## Driving superfluidity with photoassociation

Optics Express, Vol. 8, Issue 2, pp. 118-122 (2001)

http://dx.doi.org/10.1364/OE.8.000118

Acrobat PDF (134 KB)

### 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.

© Optical Society of America

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]

*raise*the value of the critical temperature. Possible means for adjustment include the magnetic-field-induced Feshbach resonance [8

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. Kos̆trun, M. Mackie, R. Côté, and J. Javanainen, “Theory of coherent photoassociation of a Bose-Einstein condensate,” Phys. Rev. A **62**, 063616 (2000) (23 *pages*). [CrossRef]

^{85}Rb [16

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 40K 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. Kos̆trun, “Instability of a mixed atom-molecule condensate under photoassociation,” Optics Express **5**, 188–194 (1999). http://www.opticsexpress.org/oearchive/source/13528.htm [CrossRef] [PubMed]

15. M. Kos̆trun, M. Mackie, R. Côté, and J. Javanainen, “Theory of coherent photoassociation of a Bose-Einstein condensate,” Phys. Rev. A **62**, 063616 (2000) (23 *pages*). [CrossRef]

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]

*ϕ*±(r), photoassociating into a bosonic molecule, given by the field

*ψ*(r). The fermions would typically be two states with different

*z*components of angular momentum in the same atom. As a result of the Pauli exclusion principle, there is no

*s*-wave photoassociation for two atoms in the same internal state, but such a restriction does not apply to two different spin components. Incidentally, this system is the neutral-particle version of the boson-fermion model of high-temperature superconductivity [21

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]

*m*is the mass of an atom and

*δ*is the detuning of the laser from the threshold of photodissociation. The detuning is positive when the photodissociation (inverse of photoassociation) channel is open. We have of course made a low-momentum approximation, so that atom-molecule coupling is given as a contact interaction [15

15. M. Kos̆trun, M. Mackie, R. Côté, and J. Javanainen, “Theory of coherent photoassociation of a Bose-Einstein condensate,” Phys. Rev. A **62**, 063616 (2000) (23 *pages*). [CrossRef]

*D*. The coupling strength

*D*may be deduced implicitly from Refs. [18

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. Kos̆trun, “Instability of a mixed atom-molecule condensate under photoassociation,” Optics Express **5**, 188–194 (1999). http://www.opticsexpress.org/oearchive/source/13528.htm [CrossRef] [PubMed]

**62**, 063616 (2000) (23 *pages*). [CrossRef]

*v*, and

*µ*=

*m*/2 is the reduced mass of two atoms. Because of the statistics, there is a factor of √2 difference in Eq. (2) from the corresponding expression for identical bosons. Finally, we have included an interspecies collisional interaction governed by the s-wave scattering length

*a*in the Hamiltonian.

*γs*.

*ψ*is

*δ*is the largest frequency parameter in the problem, and solve Eq. (3) adiabatically for the field

*ψ*. In the process we keep the imaginary part in the energy, and obtain

*γ*

_{s}. Equation (5) displays an added collisional interaction between the two spin species, as if from the s-wave scattering length

*a*is too weak for experiments on the BCS transition, and ignore the native collisions altogether.

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]

*k*

_{p}=(3

*π*

^{2}

*ρ*)

^{1/3}is the Fermi wave number for the total density of atoms

*ρ*, and

*T*

_{F}=

*ħ*

^{2}

*mk*

_{B}is the corresponding Fermi temperature. Next, using (

*ρ*/2)

^{2}for

*ϕ*

^{†}-

*ϕ*

^{†}+

*ϕ*+ϕ-, we find the loss rate per atom due to spontaneous emission from photoassociated molecules,

*T*

_{c}~

*T*

_{F}, the accuracy of the BCS theory becomes dubious; nevertheless, for the purpose of obtaining a zeroth-order estimate, we assume that the expression (7) remains reasonable.

