Abstract

In this paper, we have made a comparative study of the condensate fraction of balanced and imbalanced two-component uniform fermionic systems in the Bose–Einstein condensation-Bardeen–Cooper–Schrieffer (BEC-BCS) crossover. We have used extended BCS equations to calculate the condensate fraction of Cooper pairs as a function of chemical potential and gap energy in a balanced system using a path integral approach. For an imbalanced system, the same equation has been derived as a function of average chemical potential, imbalanced chemical potential, gap energy, and temperature. The condensate fraction in a balanced fermionic system varies with the interaction parameter, whereas its behavior in an imbalanced system changes with the interaction parameter and polarization, in different regimes. In particular, the effect of polarization on the condensate fraction has been studied in an imbalanced system for odd values of polarization. We have compared the condensate fraction for both systems analytically and graphically and observed that for an imbalanced system, it decreases with increasing polarization and almost vanishes for higher values of polarization in the BEC regime.

© 2020 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
On the condensation of polaritons

Benoit Deveaud-Plédran
J. Opt. Soc. Am. B 29(2) A138-A145 (2012)

Direct imaging of a digital-micromirror device for configurable microscopic optical potentials

G. Gauthier, I. Lenton, N. McKay Parry, M. Baker, M. J. Davis, H. Rubinsztein-Dunlop, and T. W. Neely
Optica 3(10) 1136-1143 (2016)

Quantum phases of Bose-Fermi mixtures in optical lattices

H. Fehrmann, M. Baranov, M. Lewenstein, and L. Santos
Opt. Express 12(1) 55-68 (2004)

References

  • View by:
  • |
  • |
  • |

  1. 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 269, 198–201 (1995).
    [Crossref]
  2. K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Bose-Einstein condensation in a gas of sodium atoms,” Phys. Rev. Lett. 75, 3969–3973 (1995).
    [Crossref]
  3. M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
    [Crossref]
  4. K. W. Madison, F. Chevy, V. Bretin, and J. Dalibard, “Stationary states of a rotating Bose-Einstein condensate: routes to vortex nucleation,” Phys. Rev. Lett. 86, 4443–4446 (2001).
    [Crossref]
  5. J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of vortex lattices in Bose-Einstein condensates,” Science 292, 476–479 (2001).
    [Crossref]
  6. B. DeMarco and D. S. Jin, “Onset of Fermi degeneracy in a trapped atomic gas,” Science 285, 1703–1706 (1999).
    [Crossref]
  7. C. A. Regal, M. Greiner, and D. S. Jin, “Observation of resonance condensation of fermionic atom pairs,” Phys. Rev. Lett. 92, 040403 (2004).
    [Crossref]
  8. M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, A. J. Kerman, and W. Ketterle, “Condensation of pairs of fermionic atoms near a Feshbach resonance,” Phys. Rev. Lett. 92, 120403 (2004).
    [Crossref]
  9. J. Kinast, S. L. Hemmer, M. E. Gehm, A. Turlapov, and J. E. Thomas, “Evidence for superfluidity in a resonantly interacting Fermi gas,” Phys. Rev. Lett. 92, 150402 (2004).
    [Crossref]
  10. M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, C. Chin, J. H. Denschlag, and R. Grimm, “Collective excitations of a degenerate gas at the BEC-BCS crossover,” Phys. Rev. Lett. 92, 203201 (2004).
    [Crossref]
  11. T. Bourdel, L. Khaykovich, J. Cubizolles, J. Zhang, F. Chevy, M. Teichmann, L. Tarruell, S. J. J. M. F. Kokkelmans, and C. Salomon, “Experimental study of the BEC-BCS crossover region in lithium 6,” Phys. Rev. Lett. 93, 050401 (2004).
    [Crossref]
  12. M. Greiner, C. A. Regal, and D. S. Jin, “Emergence of a molecular Bose–Einstein condensate from a Fermi gas,” Nature 426, 537–540 (2003).
    [Crossref]
  13. M. W. Zwierlein, C. H. Schunck, C. A. Stan, S. M. F. Raupach, and W. Ketterle, “Formation dynamics of a Fermion pair condensate,” Phys. Rev. Lett. 94, 180401 (2005).
    [Crossref]
  14. 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 305, 1128–1130 (2004).
    [Crossref]
  15. L. Dell’Anna, G. Mazzarella, and L. Salasnich, “Condensate fraction of a resonant Fermi gas with spin-orbit coupling in three and two dimensions,” Phys. Rev. A 84, 033633 (2011).
    [Crossref]
  16. L. Dell’Anna, G. Mazzarella, and L. Salasnich, “Tuning Rashba and Dresselhaus spin-orbit couplings: Effects on singlet and triplet condensation with Fermi atoms,” Phys. Rev. A 86, 053632 (2012).
    [Crossref]
  17. L. Salasnich, “Condensate fraction of a two-dimensional attractive Fermi gas,” Phys. Rev. A 76, 015601 (2007).
    [Crossref]
  18. L. Salasnich and F. Toigo, “Pair condensation in the BCS-BEC crossover of ultracold atoms loaded onto a two-dimensional square lattice,” Phys. Rev. A 86, 023619 (2012).
    [Crossref]
  19. L. Salasnich, P. A. Marchetti, and F. Toigo, “Superfluidity, sound velocity, and quasicondensation in the two-dimensional BCS-BEC crossover,” Phys. Rev. A 88, 053612 (2013).
    [Crossref]
  20. P. Fulde and R. A. Ferrell, “Superconductivity in a strong spin-exchange field,” Phys. Rev. 135, A550–A563 (1964).
    [Crossref]
  21. A. I. Larkin and Y. N. Ovchinnikov, “Nonuniform state of superconductors,” Zh. Eksp. Teor. Fiz. 47, 1136–1146 (1964) [Sov. Phys. JETP 20, 762 (1965)].
  22. T. Mizushima, K. Machida, and M. Ichioka, “Direct imaging of spatially modulated superfluid phases in atomic Fermion systems,” Phys. Rev. Lett. 94, 060404 (2005).
    [Crossref]
  23. P. F. Bedaque, H. Caldas, and G. Rupak, “Phase separation in asymmetrical Fermion superfluids,” Phys. Rev. Lett. 91, 247002 (2003).
    [Crossref]
  24. M. W. Zwierlein, A. Schirotzek, C. H. Schunck, and W. Ketterle, “Fermionic superfluidity with imbalanced spin populations,” Science 311, 492–496 (2006).
    [Crossref]
  25. G. B. Partridge, W. Lui, R. I. Kamar, Y. Liao, and R. G. Hulet, “Pairing and phase separation in a polarized Fermi gas,” Science 311, 503–505 (2006).
    [Crossref]
  26. A. Altland and B. Simons, Condensed Matter Field Theory (Cambridge University, 2006).
  27. J. Tempere and J. P. A. Devreese, “Path-integral description of cooper pairing,” in Superconductors–Materials, Properties and Applications (InTech, 2012), pp. 1–32.
  28. H. Vivas, “Path integral treatment of fluctuations in the BCSBEC crossover in superfluid fermi gases,” arXiv:cond-mat/0504600v2 [cond-mat.str-el] (2005).
  29. N. Nagaosa, Quantum Field Theory in Condensed Matter Physics (Springer, 1999).
  30. L. Salasnich, N. Manini, and A. Parola, “Condensate fraction of a Fermi gas in the BCS-BEC crossover,” Phys. Rev. A 72, 023621 (2005).
    [Crossref]
  31. J. Tempere, S. N. Klimin, J. T. Devreese, and V. V. Moshchalkov, “Imbalanced d-wave superfluids in the BCS-BEC crossover regime at finite temperatures,” Phys. Rev. B 77, 134502 (2008).
    [Crossref]
  32. H. T. C. Stoof, K. B. Gubbels, and D. B. M. Dickerscheid, Ultracold Quantum Fields (Springer, 2009).
  33. 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 1, 151–159 (1998).
    [Crossref]
  34. A. J. Leggett, Quantum Liquids: Bose Condensation and Cooper Pairing in Condensed-Matter Systems, Oxford Graduate Texts (Oxford University, 2006).
  35. C. E. Campbell, in Condensed Matter Theories, J. W. Clark and P. V. Panat, eds. (Nova Science, 1997), Vol. 12, pp. 131–132.
  36. L. He and X.-G. Huang, “BCS-BEC crossover in three-dimensional Fermi gases with spherical spin-orbit coupling,” Phys. Rev. B 86, 014511 (2012).
    [Crossref]
  37. J. Tempere, S. N. Klimin, and J. T. Devreese, “Phase separation in imbalanced fermion superfluids beyond the mean-field approximation,” Phys. Rev. A 78, 023626 (2008).
    [Crossref]
  38. S. N. Klimin, J. Tempere, and J. P. A. Devreese, “Pair excitations and parameters of state of imbalanced Fermi gases at finite temperatures,” J. Low Temp. Phys. 165, 261–274 (2011).
    [Crossref]
  39. Y. Nambu, “Quasi-particles and gauge invariance in the theory of superconductivity,” Phys. Rev. 117, 648–663 (1960).
    [Crossref]
  40. L. P. Gorkov, “Microscopic derivation of the Ginzburg-Landau equations in the theory of superconductivity,” Z. Eksp. Teor. Fiz. 36, 1918–1923 (1959).
  41. G. Bighin, G. Mazzarella, L. Dell’Anna, and L. Salasnich, “Pair condensation of polarized fermions in the BCS BEC crossover,” J. Phys. B 47, 195302 (2014).
    [Crossref]
  42. W. Appel, Mathematics for Physics and Physicists, 1st ed. (Princeton University, 2007).

