The European Physical Journal B

, Volume 68, Issue 3, pp 401–415 | Cite as

Number of closed-channel molecules in the BEC-BCS crossover

Article

Abstract

Using a two-channel model, we show that the number of closed-channel molecules in a two-component Fermi gas close to a Feshbach resonance is directly related to the derivative of the energy of the gas with respect to the inverse scattering length. We extract this quantity from the fixed-node Monte Carlo equation of state and we compare to the number of closed-channel molecules measured in the Rice experiment with lithium [Partridge et al., Phys. Rev. Lett. 95, 020404 (2005)]. We also discuss the effect of a difference between the trapping potentials seen by a closed-channel molecule and by an open-channel pair of atoms in terms of an effective position-dependent scattering length.

PACS

03.75.Ss Degenerate Fermi gases 67.90.+z Other topics in quantum fluids and solids 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Jochim, M. Bartenstein, A. Altmeyer, G. Hendl, S. Riedl, C. Chin, J. Hecker Denschlag, R. Grimm, Science 302, 2101 (2003)Google Scholar
  2. M. Greiner, C. Regal, D. Jin, Nature, 426, 537 (2003)Google Scholar
  3. M. Zwierlein, C. Stan, C. Schunck, S. Raupach, S. Gupta, Z. Hadzibabic, W. Ketterle, Phys. Rev. Lett. 91, 250401 (2003)Google Scholar
  4. T. Bourdel, L. Khaykovich, J. Cubizolles, J. Zhang, F. Chevy, M. Teichmann, L. Tarruell, S.J.J.M.F. Kokkelmans, C. Salomon, Phys. Rev. Lett. 93, 050401 (2004)Google Scholar
  5. G.B. Partridge, K.E. Strecker, R.I. Kamar, M.W. Jack, R.G. Hulet, Phys. Rev. Lett. 95, 020404 (2005)Google Scholar
  6. K. O’Hara, S. Hemmer, M. Gehm, S. Granade, J. Thomas, Science 298, 2179 (2002)Google Scholar
  7. C. Regal, C. Ticknor, J. Bohn, D. Jin, Nature 424, 47 (2003)Google Scholar
  8. T. Bourdel, J. Cubizolles, L. Khaykovich, K. Magalhaes, S. Kokkelmans, G. Shlyapnikov, C. Salomon, Phys. Rev. Lett. 91, 020402 (2003)Google Scholar
  9. M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, C. Chin, J. Hecker Denschlag, R. Grimm, Phys. Rev. Lett. 92, 120401 (2004)Google Scholar
  10. C. Chin, M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, J. Hecker Denschlag, R. Grimm, Science 305, 1128 (2004)Google Scholar
  11. J.E. Thomas, J. Kinast, A. Turlapov, Phys. Rev. Lett. 95, 120402 (2005)Google Scholar
  12. A. Altmeyer, S. Riedl, C. Kohstall, M.J. Wright, R. Geursen, M. Bartenstein, C. Chin, J. Hecker Denschlag, R. Grimm, Phys. Rev. Lett. 98, 040401 (2007)Google Scholar
  13. M. Zwierlein, J. Abo-Shaeer, A. Schirotzek, C. Schunck, W. Ketterle, Nature 435, 1047 (2005)Google Scholar
  14. J.T. Stewart, J.P. Gaebler, C.A. Regal, D.S. Jin, Phys. Rev. Lett. 97, 220406 (2006)Google Scholar
  15. L. Luo, B. Clancy, J. Joseph, J. Kinast, J.E. Thomas, Phys. Rev. Lett. 98, 080402 (2007)Google Scholar
  16. G.B. Partridge, W. Li, R.I. Kamar, Y. Liao, R.G. Hulet, Science 311, 503 (2006)Google Scholar
  17. Y. Shin, M. Zwierlein, C. Schunck, A. Schirotzek, W. Ketterle, Phys. Rev. Lett. 97, 030401 (2006)Google Scholar
  18. E. Timmermans, P. Tommasini, M. Hussein, A. Kerman, Phys. Rep. 315, 199 (1999)Google Scholar
  19. M. Holland, S.J.J.M.F. Kokkelmans, M.L. Chiofalo, R. Walser, Phys. Rev. Lett. 87, 120406 (2001)Google Scholar
  20. J.N. Milstein, S.J.J.M.F. Kokkelmans, M.J. Holland, Phys. Rev. A 66, 043604 (2002)Google Scholar
  21. T. Köhler, K. Góral, P.S. Julienne, Rev. Mod. Phys. 78, 1311 (2006)Google Scholar
