The European Physical Journal D

, Volume 53, Issue 1, pp 75–87 | Cite as

LOFF and breached pairing with cold atoms

Laser Cooling and Quantum Gas


We investigate here the Cooper pairing of fermionic atoms with mismatched Fermi surfaces using a variational construct for the ground state. We determine the state for different values of the mismatch of chemical potential for weak as well as strong coupling regimes including the BCS BEC cross over region. We consider Cooper pairing with both zero and finite net momentum. Within the variational approximation for the ground state and comparing the thermodynamic potentials, we show that (i) the LOFF phase is stable in the weak coupling regime; (ii) the LOFF window is maximum on the BEC side near the Feshbach resonance; and (iii) the existence of stable gapless states with a single Fermi surface for negative average chemical potential on the BEC side of the Feshbach resonance.


03.75.Ss Degenerate Fermi gases 74.20.-z Theories and models of superconducting state 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. W.V. Liu, F. Wilczek, Phys. Rev. Lett. 90, 047002 (2003); S.T. Wu, S.K. Yip, Phys. Rev. 97, 053603 (2003)Google Scholar
  2. M.W. Zwierlein, A. Schirotzek, C.H. Schunck, W. Ketterle, Science 311, 492 (2006); G.B. Patridge, W. Li, Y. Kamer, R. LandLiao, M.W. Zwierlein, A. Schirotzek, C.H. Schunck, W. Ketterle, Nature 442, 54 (2006)Google Scholar
  3. K.M. O’hara et al., Science 298, 2179 (2002); C.A. Regal, M. Greiner, D.S. Jin, Phys. Rev. Lett. 92, 040403 (2004); M. Bartenstein et al., Phys. Rev. Lett. 92, 120401 (2004); M.W. Zwierlein et al., Phys. Rev. Lett. 92, 120403 (2004); J. Kinast et al., Phys. Rev. Lett. 92, 150402 (2004); T. Bourdel et al., Phys. Rev. Lett. 93, 050401 (2004)Google Scholar
  4. For reviews see K. Rajagopal, F. Wilczek, e-print arXiv:hep-ph/0011333; D.K. Hong, Acta Phys. Polon. B 32, 1253 (2001); M.G. Alford, Ann. Rev. Nucl. Part. Sci. 51, 131 (2001); G. Nardulli, Riv. Nuovo Cim. 25N3, 1 (2002); S. Reddy, Acta Phys Polon. B 33, 4101 (2002); T. Schaefer, e-print arXiv:hep-ph/0304281; D.H. Rischke, Prog. Part. Nucl. Phys. 52, 197 (2004); H.C. Ren, e-print arXiv:hep-ph/0404074; M. Huang, Int. J. Mod. Phys. E14, 675 (2005); I. Shovkovy, Found. Phys. 35, 1309 (2005)Google Scholar
  5. See e.g. Q. Chen, J. Stajic, S. Tan, K. Levin, Phys. Rep. 412, 1 (2005) and references thereinGoogle Scholar
  6. G. Bertsch, in Proceedings of the X conference on Recent Progress in Many-Body theories, edited by R.F. Bishop et al. (World Scientific, Singapore, 2000)Google Scholar
  7. A.I. Larkin, Yu.N. Ovchinnikov, Sov. Phys. JETP 20 (1965); P. Fulde, R.A. Ferrel, Phys. Rev. A 135, 550 (1964)Google Scholar
  8. S. Takada, T. Izuyama, Prog. Theor. Phys. 41, 635 (1969)Google Scholar
  9. E. Gubankova, W.V. Liu, F. Wilczek, Phys. Rev. Lett. 94, 110402 (2003)Google Scholar
  10. B. Deb, A. Mishra, H. Mishra, P. Panigrahi, Phys. Rev. A 70, 011604(R) (2004)Google Scholar
  11. I. Shovkovy, M. Huang, Phys. Lett. B 564, 205 (2003)Google Scholar