2014 (1)

G. Bighin, G. Mazzarella, L. Dell’Anna, and L. Salasnich, “Pair condensation of polarized fermions in the BCS BEC crossover,” J. Phys. B 47, 195302 (2014).
[Crossref]

2013 (1)

L. Salasnich, P. A. Marchetti, and F. Toigo, “Superfluidity, sound velocity, and quasicondensation in the two-dimensional BCS-BEC crossover,” Phys. Rev. A 88, 053612 (2013).
[Crossref]

2012 (3)

L. Dell’Anna, G. Mazzarella, and L. Salasnich, “Tuning Rashba and Dresselhaus spin-orbit couplings: Effects on singlet and triplet condensation with Fermi atoms,” Phys. Rev. A 86, 053632 (2012).
[Crossref]

L. Salasnich and F. Toigo, “Pair condensation in the BCS-BEC crossover of ultracold atoms loaded onto a two-dimensional square lattice,” Phys. Rev. A 86, 023619 (2012).
[Crossref]

L. He and X.-G. Huang, “BCS-BEC crossover in three-dimensional Fermi gases with spherical spin-orbit coupling,” Phys. Rev. B 86, 014511 (2012).
[Crossref]

2011 (2)

S. N. Klimin, J. Tempere, and J. P. A. Devreese, “Pair excitations and parameters of state of imbalanced Fermi gases at finite temperatures,” J. Low Temp. Phys. 165, 261–274 (2011).
[Crossref]

L. Dell’Anna, G. Mazzarella, and L. Salasnich, “Condensate fraction of a resonant Fermi gas with spin-orbit coupling in three and two dimensions,” Phys. Rev. A 84, 033633 (2011).
[Crossref]

2008 (2)

J. Tempere, S. N. Klimin, and J. T. Devreese, “Phase separation in imbalanced fermion superfluids beyond the mean-field approximation,” Phys. Rev. A 78, 023626 (2008).
[Crossref]

J. Tempere, S. N. Klimin, J. T. Devreese, and V. V. Moshchalkov, “Imbalanced d-wave superfluids in the BCS-BEC crossover regime at finite temperatures,” Phys. Rev. B 77, 134502 (2008).
[Crossref]

2007 (1)

L. Salasnich, “Condensate fraction of a two-dimensional attractive Fermi gas,” Phys. Rev. A 76, 015601 (2007).
[Crossref]

2006 (2)

M. W. Zwierlein, A. Schirotzek, C. H. Schunck, and W. Ketterle, “Fermionic superfluidity with imbalanced spin populations,” Science 311, 492–496 (2006).
[Crossref]

G. B. Partridge, W. Lui, R. I. Kamar, Y. Liao, and R. G. Hulet, “Pairing and phase separation in a polarized Fermi gas,” Science 311, 503–505 (2006).
[Crossref]

2005 (3)

L. Salasnich, N. Manini, and A. Parola, “Condensate fraction of a Fermi gas in the BCS-BEC crossover,” Phys. Rev. A 72, 023621 (2005).
[Crossref]

T. Mizushima, K. Machida, and M. Ichioka, “Direct imaging of spatially modulated superfluid phases in atomic Fermion systems,” Phys. Rev. Lett. 94, 060404 (2005).
[Crossref]

M. W. Zwierlein, C. H. Schunck, C. A. Stan, S. M. F. Raupach, and W. Ketterle, “Formation dynamics of a Fermion pair condensate,” Phys. Rev. Lett. 94, 180401 (2005).
[Crossref]

2004 (6)

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 305, 1128–1130 (2004).
[Crossref]

C. A. Regal, M. Greiner, and D. S. Jin, “Observation of resonance condensation of fermionic atom pairs,” Phys. Rev. Lett. 92, 040403 (2004).
[Crossref]

M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, A. J. Kerman, and W. Ketterle, “Condensation of pairs of fermionic atoms near a Feshbach resonance,” Phys. Rev. Lett. 92, 120403 (2004).
[Crossref]

J. Kinast, S. L. Hemmer, M. E. Gehm, A. Turlapov, and J. E. Thomas, “Evidence for superfluidity in a resonantly interacting Fermi gas,” Phys. Rev. Lett. 92, 150402 (2004).
[Crossref]

M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, C. Chin, J. H. Denschlag, and R. Grimm, “Collective excitations of a degenerate gas at the BEC-BCS crossover,” Phys. Rev. Lett. 92, 203201 (2004).
[Crossref]