*T*is [22

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]

**62**, 063616 (2000) (23 *pages*). [CrossRef]

*I*is the intensity (Wcm

^{-2}) of photoassociating light, and

*κ*(cm

^{5}) is the photoassociation rate coefficients. There may be statistics dependent numerical factors in Eq. (9). However, in the current literature such factors are usually ignored, and we write Eq. (9) accordingly.

*π*,

*∊*

_{r}=

*ħ*/(2

*m*

*I*

_{0}. This gives

*π*, are there because we want to use the characteristic intensity for photoassociation defined in Ref. [15

**62**, 063616 (2000) (23 *pages*). [CrossRef]

*κ*is known at a temperature

*T*and detuning

*δ*, the critical intensity is

^{6}Li of lithium [24

24. R. Côté, 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. Côté and A. Dalgarno, “Photoassociation intensities and radiative trap loss in lithium,” Phys. Rev. A **58**, 498–508 (1998). [CrossRef]

26. R. Côté and A. Dalgarno, “Mechanism for the production of ^{6}Li_{2} and ^{7}Li_{2} ultracold molecules,” J. Mol. Spect. **195**, 236–245 (1999). [CrossRef]

**62**, 063616 (2000) (23 *pages*). [CrossRef]

*v*′=79 with the binding energy 1.05 cm

^{-1}. The characteristic intensity is then

*I*

_{0}=9.8mWcm

^{-2}, the wavelength is λ=671 nm, and the recoil frequency is

*∊*

_{r}=63.3×2

*π*kHz. We take the decay rate of the molecular state to be twice the spontaneous decay rate of the corresponding atom, so that

*γ*

_{s}=12×2

*π*MHz. In our estimate we assume λ

^{-}

^{3}

*p*=1, corresponding to the density

*ρ*=8.21×10

^{14}cm

^{-3}that is high but not unreasonable. It would then take the intermediate detuning

*δ*=2×2

*π*10

^{14}Hz and the intensity

*I*=460 MWcm

^{-2}to make

*T*

_{c}=0.1

*T*

_{F}and

*τ*=10 s.

_{2}laser. Our formalism, though, is based on the assumption that the laser is close to a photoassociating resonance. We need to amend the calculations to give meaningful estimates for the CO

_{2}laser, whose electric field is in practice direct current compared to the molecular transition frequencies involved.

*δ*→

*ω*

_{0}, and multiplying the intensity by two,

*I*→2

*1*. Applying this substitution to the scattering length, at we find that, by coincidence, the intensity required for

*T*

_{c}=0.1

*T*

_{F}again becomes 460MWcm

^{-2}. With the same substitutions, the lifetime would be about 20 s. However, as the frequency of the CO

_{2}laser is 1/16 of the resonance frequency for photoassociation, the phase space for spontaneously emitted photons is reduced, and the actual rate of spontaneous emission would be reduced by an extra factor of at least 16

^{2}~300. It is clear that spontaneous emission is not an issue with CO

_{2}laser excitation.

*v*′=79. However, with such a far-off resonant laser, one should obviously add the changes of the scattering lengths due to all molecular states. Now, in lithium as well as in other alkali atoms, most of the transition strength for dipole transitions starting from the ground state is in the

*D*lines. Just a few electronic states in a molecule then inherit most of the transition strength for photoassociation. Here we only consider the singlet and triplet excited manifolds in the 6Li dimer, for which calculations of the photoassociation matrix elements exist for all vibrational states [24

24. R. Côté, 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. Côté and A. Dalgarno, “Photoassociation intensities and radiative trap loss in lithium,” Phys. Rev. A **58**, 498–508 (1998). [CrossRef]

26. R. Côté and A. Dalgarno, “Mechanism for the production of ^{6}Li_{2} and ^{7}Li_{2} ultracold molecules,” J. Mol. Spect. **195**, 236–245 (1999). [CrossRef]

**62**, 063616 (2000) (23 *pages*). [CrossRef]

*v*′=79 level carries the fraction of 0.07 of the transition strength. Were we to include the contribution from each and every state explicitly, compared to our CO

_{2}laser example the intensity simply gets multiplied by 0.07 and becomes 30 MW cm

^{-2}.