  22. D. Lee, Phys. Rev. B 73, 11511 (2006)Google Scholar
  23. A. Bulgac, J.E. Drut, P. Magierski, Phys. Rev. Lett. 96, 090404 (2006)Google Scholar
  24. E. Burovski, N. Prokof’ev, B. Svistunov, M. Troyer, Phys. Rev. Lett. 96, 160402 (2006)Google Scholar
  25. E. Burovski, N. Prokof’ev, B. Svistunov, M. Troyer, New J. Phys. 8, 153 (2006)Google Scholar
  26. O. Juillet, New J. Phys. 9, 163 (2007)Google Scholar
  27. A. Bulgac, J.E. Drut, P. Magierski, Phys. Rev. A 78, 023625 (2008)Google Scholar
  28. E. Burovski, E. Kozik, N. Prokof’ev, B. Svistunov, M. Troyer, Phys. Rev. Lett. 101, 090402 (2008)Google Scholar
  29. Y. Castin, Lecture notes of the 2003 Les Houches Spring School, Quantum Gases in Low Dimensions, edited by M. Olshanii, H. Perrin, L. Pricoupenko, J. Phys. IV France 116, 89 (2004)Google Scholar
  30. L. Pricoupenko, Y. Castin, J. Phys. A 40, 12863 (2007)Google Scholar
  31. J. Carlson, S.Y. Chang, V.R. Pandharipande, K.E. Schmidt, Phys. Rev. Lett. 91, 050401 (2003)Google Scholar
  32. G.E. Astrakharchik, J. Boronat, J. Casulleras, S. Giorgini, Phys. Rev. Lett. 93, 200404 (2004)Google Scholar
  33. J. Carlson, S. Reddy, Phys. Rev. Lett. 95, 060401 (2005)Google Scholar
  34. C. Lobo, I. Carusotto, S. Giorgini, A. Recati, S. Stringari, Phys. Rev. Lett. 97, 100405 (2006)Google Scholar
  35. C. Lobo, A. Recati, S. Giorgini, S. Stringari, Phys. Rev. Lett. 97, 200403 (2006)Google Scholar
  36. S. Pilati, S. Giorgini, Phys. Rev. Lett. 100, 030401 (2008)Google Scholar
  37. D.S. Petrov, Phys. Rev. Lett. 93, 143201 (2004)Google Scholar
  38. Y. Castin, in Proceedings of the International School of Physics “Enrico Fermi" on Ultra-Cold Fermi gases, edited by M. Inguscio, W. Ketterle, C. Salomon (SIF, Bologna, 2007)Google Scholar
  39. S. Tan, Ann. Phys. 323, 2952 (2008)Google Scholar
  40. S. Tan, Ann. Phys. 323, 2971 (2008)Google Scholar
  41. N.N. Bogoliubov, Lectures on quantum statistics (Gordon and Breach, New York, 1967), Vol. 1Google Scholar
  42. X. Leyronas, R. Combescot, Phys. Rev. Lett. 99, 170402 (2007)Google Scholar
  43. K. Huang, C.N. Yang, Phys. Rev. 105, 767 (1957)Google Scholar
  44. T.D. Lee, C.N. Yang, Phys. Rev. 105, 1119 (1957)Google Scholar
  45. D.S. Petrov, C. Salomon, G.V. Shlyapnikov, Phys. Rev. Lett. 93, 090404 (2004)Google Scholar
  46. I.V. Brodsky, M.Y. Kagan, A.V. Klaptsov, R. Combescot, X. Leyronas, Phys. Rev. A 73, 032724 (2006)Google Scholar
  47. A.A. Abrikosov, I.M. Khalatnikov, Sov. Phys. JETP 6, 888 (1958) [J.E.T.P. (USSR) 33, 1154 (1957)]Google Scholar
  48. V.M. Galitskii, Sov. Phys. JETP 7, 104 (1958), [J.E.T.P. (USSR) 34, 151 (1958)]Google Scholar
  49. L. Pricoupenko, Y. Castin, Phys. Rev. A 69, 051601 (2004)Google Scholar
  50. A. Bulgac, G.F. Bertsch, Phys. Rev. Lett. 94, 070401 (2005)Google Scholar
  51. R. Combescot, X. Leyronas, Phys. Rev. Lett. 93, 138901 (2004)Google Scholar
  52. J. Kinast, A. Turlapov, J.E. Thomas, Phys. Rev. A 70, 051401 (2004)Google Scholar
  53. M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, C. Chin, J. Hecker Denschlag, R. Grimm, Phys. Rev. Lett. 92, 203201 (2004), see also: A. Altmeyer, S. Riedl, C. Kohstall, M.J. Wright, J. Hecker Denschlag, R. Grimm, e-print arXiv:cond-mat/0611285v2 Google Scholar
  54. G.E. Astrakharchik, R. Combescot, X. Leyronas, S. Stringari, Phys. Rev. Lett. 95, 030404 (2005) Google Scholar
  55. M. Urban, Phys. Rev. A 75, 053607 (2007)Google Scholar