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

2003 (2)

M. Greiner, C. A. Regal, and D. S. Jin, “Emergence of a molecular Bose–Einstein condensate from a Fermi gas,” Nature 426, 537–540 (2003).
[Crossref]

P. F. Bedaque, H. Caldas, and G. Rupak, “Phase separation in asymmetrical Fermion superfluids,” Phys. Rev. Lett. 91, 247002 (2003).
[Crossref]

2001 (2)

K. W. Madison, F. Chevy, V. Bretin, and J. Dalibard, “Stationary states of a rotating Bose-Einstein condensate: routes to vortex nucleation,” Phys. Rev. Lett. 86, 4443–4446 (2001).
[Crossref]

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of vortex lattices in Bose-Einstein condensates,” Science 292, 476–479 (2001).
[Crossref]

1999 (2)

B. DeMarco and D. S. Jin, “Onset of Fermi degeneracy in a trapped atomic gas,” Science 285, 1703–1706 (1999).
[Crossref]

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[Crossref]

1998 (1)

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 1, 151–159 (1998).
[Crossref]

1995 (2)

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 269, 198–201 (1995).
[Crossref]

K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Bose-Einstein condensation in a gas of sodium atoms,” Phys. Rev. Lett. 75, 3969–3973 (1995).
[Crossref]

1964 (2)

P. Fulde and R. A. Ferrell, “Superconductivity in a strong spin-exchange field,” Phys. Rev. 135, A550–A563 (1964).
[Crossref]

A. I. Larkin and Y. N. Ovchinnikov, “Nonuniform state of superconductors,” Zh. Eksp. Teor. Fiz. 47, 1136–1146 (1964) [Sov. Phys. JETP 20, 762 (1965)].

1960 (1)

Y. Nambu, “Quasi-particles and gauge invariance in the theory of superconductivity,” Phys. Rev. 117, 648–663 (1960).
[Crossref]

1959 (1)

L. P. Gorkov, “Microscopic derivation of the Ginzburg-Landau equations in the theory of superconductivity,” Z. Eksp. Teor. Fiz. 36, 1918–1923 (1959).

Abo-Shaeer, J. R.

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of vortex lattices in Bose-Einstein condensates,” Science 292, 476–479 (2001).
[Crossref]

Altland, A.

A. Altland and B. Simons, Condensed Matter Field Theory (Cambridge University, 2006).

Altmeyer, A.

M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, C. Chin, J. H. Denschlag, and R. Grimm, “Collective excitations of a degenerate gas at the BEC-BCS crossover,” Phys. Rev. Lett. 92, 203201 (2004).
[Crossref]

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 305, 1128–1130 (2004).
[Crossref]

Anderson, B. P.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[Crossref]

Anderson, M. H.

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 269, 198–201 (1995).
[Crossref]

Andrews, M. R.

K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Bose-Einstein condensation in a gas of sodium atoms,” Phys. Rev. Lett. 75, 3969–3973 (1995).
[Crossref]

Appel, W.

W. Appel, Mathematics for Physics and Physicists, 1st ed. (Princeton University, 2007).

Bartenstein, M.

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 305, 1128–1130 (2004).
[Crossref]

M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, C. Chin, J. H. Denschlag, and R. Grimm, “Collective excitations of a degenerate gas at the BEC-BCS crossover,” Phys. Rev. Lett. 92, 203201 (2004).
[Crossref]

Bedaque, P. F.

P. F. Bedaque, H. Caldas, and G. Rupak, “Phase separation in asymmetrical Fermion superfluids,” Phys. Rev. Lett. 91, 247002 (2003).
[Crossref]

Bighin, G.

G. Bighin, G. Mazzarella, L. Dell’Anna, and L. Salasnich, “Pair condensation of polarized fermions in the BCS BEC crossover,” J. Phys. B 47, 195302 (2014).
[Crossref]

Bourdel, T.

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

Bretin, V.

K. W. Madison, F. Chevy, V. Bretin, and J. Dalibard, “Stationary states of a rotating Bose-Einstein condensate: routes to vortex nucleation,” Phys. Rev. Lett. 86, 4443–4446 (2001).
[Crossref]

Caldas, H.

P. F. Bedaque, H. Caldas, and G. Rupak, “Phase separation in asymmetrical Fermion superfluids,” Phys. Rev. Lett. 91, 247002 (2003).
[Crossref]

Campbell, C. E.

C. E. Campbell, in Condensed Matter Theories, J. W. Clark and P. V. Panat, eds. (Nova Science, 1997), Vol. 12, pp. 131–132.

Chevy, F.

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

K. W. Madison, F. Chevy, V. Bretin, and J. Dalibard, “Stationary states of a rotating Bose-Einstein condensate: routes to vortex nucleation,” Phys. Rev. Lett. 86, 4443–4446 (2001).
[Crossref]

Chin, C.

M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, C. Chin, J. H. Denschlag, and R. Grimm, “Collective excitations of a degenerate gas at the BEC-BCS crossover,” Phys. Rev. Lett. 92, 203201 (2004).
[Crossref]

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 305, 1128–1130 (2004).
[Crossref]

Cornell, E. A.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[Crossref]

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 269, 198–201 (1995).
[Crossref]

Cubizolles, J.

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

Dalibard, J.

K. W. Madison, F. Chevy, V. Bretin, and J. Dalibard, “Stationary states of a rotating Bose-Einstein condensate: routes to vortex nucleation,” Phys. Rev. Lett. 86, 4443–4446 (2001).
[Crossref]

Davis, K. B.

K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Bose-Einstein condensation in a gas of sodium atoms,” Phys. Rev. Lett. 75, 3969–3973 (1995).
[Crossref]

Dell’Anna, L.

G. Bighin, G. Mazzarella, L. Dell’Anna, and L. Salasnich, “Pair condensation of polarized fermions in the BCS BEC crossover,” J. Phys. B 47, 195302 (2014).
[Crossref]

L. Dell’Anna, G. Mazzarella, and L. Salasnich, “Tuning Rashba and Dresselhaus spin-orbit couplings: Effects on singlet and triplet condensation with Fermi atoms,” Phys. Rev. A 86, 053632 (2012).
[Crossref]

L. Dell’Anna, G. Mazzarella, and L. Salasnich, “Condensate fraction of a resonant Fermi gas with spin-orbit coupling in three and two dimensions,” Phys. Rev. A 84, 033633 (2011).
[Crossref]

DeMarco, B.

B. DeMarco and D. S. Jin, “Onset of Fermi degeneracy in a trapped atomic gas,” Science 285, 1703–1706 (1999).
[Crossref]

Denschlag, J. H.

M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, C. Chin, J. H. Denschlag, and R. Grimm, “Collective excitations of a degenerate gas at the BEC-BCS crossover,” Phys. Rev. Lett. 92, 203201 (2004).
[Crossref]

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 305, 1128–1130 (2004).
[Crossref]

Devreese, J. P. A.