**62**, 063616 (2000) (23 *pages*). [CrossRef]

## References and links

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 |

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. |

3. | C. C. Bradley, C. A. Sackett, and R. G. Hulet, “Bose-Einstein condensation of lithium: Observation of limited condensate number,” Phys. Rev. Lett. |

4. | B. DeMarco and D. S. Jin, “Onset of Fermi degeneracy in a trapped atomic gas,” Science |

5. | M. J. Holland, B. DeMarco, and D. S. Jin, “Evaporative cooling of a two-component degenerate Fermi gas,” Phys. Rev. A |

6. | H. T. C. Stoof, M. Houbiers, C. A. Sackett, and R. G. Hulet, “Superfluidity of spin-polarized |

7. | M. Houbiers, H. T. C. Stoof, R. Ferwerda, W. I. McAlexander, C. A. Sackett, and R. G. Hulet, “Superfluid state of atomic |

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 |

9. | E. Tiesinga, B. J. Verhaar, and H. T. C. Stoof, “Threshold and resonance phenomena in ultracold ground-state collision,” Phys. Rev. A |

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 |

11. | A. J. Moerdijk, B. J. Verhaar, and T. M. Nagtegaal, “Collisions of dressed ground-state atoms,” Phys. Rev. A |

12. | M. Marinescu and L. You, “Controlling atom-atom interaction at ultralow temperatures by dc electric fields,” Phys. Rev. Lett. |

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. |

14. | J. L. Bohn and P. S. Julienne, “Prospects for influencing scattering lengths with far-off-resonant light,” Phys. Rev. A |

15. | M. Kos̆trun, M. Mackie, R. Côté, and J. Javanainen, “Theory of coherent photoassociation of a Bose-Einstein condensate,” Phys. Rev. A |

16. | S. L. Cornish, N. R. Claussen, J. L. Roberts, E. A. Cornell, and C. E. Wieman, “Stable |

17. | J. L. Bohn, “Cooper pairing in ultracold 40K using Feshbach resonances,” Phys. Rev. A |

18. | J. Javanainen and M. Mackie, “Coherent photoassociation of a Bose-Einstein condensate,” Phys. Rev. A |

19. | J. Javanainen and M. Kos̆trun, “Instability of a mixed atom-molecule condensate under photoassociation,” Optics Express |

20. | P. D. Drummond, K. V. Kheruntsyan, and H. He, “Coherent molecular solitons in a Bose-Einstein condensate,” Phys. Rev. Lett. |

21. | R. Friedberg and T. D. Lee, “Gap energy and long-range order in the boson-fermion model of superconductivity,” Phys. Rev. B |

22. | J. Javanainen and M. Mackie, “Probability of photoassociation from a quasicontinuum approach,” Phys. Rev. A |

23. | M. Mackie and J. Javanainen, “Quasicontinuum modeling of photoassociation,” Phys. Rev. A |

24. | R. Côté, A. Dalgarno, Y. Sun, and R. G. Hulet, “Photoabsorption by ultracold atoms and the scattering length,” Phys. Rev. Lett. |

25. | R. Côté and A. Dalgarno, “Photoassociation intensities and radiative trap loss in lithium,” Phys. Rev. A |

26. | R. Côté and A. Dalgarno, “Mechanism for the production of |

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

**OCIS Codes**

(020.1670) Atomic and molecular physics : Coherent optical effects

(190.2620) Nonlinear optics : Harmonic generation and mixing

**ToC Category:**

Focus Issue: Quantum control of photons and matter

**History**

Original Manuscript: November 9, 2000

Published: January 15, 2001

**Citation**

Matt Mackie, Eddy Timmermans, Robin Cote, and Juha Javanainen, "Driving superfluidity with photoassociation," Opt. Express **8**, 118-122 (2001)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-8-2-118

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### References

- 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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