Thermodynamics of the BCS-BEC crossover

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 75, Issue 2, 2007, Pages

  Haussmann, R ^a   Rantner, W ^b   Cerrito, S ^b,c   Zwerger, W ^c  

^a UNIVERSITY OF KONSTANZ   (Germany)

^b UNIVERSITY OF INNSBRUCK   (Austria)

^c TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ATOMIC PHYSICS; ENTROPY; EQUATIONS OF STATE; GREEN'S FUNCTION; INTEGRAL EQUATIONS; NUMERICAL ANALYSIS;

ARBITRARY COUPLING; BCS-BEC CROSSOVER; SELF-CONSISTENT THEORY;

THERMODYNAMICS;

EID: 33846943323     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.75.023610     Document Type: Article

References (85)

1. M. Greiner, C. A. Regal, and D. S. Jin, Nature (London) NATUAS 0028-0836 10.1038/nature02199 426, 537 (2003).
2. S. Jochim, M. Bartenstein, A. Altmeyer, G. Hendl, S. Riedl, C. Chin, J. Hecker Denschlag, and R. Grimm, Science SCIEAS 0036-8075 10.1126/science.1093280 302, 2101 (2003).
3. M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, S. Gupta, Z. Hadzibabic, and W. Ketterle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.250401 91, 250401 (2003).
4. C. A. Regal, M. Greiner, and D. S. Jin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.040403 92, 040403 (2004);
5. M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, C. Chin, J. Hecker Denschlag, and R. Grimm, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 92.120401 92, 120401 (2004);
6. M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, A. J. Kerman, and W. Ketterle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 92.120403 92, 120403 (2004);
7. J. Kinast, S. L. Hemmer, M. E. Gehm, A. Turlapov, and J. E. Thomas, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.150402 92, 150402 (2004);
8. T. Bourdel, L. Khaykovich, J. Cubizolles, J. Zhang, F. Chevy, M. Teichmann, L. Tarruell, S. J. J. M. F. Kokkelmans, and C. Salomon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.050401 93, 050401 (2004).
9. C. Chin, M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, J. Hecker Denschlag, and R. Grimm, Science SCIEAS 0036-8075 305, 1128 (2004).
10. M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek, C. H. Schunk, and W. Ketterle, Nature (London) NATUAS 0028-0836 10.1038/nature03858 435, 1047 (2005).
11. For a recent discussion of the Feshbach resonance physics relevant to low-energy scattering of alkali-metal atoms see N. Nygaard, B. I. Schneider, and P. S. Julienne, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.042705 73, 042705 (2006).
12. The unitarity limit is almost realized in neutron stars, where the scattering length is nearly an order of magnitude larger than the mean interparticle separation. See H. Heiselberg, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.043606 63, 043606 (2001).
13. G. A. Baker, Jr., Phys. Rev. C PRVCAN 0556-2813 10.1103/PhysRevC.60. 054311 60, 054311 (1999).
14. G. M. Bruun, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.053602 70, 053602 (2004).
15. R. B. Diener and T. L. Ho, cond-mat/0405174.
16. S. Simonucci, P. Pieri, and G. C. Strinati, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2004-10412-2 69, 713 (2005).
17. M. H. Szymanska, K. Goral, T. Köhler, and K. Burnett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.013610 72, 013610 (2005).
18. T.-L. Ho, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.090402 92, 090402 (2004).
19. P. Nikolić and Subir Sachdev, cond-mat/0609106.
20. J. Carlson, S.-Y. Chang, V. R. Pandharipande, and K. E. Schmidt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.050401 91, 050401 (2003);
21. S.-Y. Chang, V. R. Pandharipande, J. Carlson, and K. E. Schmidt, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.043602 70, 043602 (2004).
22. G. E. Astrakharchik, J. Boronat, J. Casulleras, and S. Giorgini, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.200404 93, 200404 (2004).