S. N. Klimin, J. Tempere, and J. P. A. Devreese, “Pair excitations and parameters of state of imbalanced Fermi gases at finite temperatures,” J. Low Temp. Phys. 165, 261–274 (2011).
[Crossref]

J. Tempere and J. P. A. Devreese, “Path-integral description of cooper pairing,” in Superconductors–Materials, Properties and Applications (InTech, 2012), pp. 1–32.

Devreese, J. T.

J. Tempere, S. N. Klimin, J. T. Devreese, and V. V. Moshchalkov, “Imbalanced d-wave superfluids in the BCS-BEC crossover regime at finite temperatures,” Phys. Rev. B 77, 134502 (2008).
[Crossref]

J. Tempere, S. N. Klimin, and J. T. Devreese, “Phase separation in imbalanced fermion superfluids beyond the mean-field approximation,” Phys. Rev. A 78, 023626 (2008).
[Crossref]

Dickerscheid, D. B. M.

H. T. C. Stoof, K. B. Gubbels, and D. B. M. Dickerscheid, Ultracold Quantum Fields (Springer, 2009).

Durfee, D. S.

K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Bose-Einstein condensation in a gas of sodium atoms,” Phys. Rev. Lett. 75, 3969–3973 (1995).
[Crossref]

Ensher, J. R.

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 269, 198–201 (1995).
[Crossref]

Ferrell, R. A.

P. Fulde and R. A. Ferrell, “Superconductivity in a strong spin-exchange field,” Phys. Rev. 135, A550–A563 (1964).
[Crossref]

Fulde, P.

P. Fulde and R. A. Ferrell, “Superconductivity in a strong spin-exchange field,” Phys. Rev. 135, A550–A563 (1964).
[Crossref]

Gehm, M. E.

J. Kinast, S. L. Hemmer, M. E. Gehm, A. Turlapov, and J. E. Thomas, “Evidence for superfluidity in a resonantly interacting Fermi gas,” Phys. Rev. Lett. 92, 150402 (2004).
[Crossref]

Gorkov, L. P.

L. P. Gorkov, “Microscopic derivation of the Ginzburg-Landau equations in the theory of superconductivity,” Z. Eksp. Teor. Fiz. 36, 1918–1923 (1959).

Greiner, M.

C. A. Regal, M. Greiner, and D. S. Jin, “Observation of resonance condensation of fermionic atom pairs,” Phys. Rev. Lett. 92, 040403 (2004).
[Crossref]

M. Greiner, C. A. Regal, and D. S. Jin, “Emergence of a molecular Bose–Einstein condensate from a Fermi gas,” Nature 426, 537–540 (2003).
[Crossref]

Grimm, R.

M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, C. Chin, J. H. Denschlag, and R. Grimm, “Collective excitations of a degenerate gas at the BEC-BCS crossover,” Phys. Rev. Lett. 92, 203201 (2004).
[Crossref]

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 305, 1128–1130 (2004).
[Crossref]

Gubbels, K. B.

H. T. C. Stoof, K. B. Gubbels, and D. B. M. Dickerscheid, Ultracold Quantum Fields (Springer, 2009).

Haljan, P. C.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[Crossref]

Hall, D. S.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[Crossref]

He, L.

L. He and X.-G. Huang, “BCS-BEC crossover in three-dimensional Fermi gases with spherical spin-orbit coupling,” Phys. Rev. B 86, 014511 (2012).
[Crossref]

Hemmer, S. L.

J. Kinast, S. L. Hemmer, M. E. Gehm, A. Turlapov, and J. E. Thomas, “Evidence for superfluidity in a resonantly interacting Fermi gas,” Phys. Rev. Lett. 92, 150402 (2004).
[Crossref]

Huang, X.-G.

L. He and X.-G. Huang, “BCS-BEC crossover in three-dimensional Fermi gases with spherical spin-orbit coupling,” Phys. Rev. B 86, 014511 (2012).
[Crossref]

Hulet, R. G.

G. B. Partridge, W. Lui, R. I. Kamar, Y. Liao, and R. G. Hulet, “Pairing and phase separation in a polarized Fermi gas,” Science 311, 503–505 (2006).
[Crossref]

Ichioka, M.

T. Mizushima, K. Machida, and M. Ichioka, “Direct imaging of spatially modulated superfluid phases in atomic Fermion systems,” Phys. Rev. Lett. 94, 060404 (2005).
[Crossref]

Jin, D. S.

C. A. Regal, M. Greiner, and D. S. Jin, “Observation of resonance condensation of fermionic atom pairs,” Phys. Rev. Lett. 92, 040403 (2004).
[Crossref]

M. Greiner, C. A. Regal, and D. S. Jin, “Emergence of a molecular Bose–Einstein condensate from a Fermi gas,” Nature 426, 537–540 (2003).
[Crossref]

B. DeMarco and D. S. Jin, “Onset of Fermi degeneracy in a trapped atomic gas,” Science 285, 1703–1706 (1999).
[Crossref]

Jochim, S.

M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, C. Chin, J. H. Denschlag, and R. Grimm, “Collective excitations of a degenerate gas at the BEC-BCS crossover,” Phys. Rev. Lett. 92, 203201 (2004).
[Crossref]

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 305, 1128–1130 (2004).
[Crossref]

Kamar, R. I.

G. B. Partridge, W. Lui, R. I. Kamar, Y. Liao, and R. G. Hulet, “Pairing and phase separation in a polarized Fermi gas,” Science 311, 503–505 (2006).
[Crossref]

Kerman, A. J.

M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, A. J. Kerman, and W. Ketterle, “Condensation of pairs of fermionic atoms near a Feshbach resonance,” Phys. Rev. Lett. 92, 120403 (2004).
[Crossref]

Ketterle, W.

M. W. Zwierlein, A. Schirotzek, C. H. Schunck, and W. Ketterle, “Fermionic superfluidity with imbalanced spin populations,” Science 311, 492–496 (2006).
[Crossref]

M. W. Zwierlein, C. H. Schunck, C. A. Stan, S. M. F. Raupach, and W. Ketterle, “Formation dynamics of a Fermion pair condensate,” Phys. Rev. Lett. 94, 180401 (2005).
[Crossref]

M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, A. J. Kerman, and W. Ketterle, “Condensation of pairs of fermionic atoms near a Feshbach resonance,” Phys. Rev. Lett. 92, 120403 (2004).
[Crossref]

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of vortex lattices in Bose-Einstein condensates,” Science 292, 476–479 (2001).
[Crossref]

K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Bose-Einstein condensation in a gas of sodium atoms,” Phys. Rev. Lett. 75, 3969–3973 (1995).
[Crossref]

Khaykovich, L.

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

Kinast, J.

J. Kinast, S. L. Hemmer, M. E. Gehm, A. Turlapov, and J. E. Thomas, “Evidence for superfluidity in a resonantly interacting Fermi gas,” Phys. Rev. Lett. 92, 150402 (2004).
[Crossref]

Klimin, S. N.

