholar 

  171. O. Goulko and M. Wingate, Thermodynamics of balanced and slightly spin-imbalanced Fermi gases at unitarity, Phys. Rev. A, 2010, 82(5): 053621

    ADS  Google Scholar 

  172. J. Kinnunen, M. Rodríguez, and P. Törmä, Pairing gap and in-gap excitations in trapped fermionic superfluids, Science, 2004, 305(5687): 1131

    ADS  Google Scholar 

  173. Y. He, Q. J. Chen, and K. Levin, Radio-frequency spectroscopy and the pairing gap in trapped Fermi gases, Phys. Rev. A, 2005, 72: 011602(R)

    ADS  Google Scholar 

  174. P. Massignan, G. M. Bruun, and H. T. C. Stoof, Twin peaks in RF spectra of Fermi gases at unitarity, Phys. Rev. A, 2008, 77: 031601(R)

    ADS  Google Scholar 

  175. J. T. Stewart, J. P. Gaebler, and D. S. Jin, Using photoemission spectroscopy to probe a strongly interacting Fermi gas, Nature, 2008, 454(7205): 744

    ADS  Google Scholar 

  176. Q. J. Chen and K. Levin, Momentum resolved radio frequency spectroscopy in trapped fermi gases, Phys. Rev. Lett., 2009, 102(19): 190402

    ADS  Google Scholar 

  177. D. S. Jin, Private communications; D.S. Jin, American Physical Society March Meeting Talk B8.00002, 2009, abstract avail-able at http://meetings.aps.org/link/BAPS.2009.MAR.B8.2

    Google Scholar 

  178. J. P. Gaebler, J. T. Stewart, T. E. Drake, D. S. Jin, A. Perali, P. Pieri, and G. C. Strinati, Observation of pseudogap behaviour in a strongly interacting Fermi gas, Nat. Phys., 2010, 6(8): 569

    Google Scholar 

  179. A. Perali, F. Palestini, P. Pieri, G. C. Strinati, J. T. Stewart, J. P. Gaebler, T. E. Drake, and D. S. Jin, Evolution of the normal state of a strongly interacting Fermi gas from a pseudogap phase to a molecular Bose gas, Phys. Rev. Lett., 2011, 106(6): 060402

    ADS  Google Scholar 

  180. A. Perali, P. Pieri, G. C. Strinati, and C. Castellani, Pseudogap and spectral function from superconducting fluctuations to the bosonic limit, Phys. Rev. B, 2002, 66(2): 024510

    ADS  Google Scholar 

  181. P. Pieri, L. Pisani, and G. C. Strinati, Pairing fluctuation effects on the single-particle spectra for the superconducting state, Phys. Rev. Lett., 2004, 92(11): 110401

    ADS  Google Scholar 

  182. Y. Shin, M. W. Zwierlein, C. H. Schunck, A. Schirotzek, and W. Ketterle, Observation of phase separation in a strongly interacting imbalanced Fermi gas, Phys. Rev. Lett., 2006, 97(3): 030401

    ADS  Google Scholar 

  183. S. Nascimbène, N. Navon, K. Jiang, F. Chevy, and C. Salomon, Exploring the thermodynamics of a universal Fermi gas, Nature, 2010, 463(7284): 1057

    ADS  Google Scholar 

  184. S. Nascimbène, N. Navon, S. Pilati, F. Chevy, S. Giorgini, A. Georges, and C. Salomon, Fermi-liquid behavior of the normal phase of a strongly interacting gas of cold atoms, Phys. Rev. Lett., 2011, 106(21): 215303

    ADS  Google Scholar 

  185. L. P. Gor’kov and T. K. Melik-Barkhudarov, Contribution to the theory of superfluidity in an imperfect fermi gas, Sov. Phys. JETP, 1961, 13: 1018

    MATH  Google Scholar 

  186. H. Heiselberg, C. J. Pethick, H. Smith, and L. Viverit, Influence of induced interactions on the superfluid transition in dilute Fermi gases, Phys. Rev. Lett., 2000, 85(12): 2418

    ADS  Google Scholar 

  187. D. H. Kim, P. Törmä, and J.-P. Martikainen, Induced interactions for ultracold Fermi gases in optical lattices, Phys. Rev. Lett., 2009, 102(24): 245301

    ADS  Google Scholar 

  188. J. P. Martikainen, J. J. Kinnunen, P. Törmä, and C. J. Pethick, Induced interactions and the superfluid transition temperature in a three-component Fermi gas, Phys. Rev. Lett., 2009, 103(26): 260403

    ADS  Google Scholar 

  189. Z. Q. Yu, K. Huang, and L. Yin, Induced interaction in a Fermi gas with a BEC-BCS crossover, Phys. Rev. A, 2009, 79(5): 053636

    ADS  Google Scholar 

  190. Q. J. Chen, Effect of the particle-hole channel on BCS-Bose-Einstein condensation crossover in atomic Fermi gases, arXiv: 1109.2307, 2011

    Google Scholar 

  191. Q. J. Chen and K. Levin, Population of closed-channel molecules in trapped Fermi gases with broad Feshbach resonances, Phys. Rev. Lett., 2005, 95(26): 260406

    ADS  Google Scholar 

  192. G. B. Partridge, K. E. Strecker, R. I. Kamar, M. W. Jack, and R. G. Hulet, Molecular probe of pairing in the BEC-BCS crossover, Phys. Rev. Lett., 2005, 95(2): 020404

    ADS  Google Scholar 

  193. H. Guo, C.-C. Chien, and K. Levin, Establishing the presence of coherence in atomic Fermi superfluids: Spin-flip and spin-preserving Bragg scattering at finite temperatures, Phys. Rev. Lett., 2010, 105(12): 120401

    ADS  Google Scholar 

  194. M. G. Lingham, K. Fenech, S. Hoinka, and C. J. Vale, Local observation of pair condensation in a Fermi gas at unitarity, Phys. Rev. Lett., 2014, 112(10): 100404

    ADS  Google Scholar 

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Chen, Q., Wang, J. Pseudogap phenomena in ultracold atomic Fermi gases. Front. Phys. 9, 539–570 (2014). https://doi.org/10.1007/s11467-014-0448-7

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