23. G. E. Astrakharchik, J. Boronat, J. Casulleras, and S. Giorgini, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.230405 95, 230405 (2005).
24. In the case of a p -wave Feshbach resonance the crossover is associated with a quantum phase transition at zero temperature whose critical point is determined by the vanishing of the chemical potential. See, e.g., F. R. Klinkhamer and G. E. Volovik, JETP Lett. JTPLA2 0021-3640 10.1134/1.1825119 80, 343 (2004) and
25. V. Gurarie, L. Radzihovsky, and A. V. Andreev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.230403 94, 230403 (2005).
26. D. S. Petrov, C. Salomon, and G. V. Shlyapnikov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.090404 93, 090404 (2004).
27. D. M. Eagles, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.186.456 186, 456 (1969).
28. A. J. Leggett, J. Phys. (Paris), Colloq. JPQCAK 0449-1947 41, C7 (1980).
29. Recently, G. Ortiz and J. Dukelsky, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.043611 72, 043611 (2005), have used the exactly solvable Richardson model to describe the BCS-BEC crossover at zero temperature. The model, however, does not contain the interaction between pairs and thus misses already the leading corrections to the ideal BCS and BEC limits.
30. Y. Nishida and D. T. Son, cond-mat/0607835;
31. Y. Nishida and D. T. Son, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.050403 97, 050403 (2006).
32. Z. Nussinov and S. Nussinov, cond-mat/0410597.
33. Y. Nishida, cond-mat/0608321.
34. A. Bulgac, J. E. Drut, and P. Magierski, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.090404 96, 090404 (2006).
35. E. Burovski, N. Prokof'ev, B. Svistunov, and M. Troyer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.160402 96, 160402 (2006).
36. R. Haussmann, Z. Phys. B: Condens. Matter ZPCMDN 0722-3277 10.1007/BF01344058 91, 291 (1993).
37. R. Haussmann, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.49.12975 49, 12975 (1994).
38. R. Haussmann, Self-consistent Quantum-field Theory and Bosonization for Strongly Correlated Electron Systems, Lecture Notes in Physics, Vol. 56 (Springer, Berlin, 1999).
39. L. D. Carr, G. V. Shlyapnikov, and Y. Castin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.150404 92, 150404 (2004).
40. M. Holland, S. J. J. M. F. Kokkelmans, M. L. Chiofalo, and R. Walser, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.120406 87, 120406 (2001);
41. J. N. Milstein, S. J. J. M. F. Kokkelmans, and M. J. Holland, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.043604 66, 043604 (2002).
42. Y. Ohashi and A. Griffin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.130402 89, 130402 (2002).
43. J. M. Luttinger and J. C. Ward, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.118.1417 118, 1417 (1960).
44. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-particle Systems (McGraw-Hill, New York, 1971).
45. P. Pieri and G. C. Strinati, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.61.15370 61, 15370 (2000).
46. C. De Dominicis and P. C. Martin, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704062 5, 14 (1964);
47. C. De Dominicis and P. C. Martin, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704064 5, 31 (1964).
48. D. J. Thouless, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(60) 90122-6 10, 553 (1960).
49. P. C. Hohenberg and P. C. Martin, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(65)90280-0 34, 291 (1965).
50. G. C. Strinati and P. Pieri, Europhys. Lett. EULEEJ 0295-5075 71, 359 (2005).
51. T. Kita, J. Phys. Soc. Jpn. JUPSAU 0031-9015 75, 044603 (2006).
52. N. M. Hugenholtz and D. Pines, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.116.489 116, 489 (1959).
53. L. Reatto and J. P. Straley, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.183.321 183, 321 (1969).