S. N. Klimin, J. Tempere, and J. P. A. Devreese, “Pair excitations and parameters of state of imbalanced Fermi gases at finite temperatures,” J. Low Temp. Phys. 165, 261–274 (2011).
[Crossref]

J. Tempere, S. N. Klimin, and J. T. Devreese, “Phase separation in imbalanced fermion superfluids beyond the mean-field approximation,” Phys. Rev. A 78, 023626 (2008).
[Crossref]

J. Tempere, S. N. Klimin, J. T. Devreese, and V. V. Moshchalkov, “Imbalanced d-wave superfluids in the BCS-BEC crossover regime at finite temperatures,” Phys. Rev. B 77, 134502 (2008).
[Crossref]

Kokkelmans, S. J. J. M. F.

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

Kurn, D. M.

K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Bose-Einstein condensation in a gas of sodium atoms,” Phys. Rev. Lett. 75, 3969–3973 (1995).
[Crossref]

Larkin, A. I.

A. I. Larkin and Y. N. Ovchinnikov, “Nonuniform state of superconductors,” Zh. Eksp. Teor. Fiz. 47, 1136–1146 (1964) [Sov. Phys. JETP 20, 762 (1965)].

Leggett, A. J.

A. J. Leggett, Quantum Liquids: Bose Condensation and Cooper Pairing in Condensed-Matter Systems, Oxford Graduate Texts (Oxford University, 2006).

Liao, Y.

G. B. Partridge, W. Lui, R. I. Kamar, Y. Liao, and R. G. Hulet, “Pairing and phase separation in a polarized Fermi gas,” Science 311, 503–505 (2006).
[Crossref]

Lui, W.

G. B. Partridge, W. Lui, R. I. Kamar, Y. Liao, and R. G. Hulet, “Pairing and phase separation in a polarized Fermi gas,” Science 311, 503–505 (2006).
[Crossref]

Machida, K.

T. Mizushima, K. Machida, and M. Ichioka, “Direct imaging of spatially modulated superfluid phases in atomic Fermion systems,” Phys. Rev. Lett. 94, 060404 (2005).
[Crossref]

Madison, K. W.

K. W. Madison, F. Chevy, V. Bretin, and J. Dalibard, “Stationary states of a rotating Bose-Einstein condensate: routes to vortex nucleation,” Phys. Rev. Lett. 86, 4443–4446 (2001).
[Crossref]

Manini, N.

L. Salasnich, N. Manini, and A. Parola, “Condensate fraction of a Fermi gas in the BCS-BEC crossover,” Phys. Rev. A 72, 023621 (2005).
[Crossref]

Marchetti, P. A.

L. Salasnich, P. A. Marchetti, and F. Toigo, “Superfluidity, sound velocity, and quasicondensation in the two-dimensional BCS-BEC crossover,” Phys. Rev. A 88, 053612 (2013).
[Crossref]

Marini, M.

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 1, 151–159 (1998).
[Crossref]

Matthews, M. R.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[Crossref]

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 269, 198–201 (1995).
[Crossref]

Mazzarella, G.

G. Bighin, G. Mazzarella, L. Dell’Anna, and L. Salasnich, “Pair condensation of polarized fermions in the BCS BEC crossover,” J. Phys. B 47, 195302 (2014).
[Crossref]

L. Dell’Anna, G. Mazzarella, and L. Salasnich, “Tuning Rashba and Dresselhaus spin-orbit couplings: Effects on singlet and triplet condensation with Fermi atoms,” Phys. Rev. A 86, 053632 (2012).
[Crossref]

L. Dell’Anna, G. Mazzarella, and L. Salasnich, “Condensate fraction of a resonant Fermi gas with spin-orbit coupling in three and two dimensions,” Phys. Rev. A 84, 033633 (2011).
[Crossref]

Mewes, M.-O.

K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Bose-Einstein condensation in a gas of sodium atoms,” Phys. Rev. Lett. 75, 3969–3973 (1995).
[Crossref]

Mizushima, T.

T. Mizushima, K. Machida, and M. Ichioka, “Direct imaging of spatially modulated superfluid phases in atomic Fermion systems,” Phys. Rev. Lett. 94, 060404 (2005).
[Crossref]

Moshchalkov, V. V.

J. Tempere, S. N. Klimin, J. T. Devreese, and V. V. Moshchalkov, “Imbalanced d-wave superfluids in the BCS-BEC crossover regime at finite temperatures,” Phys. Rev. B 77, 134502 (2008).
[Crossref]

Nagaosa, N.

N. Nagaosa, Quantum Field Theory in Condensed Matter Physics (Springer, 1999).

Nambu, Y.

Y. Nambu, “Quasi-particles and gauge invariance in the theory of superconductivity,” Phys. Rev. 117, 648–663 (1960).
[Crossref]

Ovchinnikov, Y. N.

A. I. Larkin and Y. N. Ovchinnikov, “Nonuniform state of superconductors,” Zh. Eksp. Teor. Fiz. 47, 1136–1146 (1964) [Sov. Phys. JETP 20, 762 (1965)].

Parola, A.

L. Salasnich, N. Manini, and A. Parola, “Condensate fraction of a Fermi gas in the BCS-BEC crossover,” Phys. Rev. A 72, 023621 (2005).
[Crossref]

Partridge, G. B.

G. B. Partridge, W. Lui, R. I. Kamar, Y. Liao, and R. G. Hulet, “Pairing and phase separation in a polarized Fermi gas,” Science 311, 503–505 (2006).
[Crossref]

Pistolesi, F.

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 1, 151–159 (1998).
[Crossref]

Raman, C.

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of vortex lattices in Bose-Einstein condensates,” Science 292, 476–479 (2001).
[Crossref]

Raupach, S. M. F.

M. W. Zwierlein, C. H. Schunck, C. A. Stan, S. M. F. Raupach, and W. Ketterle, “Formation dynamics of a Fermion pair condensate,” Phys. Rev. Lett. 94, 180401 (2005).
[Crossref]

M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, A. J. Kerman, and W. Ketterle, “Condensation of pairs of fermionic atoms near a Feshbach resonance,” Phys. Rev. Lett. 92, 120403 (2004).
[Crossref]

Regal, C. A.

C. A. Regal, M. Greiner, and D. S. Jin, “Observation of resonance condensation of fermionic atom pairs,” Phys. Rev. Lett. 92, 040403 (2004).
[Crossref]

M. Greiner, C. A. Regal, and D. S. Jin, “Emergence of a molecular Bose–Einstein condensate from a Fermi gas,” Nature 426, 537–540 (2003).
[Crossref]

Riedl, S.

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 305, 1128–1130 (2004).
[Crossref]

M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, C. Chin, J. H. Denschlag, and R. Grimm, “Collective excitations of a degenerate gas at the BEC-BCS crossover,” Phys. Rev. Lett. 92, 203201 (2004).
[Crossref]

Rupak, G.

P. F. Bedaque, H. Caldas, and G. Rupak, “Phase separation in asymmetrical Fermion superfluids,” Phys. Rev. Lett. 91, 247002 (2003).
[Crossref]

Salasnich, L.

