Abstract

We theoretically examine photoassociation of a two-component Fermi degenerate gas. Our focus is on adjusting the atom-atom interaction, and thereby increasing the critical temperature of the BCS transition to the superfluid state. In order to avoid spontaneous decay of the molecules, the photoassociating light must be far-off resonance. Very high light intensities are therefore required for effective control of the BCS transition.

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References

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  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] [PubMed]
  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] [PubMed]
  3. C. C. Bradley, C. A. Sackett, and R. G. Hulet, "Bose-Einstein condensation of lithium: Observation of limited condensate number," Phys. Rev. Lett. 78, 985-989 (1997).
    [CrossRef]
  4. B. DeMarco and D. S. Jin, "Onset of Fermi degeneracy in a trapped atomic gas," Science 285, 1703-1706 (1999).
    [CrossRef] [PubMed]
  5. M. J. Holland, B. DeMarco, and D. S. Jin, "Evaporative cooling of a two-component degenerate Fermi gas," Phys. Rev. A 61, 053610 (2000) (6 pages).
    [CrossRef]
  6. H. T. C. Stoof, M. Houbiers, C. A. Sackett, and R. G. Hulet, "Superfluidity of spin-polarized 6 Li," Phys. Rev. Lett. 76, 10-13 (1996).
    [CrossRef] [PubMed]
  7. M. Houbiers, H. T. C. Stoof, R. Ferwerda, W. I. McAlexander, C. A. Sackett, and R. G. Hulet, "Superfluid state of atomic 6 Li in a magnetic trap," Phys. Rev. A 56, 4864-4878 (1997).
    [CrossRef]
  8. E. Tiesinga, A. J. Moerdijk, B. J. Verhaar, and H. T. C. Stoof, "Conditions for Bose-Einstein condensation in magnetically trapped atomic cesium," Phys. Rev. A 46, R1167-R1170 (1992).
    [CrossRef] [PubMed]
  9. E. Tiesinga, B. J. Verhaar, and H. T. C. Stoof, "Threshold and resonance phenomena in ultracold ground-state collision," Phys. Rev. A 47 4114-4122 (1993).
    [CrossRef] [PubMed]
  10. J. M. Vogels, C. C. Tsai, R. S. Freeland, S. J. J. M. F. Kokkelmans, B. J. Verhaar, and D. J. Heinzen, "Prediction of Feshbach resonances in collisions of ultracold rubidium atoms," Phys. Rev. A 56, R1067-R1070 (1997).
    [CrossRef]
  11. A. J. Moerdijk, B. J. Verhaar, and T. M. Nagtegaal, "Collisions of dressed ground-state atoms," Phys. Rev. A 53, 4343-4351 (1996).
    [CrossRef] [PubMed]
  12. M. Marinescu and L. You, "Controlling atom-atom interaction at ultralow temperatures by dc electric fields," Phys. Rev. Lett. 81, 4596-4599 (1998).
    [CrossRef]
  13. P. O. Fedichev, Yu. Kagan, G. V. Shlyapnikov, and J. T. M. Walraven, "Influence of nearly resonant light on the scattering length in low-temperature atomic gases," Phys. Rev. Lett. 77, 2913-2916 (1996).
    [CrossRef] [PubMed]
  14. J. L. Bohn and P. S. Julienne, "Prospects for influencing scattering lengths with far-off-resonant light," Phys. Rev. A 56, 1486-1491 (1997).
    [CrossRef]
  15. M. Ko�trun, M. Mackie, R. C�t�, and J. Javanainen, "Theory of coherent photoassociation of a Bose-Einstein condensate," Phys. Rev. A 62, 063616 (2000) (23 pages).
    [CrossRef]
  16. S. L. Cornish, N. R. Claussen, J. L. Roberts, E. A. Cornell, and C. E. Wieman, "Stable 85 Rb Bose-Einstein condensates with widely tunable interactions," Phys. Rev. Lett. 85, 1795-1798 (2000).
    [CrossRef] [PubMed]
  17. J. L. Bohn, "Cooper pairing in ultracold 40 K using Feshbach resonances," Phys. Rev. A 61, 053409 (2000) (4 pages).
    [CrossRef]
  18. J. Javanainen and M. Mackie, "Coherent photoassociation of a Bose-Einstein condensate," Phys. Rev. A 59, R3186-R3189 (1999).
    [CrossRef]
  19. J. Javanainen and M. Ko�trun, "Instability of a mixed atom-molecule condensate under photoassociation," Opt. Express 5, 188-194 (1999). http://www.opticsexpress.org/oearchive/source/13528.htm
    [CrossRef] [PubMed]
  20. P. D. Drummond, K. V. Kheruntsyan, and H. He, "Coherent molecular solitons in a Bose-Einstein condensate," Phys. Rev. Lett. 81, 3055-3058 (1998).
    [CrossRef]
  21. R. Friedberg and T. D. Lee, "Gap energy and long-range order in the boson-fermion model of superconductivity," Phys. Rev. B 40, 6745-6762 (1989).
    [CrossRef]
  22. J. Javanainen and M. Mackie, "Probability of photoassociation from a quasicontinuum approach," Phys. Rev. A 58, R789-R792 (1998).
    [CrossRef]
  23. M. Mackie and J. Javanainen, "Quasicontinuum modeling of photoassociation," Phys. Rev. A 60, 3174-3187 (1999).
    [CrossRef]
  24. R. C�t�, A. Dalgarno, Y. Sun, and R. G. Hulet, "Photoabsorption by ultracold atoms and the scattering length," Phys. Rev. Lett. 74, 3581-3583 (1995).
    [CrossRef] [PubMed]
  25. R. C�t� and A. Dalgarno, "Photoassociation intensities and radiative trap loss in lithium," Phys. Rev. A 58, 498-508 (1998).
    [CrossRef]
  26. R. C�t� and A. Dalgarno, "Mechanism for the production of 6 Li2 and 7 Li2 ultracold molecules," J. Mol. Spect. 195, 236-245 (1999).
    [CrossRef]
  27. It should be noted that the photoassociation rates calculated in Refs. [24, 25, 26] are inadvertently low by a factor of (2 pi) 5 .