54. N. Shohno, Prog. Theor. Phys. PTPKAV 0033-068X 31, 553 (1964);
55. N. Shohno, Prog. Theor. Phys. PTPKAV 0033-068X 32, 370 (1964).
56. C. A. R. Sá de Melo, M. Randeria, and J. R. Engelbrecht, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.3202 71, 3202 (1993).
57. R. Haussmann (unpublished).
58. L. P. Gorkov and T. K. Melik-Barkhudarov, Sov. Phys. JETP SPHJAR 0038-5646 13, 1018 (1961).
59. H. Heiselberg, C. J. Pethick, H. Smith, and L. Viverit, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.2418 85, 2418 (2000).
60. D. S. Petrov, C. Salomon, and G. V. Shlyapnikov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.012708 71, 012708 (2005).
61. G. Baym, J.-P. Blaizot, M. Holzmann, F. Laloë, and D. Vautherin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.1703 83, 1703 (1999);
62. G. Baym, J.-P. Blaizot, M. Holzmann, F. Laloë, and D. Vautherin, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/s100510170028 24, 107 (2001);
63. G. Baym, J.-P. Blaizot, and J. Zinn-Justin, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2000-00130-3 49, 150 (2000).
64. P. Arnold and G. D. Moore, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.120401 87, 120401 (2001);
65. P. Arnold and G. D. Moore, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.066113 64, 066113 (2001).
66. V. A. Kashurnikov, N. V. Prokof'ev, and B. V. Svistunov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.120402 87, 120402 (2001).
67. P. Nozières and S. Schmitt-Rink, J. Low Temp. Phys. JLTPAC 0022-2291 10.1007/BF00683774 59, 195 (1985).
68. M. Randeria, in Bose-Einstein Condensation, edited by, A. Griffin, D. W. Snoke, and, S. Stringari, (Cambridge University Press, Cambridge, England, 1995), p. 355.
69. R. A. Ferrell, N. Menyhard, H. Schmidt, F. Schwabl, and P. Szépfalusy, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(68) 90214-5 47, 565 (1968).
70. W. Lenz, Z. Phys. ZEPYAA 0044-3328 10.1007/BF01340138 56, 778 (1929).
71. K. Huang and C. N. Yang, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.105. 767 105, 767 (1957);
72. T. D. Lee and C. N. Yang, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.105.119 105, 1119 (1957).
73. W. Rantner, R. Haussmann, S. Cerrito, and W. Zwerger (unpublished).
74. T. L. Ho and E. J. Mueller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.160404 92, 160404 (2004).
75. M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, C. Chin, J. Hecker Denschlag, and R. Grimm, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 92.120401 92, 120401 (2004).
76. T. Bourdel, L. Khaykovich, J. Cubizolles, J. Zhang, F. Chevy, M. Teichmann, L. Tarruell, S. J. J. M. F. Kokkelmans, and C. Salomon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.050401 93, 050401 (2004).
77. J. Kinast, A. Turlapov, J. Thomas, Q. Chen, J. Stajic, and K. Levin, Science SCIEAS 0036-8075 10.1126/science.1109220 307, 1296 (2005).
78. G. B. Partridge, W. Li, R. I. Kamar, Y. Liao, and R. G. Hulet, Science SCIEAS 0036-8075 10.1126/science.1122876 311, 503 (2006).
79. A. Perali, P. Pieri, and G. C. Strinati, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.100404 93, 100404 (2004).
80. H. Hu, X. J. Liu, and P. D. Drummond, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.023617 73, 023617 (2006).
81. H. Hu, X. J. Liu, and P. D. Drummond, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2006-10023-y 74, 574 (2006).
82. M. Holzmann and G. Baym, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.040402 90, 040402 (2003).
83. N. E. Bickers and D. J. Scalapino, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.8050 46, 8050 (1992).
84. M. W. Zwierlein, A. Schirotzek, C. H. Schunck, and W. Ketterle, Science SCIEAS 0036-8075 10.1126/science.1122318 311, 492 (2006).
85. W. Götze and R. Haussmann, Z. Phys. B: Condens. Matter ZPCMDN 0722-3277 10.1007/BF01312829 72, 403 (1988).