G. Bighin, G. Mazzarella, L. Dell’Anna, and L. Salasnich, “Pair condensation of polarized fermions in the BCS BEC crossover,” J. Phys. B 47, 195302 (2014).
[Crossref]

L. Salasnich, P. A. Marchetti, and F. Toigo, “Superfluidity, sound velocity, and quasicondensation in the two-dimensional BCS-BEC crossover,” Phys. Rev. A 88, 053612 (2013).
[Crossref]

L. Salasnich and F. Toigo, “Pair condensation in the BCS-BEC crossover of ultracold atoms loaded onto a two-dimensional square lattice,” Phys. Rev. A 86, 023619 (2012).
[Crossref]

L. Dell’Anna, G. Mazzarella, and L. Salasnich, “Tuning Rashba and Dresselhaus spin-orbit couplings: Effects on singlet and triplet condensation with Fermi atoms,” Phys. Rev. A 86, 053632 (2012).
[Crossref]

L. Dell’Anna, G. Mazzarella, and L. Salasnich, “Condensate fraction of a resonant Fermi gas with spin-orbit coupling in three and two dimensions,” Phys. Rev. A 84, 033633 (2011).
[Crossref]

L. Salasnich, “Condensate fraction of a two-dimensional attractive Fermi gas,” Phys. Rev. A 76, 015601 (2007).
[Crossref]

L. Salasnich, N. Manini, and A. Parola, “Condensate fraction of a Fermi gas in the BCS-BEC crossover,” Phys. Rev. A 72, 023621 (2005).
[Crossref]

Salomon, C.

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

Schirotzek, A.

M. W. Zwierlein, A. Schirotzek, C. H. Schunck, and W. Ketterle, “Fermionic superfluidity with imbalanced spin populations,” Science 311, 492–496 (2006).
[Crossref]

Schunck, C. H.

M. W. Zwierlein, A. Schirotzek, C. H. Schunck, and W. Ketterle, “Fermionic superfluidity with imbalanced spin populations,” Science 311, 492–496 (2006).
[Crossref]

M. W. Zwierlein, C. H. Schunck, C. A. Stan, S. M. F. Raupach, and W. Ketterle, “Formation dynamics of a Fermion pair condensate,” Phys. Rev. Lett. 94, 180401 (2005).
[Crossref]

M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, A. J. Kerman, and W. Ketterle, “Condensation of pairs of fermionic atoms near a Feshbach resonance,” Phys. Rev. Lett. 92, 120403 (2004).
[Crossref]

Simons, B.

A. Altland and B. Simons, Condensed Matter Field Theory (Cambridge University, 2006).

Stan, C. A.

M. W. Zwierlein, C. H. Schunck, C. A. Stan, S. M. F. Raupach, and W. Ketterle, “Formation dynamics of a Fermion pair condensate,” Phys. Rev. Lett. 94, 180401 (2005).
[Crossref]

M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, A. J. Kerman, and W. Ketterle, “Condensation of pairs of fermionic atoms near a Feshbach resonance,” Phys. Rev. Lett. 92, 120403 (2004).
[Crossref]

Stoof, H. T. C.

H. T. C. Stoof, K. B. Gubbels, and D. B. M. Dickerscheid, Ultracold Quantum Fields (Springer, 2009).

Strinati, G. C.

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 1, 151–159 (1998).
[Crossref]

Tarruell, L.

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

Teichmann, M.

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

Tempere, J.

S. N. Klimin, J. Tempere, and J. P. A. Devreese, “Pair excitations and parameters of state of imbalanced Fermi gases at finite temperatures,” J. Low Temp. Phys. 165, 261–274 (2011).
[Crossref]

J. Tempere, S. N. Klimin, and J. T. Devreese, “Phase separation in imbalanced fermion superfluids beyond the mean-field approximation,” Phys. Rev. A 78, 023626 (2008).
[Crossref]

J. Tempere, S. N. Klimin, J. T. Devreese, and V. V. Moshchalkov, “Imbalanced d-wave superfluids in the BCS-BEC crossover regime at finite temperatures,” Phys. Rev. B 77, 134502 (2008).
[Crossref]

J. Tempere and J. P. A. Devreese, “Path-integral description of cooper pairing,” in Superconductors–Materials, Properties and Applications (InTech, 2012), pp. 1–32.

Thomas, J. E.

J. Kinast, S. L. Hemmer, M. E. Gehm, A. Turlapov, and J. E. Thomas, “Evidence for superfluidity in a resonantly interacting Fermi gas,” Phys. Rev. Lett. 92, 150402 (2004).
[Crossref]

Toigo, F.

L. Salasnich, P. A. Marchetti, and F. Toigo, “Superfluidity, sound velocity, and quasicondensation in the two-dimensional BCS-BEC crossover,” Phys. Rev. A 88, 053612 (2013).
[Crossref]

L. Salasnich and F. Toigo, “Pair condensation in the BCS-BEC crossover of ultracold atoms loaded onto a two-dimensional square lattice,” Phys. Rev. A 86, 023619 (2012).
[Crossref]

Turlapov, A.

J. Kinast, S. L. Hemmer, M. E. Gehm, A. Turlapov, and J. E. Thomas, “Evidence for superfluidity in a resonantly interacting Fermi gas,” Phys. Rev. Lett. 92, 150402 (2004).
[Crossref]

van Druten, N. J.

K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Bose-Einstein condensation in a gas of sodium atoms,” Phys. Rev. Lett. 75, 3969–3973 (1995).
[Crossref]

Vivas, H.

H. Vivas, “Path integral treatment of fluctuations in the BCSBEC crossover in superfluid fermi gases,” arXiv:cond-mat/0504600v2 [cond-mat.str-el] (2005).

Vogels, J. M.

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of vortex lattices in Bose-Einstein condensates,” Science 292, 476–479 (2001).
[Crossref]

Wieman, C. E.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[Crossref]

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 269, 198–201 (1995).
[Crossref]

Zhang, J.

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

Zwierlein, M. W.