Other (27)

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] [PubMed]

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] [PubMed]

C. C. Bradley, C. A. Sackett, and R. G. Hulet, "Bose-Einstein condensation of lithium: Observation of limited condensate number," Phys. Rev. Lett. 78, 985-989 (1997).
[CrossRef]

B. DeMarco and D. S. Jin, "Onset of Fermi degeneracy in a trapped atomic gas," Science 285, 1703-1706 (1999).
[CrossRef] [PubMed]

M. J. Holland, B. DeMarco, and D. S. Jin, "Evaporative cooling of a two-component degenerate Fermi gas," Phys. Rev. A 61, 053610 (2000) (6 pages).
[CrossRef]

H. T. C. Stoof, M. Houbiers, C. A. Sackett, and R. G. Hulet, "Superfluidity of spin-polarized 6 Li," Phys. Rev. Lett. 76, 10-13 (1996).
[CrossRef] [PubMed]

M. Houbiers, H. T. C. Stoof, R. Ferwerda, W. I. McAlexander, C. A. Sackett, and R. G. Hulet, "Superfluid state of atomic 6 Li in a magnetic trap," Phys. Rev. A 56, 4864-4878 (1997).
[CrossRef]

E. Tiesinga, A. J. Moerdijk, B. J. Verhaar, and H. T. C. Stoof, "Conditions for Bose-Einstein condensation in magnetically trapped atomic cesium," Phys. Rev. A 46, R1167-R1170 (1992).
[CrossRef] [PubMed]

E. Tiesinga, B. J. Verhaar, and H. T. C. Stoof, "Threshold and resonance phenomena in ultracold ground-state collision," Phys. Rev. A 47 4114-4122 (1993).
[CrossRef] [PubMed]

J. M. Vogels, C. C. Tsai, R. S. Freeland, S. J. J. M. F. Kokkelmans, B. J. Verhaar, and D. J. Heinzen, "Prediction of Feshbach resonances in collisions of ultracold rubidium atoms," Phys. Rev. A 56, R1067-R1070 (1997).
[CrossRef]

A. J. Moerdijk, B. J. Verhaar, and T. M. Nagtegaal, "Collisions of dressed ground-state atoms," Phys. Rev. A 53, 4343-4351 (1996).
[CrossRef] [PubMed]

M. Marinescu and L. You, "Controlling atom-atom interaction at ultralow temperatures by dc electric fields," Phys. Rev. Lett. 81, 4596-4599 (1998).
[CrossRef]

P. O. Fedichev, Yu. Kagan, G. V. Shlyapnikov, and J. T. M. Walraven, "Influence of nearly resonant light on the scattering length in low-temperature atomic gases," Phys. Rev. Lett. 77, 2913-2916 (1996).
[CrossRef] [PubMed]