  12. R. Cassalbuoni, G. Nardulli, Rev. Mod. Phys. 76, 263 (2004); M. Mannarelli, G. Nardulli, M. Ruggieri, e-print arXiv:cond-mat/0604579 Google Scholar
  13. X.J. Liu, H. Hu, Europhys. Lett. 75, 364 (2006); H. Hu, X.J. Liu, Phys. Rev. A 73, 051603(R) (2006)Google Scholar
  14. L. He, M. Jin, P. Zhuang, Phys. Rev. B 73, 214527 (2006)Google Scholar
  15. M. Mannareli, K. Rajagopal, R. Shrma, Phys. Rev. D 73, 114012 (2006); M.G. Alford, K. Bowers, K. Rajagopal, Phys. Rev. D 63, 074016 (2001); R. Casalbuoni, R. Gatto, M. Mannarelli, G. Nardulli, Phys. Lett. B 511, 218 (2001); R. Casalbuoni, M. Cimanale, M. Mannarelli, G. Nardulli, M. Ruggieri, R. Gatto, Phys. Rev. D 70, 054004 (2004)Google Scholar
  16. M. Kitazawa, D.H. Rischke, I. Shovkovy, Phys. Lett. B 637, 367 (2006)Google Scholar
  17. S. Silotri, D. Angom, H. Mishra, A. Mishra, Eur. Phys. J. D 49, 383 (2008)Google Scholar
  18. E. Gubankova, A. Schmitt, F. Wilczek, Phys. Rev. B 74, 064505 (2006)Google Scholar
  19. H. Mishra, S.P. Misra, Phys. Rev. D 48, 5376 (1993)Google Scholar
  20. H. Mishra, J.C. Parikh, Nucl. Phys. A 679, 597 (2001)Google Scholar
  21. A. Mishra, H. Mishra, Phys. Rev. D 69, 014014 (2004)Google Scholar
  22. A. Mishra, H. Mishra, Phys. Rev. D 71, 074023 (2005)Google Scholar
  23. A. Mishra, H. Mishra, Phys. Rev. D 74, 054024 (2006)Google Scholar
  24. C.A.R. Sa de Melo, M. Randeria, J.R. Engelbrecht, Phys. Rev. Lett. 71, 3202 (1993); C.A.R. Sa de Melo, M. Randeria, J.R. Engelbrecht, Phys. Rev. B 55, 15153 (1997)Google Scholar
  25. M. Marini, F. Pistolesi, G.C. Strinati, Eur. Phys. J. B 1, 151(1998)Google Scholar
  26. H. Umezawa, H. Matsumoto, M. Tachiki, Thermofield dynamics and condensed states (North Holland, Amsterdam, 1982); P.A. Henning, Phys. Rep. 253, 235 (1995)Google Scholar
  27. A. Mishra, H. Mishra, J. Phys. G 23, 143 (1997)Google Scholar
  28. H. Caldas, e-print arXiv:cond-mat/0605005 Google Scholar
  29. A.A. Abrikosov, L.P. Gorkov, Zh. Eskp. Teor. 39, 1781 (1960)Google Scholar
  30. M.G. Alford, J. Berges, K. Rajagopal, Phys. Rev. Lett. 84, 598 (2000)Google Scholar
  31. H. Heiselberg, Phys. Rev. A 63, 043606 (2003)Google Scholar
  32. A.M. Clogston, Phys. Rev. Lett. 9, 266 (1962); B.S. Chandrasekhar, Appl. Phys. Lett. 1, 7 (1962)Google Scholar
  33. P.F. Bedaque, H. Caldas, G. Rupak, Phys. Rev. Lett. 91, 247002 (2003)Google Scholar
  34. J. Carlson, S. Reddy, Phys. Rev. Lett. 95, 060401 (2005)Google Scholar
  35. M. Iskin, C.A.R. Sa de Melo, Phys. Rev. A 78, 013607 (2008); T.K. Koponen, T. Paananen, J.-P. Martikainen, P. Torma, Phys. Rev. Lett. 99, 120403 (2007)Google Scholar
  36. Y. Nishida, D.T. Son, Phys. Rev. Lett. 97, 050403 (2006)Google Scholar
  37. I. Giannakis, H. Ren, Phys. Lett. B 611, 137 (2005); I. Giannakis, H. Ren, Nucl. Phys. 723, 255 (2005)Google Scholar
  38. D. Silotri, D. Angom, A. Mishra, H. Mishra, in preparationGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of PhysicsIndian Institute of TechnologyNew DelhiIndia
  2. 2.Theory DivisionPhysical Research LaboratoryAhmedabadIndia
  3. 3.School of Physical Sciences, Jawaharlal Nehru UniversityNew DelhiIndia

Personalised recommendations