M. W. Zwierlein, A. Schirotzek, C. H. Schunck, and W. Ketterle, “Fermionic superfluidity with imbalanced spin populations,” Science 311, 492–496 (2006).
[Crossref]

M. W. Zwierlein, C. H. Schunck, C. A. Stan, S. M. F. Raupach, and W. Ketterle, “Formation dynamics of a Fermion pair condensate,” Phys. Rev. Lett. 94, 180401 (2005).
[Crossref]

M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, A. J. Kerman, and W. Ketterle, “Condensation of pairs of fermionic atoms near a Feshbach resonance,” Phys. Rev. Lett. 92, 120403 (2004).
[Crossref]

Eur. Phys. J. B (1)

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 1, 151–159 (1998).
[Crossref]

J. Low Temp. Phys. (1)

S. N. Klimin, J. Tempere, and J. P. A. Devreese, “Pair excitations and parameters of state of imbalanced Fermi gases at finite temperatures,” J. Low Temp. Phys. 165, 261–274 (2011).
[Crossref]

J. Phys. B (1)

G. Bighin, G. Mazzarella, L. Dell’Anna, and L. Salasnich, “Pair condensation of polarized fermions in the BCS BEC crossover,” J. Phys. B 47, 195302 (2014).
[Crossref]

Nature (1)

M. Greiner, C. A. Regal, and D. S. Jin, “Emergence of a molecular Bose–Einstein condensate from a Fermi gas,” Nature 426, 537–540 (2003).
[Crossref]

Phys. Rev. (2)

P. Fulde and R. A. Ferrell, “Superconductivity in a strong spin-exchange field,” Phys. Rev. 135, A550–A563 (1964).
[Crossref]

Y. Nambu, “Quasi-particles and gauge invariance in the theory of superconductivity,” Phys. Rev. 117, 648–663 (1960).
[Crossref]

Phys. Rev. A (7)

L. Salasnich, N. Manini, and A. Parola, “Condensate fraction of a Fermi gas in the BCS-BEC crossover,” Phys. Rev. A 72, 023621 (2005).
[Crossref]

L. Dell’Anna, G. Mazzarella, and L. Salasnich, “Condensate fraction of a resonant Fermi gas with spin-orbit coupling in three and two dimensions,” Phys. Rev. A 84, 033633 (2011).
[Crossref]

L. Dell’Anna, G. Mazzarella, and L. Salasnich, “Tuning Rashba and Dresselhaus spin-orbit couplings: Effects on singlet and triplet condensation with Fermi atoms,” Phys. Rev. A 86, 053632 (2012).
[Crossref]

L. Salasnich, “Condensate fraction of a two-dimensional attractive Fermi gas,” Phys. Rev. A 76, 015601 (2007).
[Crossref]

L. Salasnich and F. Toigo, “Pair condensation in the BCS-BEC crossover of ultracold atoms loaded onto a two-dimensional square lattice,” Phys. Rev. A 86, 023619 (2012).
[Crossref]

L. Salasnich, P. A. Marchetti, and F. Toigo, “Superfluidity, sound velocity, and quasicondensation in the two-dimensional BCS-BEC crossover,” Phys. Rev. A 88, 053612 (2013).
[Crossref]

J. Tempere, S. N. Klimin, and J. T. Devreese, “Phase separation in imbalanced fermion superfluids beyond the mean-field approximation,” Phys. Rev. A 78, 023626 (2008).
[Crossref]

Phys. Rev. B (2)

J. Tempere, S. N. Klimin, J. T. Devreese, and V. V. Moshchalkov, “Imbalanced d-wave superfluids in the BCS-BEC crossover regime at finite temperatures,” Phys. Rev. B 77, 134502 (2008).
[Crossref]

L. He and X.-G. Huang, “BCS-BEC crossover in three-dimensional Fermi gases with spherical spin-orbit coupling,” Phys. Rev. B 86, 014511 (2012).
[Crossref]

Phys. Rev. Lett. (11)

T. Mizushima, K. Machida, and M. Ichioka, “Direct imaging of spatially modulated superfluid phases in atomic Fermion systems,” Phys. Rev. Lett. 94, 060404 (2005).
[Crossref]

P. F. Bedaque, H. Caldas, and G. Rupak, “Phase separation in asymmetrical Fermion superfluids,” Phys. Rev. Lett. 91, 247002 (2003).
[Crossref]

M. W. Zwierlein, C. H. Schunck, C. A. Stan, S. M. F. Raupach, and W. Ketterle, “Formation dynamics of a Fermion pair condensate,” Phys. Rev. Lett. 94, 180401 (2005).
[Crossref]

K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Bose-Einstein condensation in a gas of sodium atoms,” Phys. Rev. Lett. 75, 3969–3973 (1995).
[Crossref]

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[Crossref]

K. W. Madison, F. Chevy, V. Bretin, and J. Dalibard, “Stationary states of a rotating Bose-Einstein condensate: routes to vortex nucleation,” Phys. Rev. Lett. 86, 4443–4446 (2001).
[Crossref]

C. A. Regal, M. Greiner, and D. S. Jin, “Observation of resonance condensation of fermionic atom pairs,” Phys. Rev. Lett. 92, 040403 (2004).
[Crossref]

M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, A. J. Kerman, and W. Ketterle, “Condensation of pairs of fermionic atoms near a Feshbach resonance,” Phys. Rev. Lett. 92, 120403 (2004).
[Crossref]

J. Kinast, S. L. Hemmer, M. E. Gehm, A. Turlapov, and J. E. Thomas, “Evidence for superfluidity in a resonantly interacting Fermi gas,” Phys. Rev. Lett. 92, 150402 (2004).
[Crossref]

M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, C. Chin, J. H. Denschlag, and R. Grimm, “Collective excitations of a degenerate gas at the BEC-BCS crossover,” Phys. Rev. Lett. 92, 203201 (2004).
[Crossref]

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

Science (6)

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of vortex lattices in Bose-Einstein condensates,” Science 292, 476–479 (2001).
[Crossref]

B. DeMarco and D. S. Jin, “Onset of Fermi degeneracy in a trapped atomic gas,” Science 285, 1703–1706 (1999).
[Crossref]

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 305, 1128–1130 (2004).
[Crossref]

M. W. Zwierlein, A. Schirotzek, C. H. Schunck, and W. Ketterle, “Fermionic superfluidity with imbalanced spin populations,” Science 311, 492–496 (2006).
[Crossref]

G. B. Partridge, W. Lui, R. I. Kamar, Y. Liao, and R. G. Hulet, “Pairing and phase separation in a polarized Fermi gas,” Science 311, 503–505 (2006).
[Crossref]

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 269, 198–201 (1995).
[Crossref]

Z. Eksp. Teor. Fiz. (1)

L. P. Gorkov, “Microscopic derivation of the Ginzburg-Landau equations in the theory of superconductivity,” Z. Eksp. Teor. Fiz. 36, 1918–1923 (1959).

Zh. Eksp. Teor. Fiz. (1)

A. I. Larkin and Y. N. Ovchinnikov, “Nonuniform state of superconductors,” Zh. Eksp. Teor. Fiz. 47, 1136–1146 (1964) [Sov. Phys. JETP 20, 762 (1965)].

Other (8)

H. T. C. Stoof, K. B. Gubbels, and D. B. M. Dickerscheid, Ultracold Quantum Fields (Springer, 2009).

A. J. Leggett, Quantum Liquids: Bose Condensation and Cooper Pairing in Condensed-Matter Systems, Oxford Graduate Texts (Oxford University, 2006).

C. E. Campbell, in Condensed Matter Theories, J. W. Clark and P. V. Panat, eds. (Nova Science, 1997), Vol. 12, pp. 131–132.

A. Altland and B. Simons, Condensed Matter Field Theory (Cambridge University, 2006).

J. Tempere and J. P. A. Devreese, “Path-integral description of cooper pairing,” in Superconductors–Materials, Properties and Applications (InTech, 2012), pp. 1–32.