  56. M. Bartenstein, A. Altmeyer, S. Riedl, R. Geursen, S. Jochim, C. Chin, J. Hecker Denschlag, R. Grimm, A. Simoni, E. Tiesinga, C.J. Williams, P.S. Julienne, Phys. Rev. Lett. 94, 103201 (2005)Google Scholar
  57. G.M. Falco, H.T.C. Stoof, Phys. Rev. A 71, 063614 (2005)Google Scholar
  58. R. Hulet, private communicationGoogle Scholar
  59. E. Braaten, L. Platter, Phys. Rev. Lett. 100, 205301 (2008)Google Scholar
  60. D.M. Gangardt, G.V. Shlyapnikov, Phys. Rev. Lett. 90, 010401 (2003)Google Scholar
  61. T. Kinoshita, T. Wenger, D.S. Weiss, Phys. Rev. Lett. 95, 190406 (2005)Google Scholar
  62. M. Yasuda, F. Shimizu, Phys. Rev. Lett. 77, 3090 (1996)Google Scholar
  63. M. Schellekens, R. Hoppeler, A. Perrin, J.V. Gomes, D. Boiron, A. Aspect, C.I. Westbrook, Science 310, 648 (2005)Google Scholar
  64. T. Jeltes, J.M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, C.I. Westbrook, Nature 445, 402 (2007)Google Scholar
  65. C. Lobo, S.D. Gensemer, Phys. Rev. A 78, 023618 (2008)Google Scholar
  66. E.H. Lieb, W. Liniger, Phys. Rev. 130, 1605 (1963)Google Scholar
  67. J. Yvon, C. R. Acad. Sci. 246, 2858 (1958)Google Scholar
  68. R. Snider, J. Chem. Phys. 32, 1051 (1960)Google Scholar
  69. K. Huang, Statistical Mechanics (Wiley, New York, 1963)Google Scholar
  70. M. Holzmann, Y. Castin, Eur. Phys. J. D 7, 425 (1999)Google Scholar
  71. A.J. Leggett, Lecture 2 at the international quantum gases workshop (Institut Henri Poincaré, Paris, 2007), www.phys.ens.fr/tildecastin/files_pdf.html Google Scholar
  72. C.A. Regal, M. Greiner, S. Giorgini, M. Holland, D.S. Jin, Phys. Rev. Lett. 95, 250404 (2005)Google Scholar
  73. L. Tarruell, M. Teichmann, J. McKeever, T. Bourdel, J. Cubizolles, L. Khaykovich, J. Zhang, N. Navon, F. Chevy, C. Salomon, in Proceedings of the International School of Physics “Enrico Fermi" on Ultra-Cold Fermi gases, edited by M. Inguscio, W. Ketterle, C. Salomon (SIF, Bologna, 2007)Google Scholar
  74. Q. Chen, C.A. Regal, D.S. Jin, K. Levin, Phys. Rev. A 74, 011601 (2006)Google Scholar
  75. M.L. Chiofalo, S. Giorgini, M. Holland, Phys. Rev. Lett. 97, 070404 (2006)Google Scholar
  76. G.E. Astrakharchik, J. Boronat, J. Casulleras, S. Giorgini, Phys. Rev. Lett. 95, 230405 (2005)Google Scholar
  77. M. Olshanii, V. Dunjko, Phys. Rev. Lett. 91, 090401 (2003)Google Scholar
  78. Y. Castin, I. Carusotto, Opt. Comm. 243, 81 (2004)Google Scholar
  79. M. Punk, W. Zwerger, Phys. Rev. Lett. 99, 170404 (2007)Google Scholar
  80. G. Baym, C.J. Pethick, Z. Yu, M.W. Zwierlein, Phys. Rev. Lett. 99, 190407 (2007)Google Scholar
  81. F. Werner, Y. Castin, Phys. Rev. A 74, 053604 (2006)Google Scholar
  82. J.E. Thomas, Phys. Rev. A 78, 013630 (2008)Google Scholar
  83. S. Tan, Ann. Phys. 323, 2987 (2008)Google Scholar
  84. F. Werner, Phys. Rev. A 78, 025601 (2008)Google Scholar
  85. E. Braaten, D. Kang, L. Platter, e-print arXiv:0806.2277v1 Google Scholar
  86. S. Zhang, A.J. Leggett, e-print arXiv:0809.1892v1 Google Scholar
  87. S. Simonucci, P. Pieri, G. Strinati, Europhys. Lett. 69, 713 (2005)Google Scholar
  88. I. Schmidt-Mink, W. Müller, W. Meyer, Chem. Phys. 92, 263 (1985)Google Scholar
  89. R. Hulet, private communicationGoogle Scholar
  90. N. Manini, L. Salasnich, Phys. Rev. A 71, 033625 (2005)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Laboratoire Kastler Brossel, École Normale Supérieure, UPMC and CNRSParis Cedex 05France

Personalised recommendations