J. L. Bohn and P. S. Julienne, "Prospects for influencing scattering lengths with far-off-resonant light," Phys. Rev. A 56, 1486-1491 (1997).
[CrossRef]

M. Ko�trun, M. Mackie, R. C�t�, and J. Javanainen, "Theory of coherent photoassociation of a Bose-Einstein condensate," Phys. Rev. A 62, 063616 (2000) (23 pages).
[CrossRef]

S. L. Cornish, N. R. Claussen, J. L. Roberts, E. A. Cornell, and C. E. Wieman, "Stable 85 Rb Bose-Einstein condensates with widely tunable interactions," Phys. Rev. Lett. 85, 1795-1798 (2000).
[CrossRef] [PubMed]

J. L. Bohn, "Cooper pairing in ultracold 40 K using Feshbach resonances," Phys. Rev. A 61, 053409 (2000) (4 pages).
[CrossRef]

J. Javanainen and M. Mackie, "Coherent photoassociation of a Bose-Einstein condensate," Phys. Rev. A 59, R3186-R3189 (1999).
[CrossRef]

J. Javanainen and M. Ko�trun, "Instability of a mixed atom-molecule condensate under photoassociation," Opt. Express 5, 188-194 (1999). http://www.opticsexpress.org/oearchive/source/13528.htm
[CrossRef] [PubMed]

P. D. Drummond, K. V. Kheruntsyan, and H. He, "Coherent molecular solitons in a Bose-Einstein condensate," Phys. Rev. Lett. 81, 3055-3058 (1998).
[CrossRef]

R. Friedberg and T. D. Lee, "Gap energy and long-range order in the boson-fermion model of superconductivity," Phys. Rev. B 40, 6745-6762 (1989).
[CrossRef]

J. Javanainen and M. Mackie, "Probability of photoassociation from a quasicontinuum approach," Phys. Rev. A 58, R789-R792 (1998).
[CrossRef]

M. Mackie and J. Javanainen, "Quasicontinuum modeling of photoassociation," Phys. Rev. A 60, 3174-3187 (1999).
[CrossRef]

R. C�t�, A. Dalgarno, Y. Sun, and R. G. Hulet, "Photoabsorption by ultracold atoms and the scattering length," Phys. Rev. Lett. 74, 3581-3583 (1995).
[CrossRef] [PubMed]

R. C�t� and A. Dalgarno, "Photoassociation intensities and radiative trap loss in lithium," Phys. Rev. A 58, 498-508 (1998).
[CrossRef]

R. C�t� and A. Dalgarno, "Mechanism for the production of 6 Li2 and 7 Li2 ultracold molecules," J. Mol. Spect. 195, 236-245 (1999).
[CrossRef]

It should be noted that the photoassociation rates calculated in Refs. [24, 25, 26] are inadvertently low by a factor of (2 pi) 5 .

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Equations (15)

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

𝓗 = ϕ + 2 2 m ϕ + ϕ 2 2 m ϕ + ψ [ 2 4 m + δ 1 2 i γ s ] ψ
[ 𝓓 ψ ϕ + ϕ + 𝓓 * ϕ ϕ ψ ] + 4 π a m ϕ ϕ + ϕ + ϕ ,
𝓓 ( r ) = lim υ 0 π 2 Γ ( r ) υ μ 2
i ψ ˙ = [ 2 4 m + δ 1 2 i γ s ] ψ 𝓓 ϕ + ϕ .
ψ [ 𝓓 δ + i γ s 𝓓 2 δ 2 ] ϕ + ϕ .
𝓗 ϕ + 2 2 m ϕ + ϕ 2 2 m ϕ + 4 π a m ϕ ϕ + ϕ + ϕ
+ [ 𝓓 2 δ i γ s 𝓓 2 2 δ 2 ] ϕ ϕ + ϕ + ϕ .
a - = 𝓓 2 m 4 π δ .
T c = T F exp [ π 2 k F a ¯ ] = T F exp [ 2 π 2 δ k F m 𝓓 2 ] .
1 τ = γ s 𝓓 2 ρ 2 δ 2 .
R = λ D 3 ρ e δ k B T Γ ρ ( I ω ) k .
a ¯ ƛ = 0.0140077 I I 0 R δ ,
T c T F = exp [ 36.2478 1 ( ƛ 3 ρ ) 1 3 δ R I 0 I ] ,
R τ = 4 δ 2 R γ s I 0 I 1 ƛ 3 ρ .
I 0 = π δ c 4 2 km 2 ( k B T ) 3 2 ƛ 2 e δ k B T .

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