H. Vivas, “Path integral treatment of fluctuations in the BCSBEC crossover in superfluid fermi gases,” arXiv:cond-mat/0504600v2 [cond-mat.str-el] (2005).

N. Nagaosa, Quantum Field Theory in Condensed Matter Physics (Springer, 1999).

W. Appel, Mathematics for Physics and Physicists, 1st ed. (Princeton University, 2007).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1. Behavior of condensate fraction of balanced uniform fermionic system in the BCS (left) and BEC (right) regimes.
Fig. 2.
Fig. 2. Behavior of condensate fraction of imbalanced uniform fermionic system in the BCS (left) and BEC (right) regimes.
Fig. 3.
Fig. 3. Residue of poles (crosses).
Fig. 4.
Fig. 4. Residue of pole (dot).

Equations (44)

Equations on this page are rendered with MathJax. Learn more.

L = σ = a , b ψ σ ( r , τ ) ( τ 2 2 2 m μ ) ψ σ ( r , τ ) + g ψ a ( r , τ ) ψ b ( r , τ ) ψ b ( r , τ ) ψ a ( r , τ ) .
Z = D ψ σ D ψ σ exp [ S [ ψ σ , ψ σ ] ] .
S f [ ψ σ , ψ σ ] = 0 β d τ v d 3 r σ = a , b ψ σ ( r , τ ) × ( τ 2 2 2 m μ ) ψ σ ( r , τ ) , S i [ ψ σ , ψ σ ] = g 0 β d τ v d 3 r ψ a ( r , τ ) ψ b ( r , τ ) × ψ b ( r , τ ) ψ a ( r , τ ) ,
exp ( S [ ψ σ , ψ σ ] ) D Δ D Δ exp ( S hs [ ψ σ , ψ σ , Δ , Δ ] ) .
Δ q , n = Δ 0 + χ q , m .
Δ q , n = Δ 0 .
[ G 1 ] = ( i w n + k 2 2 m μ Δ 0 Δ 0 i w n k 2 2 m + μ ) .
E k = ξ k 2 + Δ 0 2 ,
Z sp = exp ( S sp ) ,
S e = V Δ 0 2 g + k ξ k k ( ln ( ( i w n + E k ) ( i w n E k ) ) ) β .
Ω = k ( ξ k E k ) V Δ 0 2 g 2 β k ln ( 1 + exp ( β E k ) ) .
1 g = 1 V k tanh ( β E k 2 ) 2 E k ,
N = 1 V k ( 1 ξ k E k tanh ( β E k 2 ) ) .
m 4 π a = 1 V k [ 1 2 ϵ k 1 2 E k ] .
α N o N ,
N 0 = 1 β 2 p n l G 21 ( p , i w n ) G 12 ( p , i w l ) ,
G 12 ( k , i w n ) = Δ 0 i w n 2 ξ k 2 Δ 0 2 , G 12 ( k , i w n ) = G 21 ( k , i w n ) .
N 0 = k Δ 0 2 4 E k 2 ( 1 2 tanh ( β 2 ( E k ) ) + 1 2 tanh ( β 2 ( E k ) ) ) 2 .
N 0 = k Δ 0 2 4 E k 2 .
N 0 = V ( m 3 2 8 π ) Δ 0 3 2 μ Δ 0 + 1 + μ 2 Δ 0 2 .
1 a = 2 ( 2 m Δ 0 ) 1 / 2 π I a ( x 0 ) ,
N = V ( 2 m Δ 0 ) 3 / 2 2 π 2 I b ( x 0 ) ,
N 0 N = ( 3 π 2 e 2 ) exp ( y π 2 ) ,
N 0 N = Δ 0 2 m 2 a f 8 π .
L = σ = a , b ψ ( r , τ ) ( τ 2 2 2 m μ σ ) ψ ( r , τ ) + g ψ a ( r , τ ) ψ b ( r , τ ) ψ b ( r , τ ) ψ a ( r , τ ) .
μ μ a + μ b 2 , ζ μ a μ b 2 , a n d P N a N b N a + N b .
[ G 1 ] = ( i w n + k 2 2 m μ ζ Δ 0 Δ 0 i w n k 2 2 m + μ ζ ) ,
E k ± = ξ k 2 + Δ 0 2 ± ζ ,
S e = V Δ 0 2 g + k ξ k 1 β k ln ( 2 cosh ( β ζ ) + 2 cosh ( β E k ) ) .
1 g = 1 V k sinh ( β E k ) E k ( 2 cosh ( β ζ ) + 2 cosh ( β E k ) ) .
N = k ( 1 ξ k ( sinh ( β E k ) ) E k ( cosh ( β ζ ) + cosh ( β E k ) ) ) .
δ N = k [ ( sinh ( β ζ ) ) ( cosh ( β ζ ) + cosh ( β E k ) ) ] .
m 4 π a = 1 2 V k [ 1 ϵ k sinh ( β E k ) E k ( 2 cosh ( β ζ ) + 2 cosh ( β E k ) ) ] .
Ω T = 0 = k ( ξ k E k ) V Δ 2 g + | k | k , k + ] ( E k ζ ) ,
k = 2 m max ( μ ζ 2 Δ 0 2 , k + = 2 m max ( μ + ζ 2 Δ 0 2 .
N 0 = k Δ 0 2 4 E k 2 ( 1 2 tanh ( β 2 ( E k + ζ ) ) + 1 2 tanh ( β 2 ( E k ζ ) ) ) 2 .
N 0 = | k | [ k , k + ] Δ 0 2 4 E k 2 ,
S = 1 β n f ( i w n ) ,
S = 1 β n f ( i w n ) = 1 β C f ( i w n ) d z β 2 tanh ( β z 2 ) ,
S = 1 β i R e s [ f ( z ) β 2 tanh ( β z 2 ) ] ( z i ) ,
N 0 = 1 β 2 p n l G 21 ( p , i w n ) G 12 ( p , i w l ) , G 12 ( k , i w n ) = Δ 0 i w n 2 ξ k 2 Δ 0 2 , G 12 ( k , i w n ) = G 21 ( k , i w n ) , E k 2 = ξ k 2 + Δ 0 2 , N 0 = 1 β 2 k n ( Δ 0 i w n 2 E k 2 ) ( Δ 0 i w n 2 E k 2 ) .
R e s [ Δ 0 i w n 2 E k 2 β 2 tanh ( β z 2 ) ] ( z = ± E k ) = β Δ 0 tanh ( β E k 2 ) 4 E k .
1 β n ( Δ 0 i w n 2 E k 2 ) = Δ 0 tanh ( β E k 2 ) 2 E k .
1 β n ( Δ 0 i w n 2 E k 2 ) = Δ 0 tanh ( β E k 2 ) 2 E k , N 0 = k Δ 0 2 tanh 2 ( β E k 2 ) 4 E k 2 , N 0 = k Δ 0 2 4 E k 2 ( 1 2 tanh ( β E k 2 ) + 1 2 tanh ( β E k 2 ) ) 2 .