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Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 8, Iss. 2 — Jan. 15, 2001
  • pp: 118–122
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Driving superfluidity with photoassociation

Matt Mackie, Eddy Timmermans, Robin Côté, and Juha Javanainen  »View Author Affiliations


Optics Express, Vol. 8, Issue 2, pp. 118-122 (2001)
http://dx.doi.org/10.1364/OE.8.000118


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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

As the field of quantum degenerate vapors emerges from its burgeoning adolescence, attention is increasingly shifting from Bose [1

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

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

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]

] to Fermi [4

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

] systems. Beyond degeneracy itself, much of this effort is concentrated on observing the BCS transition to a superfluid state. However, such investigations are currently at an impasse: the lowest temperature that has been achieved is about a third of the Fermi temperature [5

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]

], whereas the formation of Cooper pairs requires temperatures colder by at least an order of magnitude [6

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

, 7

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

]. Rather than finesse the experiments to lower the temperature of the gas further, a more fruitful approach might be to adjust the atom-atom interaction so as to 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

9. E. Tiesinga, B. J. Verhaar, and H. T. C. Stoof, “Threshold and resonance phenomena in ultracold ground-state collision,” Phys. Rev. A 474114–4122 (1993). [CrossRef] [PubMed]

, 10

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]

], rf microwave fields [11

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]

], dc electric fields [12

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]

], and photoassociation [13

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

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

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]

]. In fact, the Feshbach resonance has been recently applied in this manner to induce condensation in the otherwise incondensable 85Rb [16

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

], and was additionally explored (theoretically) for its usefulness in spurring the superfluid transition [17

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

].

The purpose of this paper is to investigate the utility of photoassociation for inducing the BCS transition. We [18

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

, 19

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

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]

] and others [20

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]

] have earlier written down field theories for photoassociation of bosons. In the present case we consider instead a binary mixture of fermionic atoms, given by the fields 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]

].

We thus have a model Hamiltonian density governing photoassociation,

𝓗=ϕ+22mϕ+ϕ22mϕ+ψ[24m+δ12iγs]ψ
[𝓓ψϕ+ϕ+𝓓*ϕϕψ]+4πamϕϕ+ϕ+ϕ,
(1)

where 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]

] of strength 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

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]

], and is discussed explicitly in Ref. [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]

]. Either way, we have

𝓓(r)=limυ0π2Γ(r)υμ2
(2)

Here Γ(r) is the photodissociation rate that a light with the intensity prevailing at r would cause in a nondegenerate gas of molecules, given that the laser is tuned in such a way that the relative velocity of the molecular fragments (atoms) is 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.

Under ordinary circumstances photoassociation by absorption of a photon leads to a molecular state that is unstable against spontaneous emission. There is no particular reason why spontaneous break-up of a primarily photoassociated molecule would deposit the ensuing atoms back to the degenerate Fermi gases. A spontaneously decaying molecule is considered lost for our purposes. Correspondingly, we add to the Hamiltonian a nonhermitian term proportional to the spontaneous emission rate of the molecular state γs.

The Heisenberg equation of motion for the molecular field ψ is

iψ˙=[24m+δ12iγs]ψ𝓓ϕ+ϕ.
(3)

We assume that the detuning 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

ψ[𝓓δ+iγs𝓓2δ2]ϕ+ϕ.
(4)

Inserting into Eq. (1), we find an effective Hamiltonian density for fermions only,

𝓗ϕ+22mϕ+ϕ22mϕ+4πamϕϕ+ϕ+ϕ
+[𝓓2δiγs𝓓22δ2]ϕϕ+ϕ+ϕ.
(5)

Let us first ignore the decay term ∝ γs . Equation (5) displays an added collisional interaction between the two spin species, as if from the s-wave scattering length

a-=𝓓2m4πδ.
(6)

The interaction is attractive if the detuning is positive. But an attractive interaction is exactly what is needed for the BCS transition. To simplify matters we assume here that the collisional interaction in the absence of light ∝ a is too weak for experiments on the BCS transition, and ignore the native collisions altogether.

The critical temperature for the BCS transition is [6

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

, 7

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

]

Tc=TFexp[π2kFa¯]=TFexp[2π2δkFm𝓓2].
(7)

Here kp =(3π 2 ρ)1/3 is the Fermi wave number for the total density of atoms ρ, and TF =ħ 2 kF2 /2mkB 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,

1τ=γs𝓓2ρ2δ2.
(8)

Finally, it is important to note that, with our stated goal of achieving Tc ~TF , 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.

To estimate practical experimental numbers, we first note that the rate of photoassociation in a nondegenerate sample at temperature 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

23. M. Mackie and J. Javanainen, “Quasicontinuum modeling of photoassociation,” Phys. Rev. A 60, 3174–3187 (1999). [CrossRef]

, 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]

]

R=λD3ρeδkBTΓρ(Iω)k.
(9)

Here λD=2π2μkBT is the thermal deBroglie wavelength, I is the intensity (Wcm-2) of photoassociating light, and κ (cm5) 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.

Using Eq. (9), a calculation or a measurement of the photoassociation rate in a thermal sample may be converted into a prediction of effective scattering length, transition temperature, and lifetime in a degenerate Fermi-Dirac gas. We express the results in terms of ƛ =λ/2π, wavelength of photoassociating light divided by 2π, r =ħ/(2m ƛ 2), familiar photon recoil frequency, and a characteristic intensity for the given photoassociation transition, I 0. This gives

a¯ƛ=0.0140077II0Rδ,
(10)
TcTF=exp[36.24781(ƛ3ρ)13δRI0I],
(11)
Rτ=4δ2RγsI0I1ƛ3ρ.
(12)

The obscure numerical factors, powers of 2 and π, are there because we want to use the characteristic intensity for photoassociation defined in Ref. [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]

]. For instance, if the photoassociation rate coefficient κ is known at a temperature T and detuning δ, the critical intensity is

I0=πδc42km2(kBT)32ƛ2eδkBT.
(13)

Detailed microscopic calculations (or measurements) of photoassociation rates are sparse, but they exist for the fermionic isotope 6Li 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

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

, 26

26. R. Côté and A. Dalgarno, “Mechanism for the production of 6Li2 and 7Li2 ultracold molecules,” J. Mol. Spect. 195, 236–245 (1999). [CrossRef]

, 27

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

]. Let us consider an example already discussed in Ref. [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]

], transitions to the triplet vibrational state 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 =63.3×2π kHz. We take the decay rate of the molecular state to be twice the spontaneous decay rate of the corresponding atom, so that γs =12×2π MHz. In our estimate we assume λ- 3 p=1, corresponding to the density ρ=8.21×1014 cm-3 that is high but not unreasonable. It would then take the intermediate detuning δ=2×2π 1014 Hz and the intensity I=460 MWcm-2 to make Tc =0.1 TF and τ=10 s.

The intensity came out very high for a continuous-wave laser, so it seems that the only potential candidate for experiments is a tightly focused, powerful CO2 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 CO2 laser, whose electric field is in practice direct current compared to the molecular transition frequencies involved.

To this effect we first note that in an ordinary two-level system one may carry out perturbation theory both within the rotating-wave approximation, and in the quasistatic limit without the rotating-wave approximation as well. The result is that the quasistatic results are obtained from the near-resonance formulas by replacing the detuning with the molecular transition frequency, δω0 , and multiplying the intensity by two, I→21. Applying this substitution to the scattering length, at 2 we find that, by coincidence, the intensity required for Tc =0.1TF again becomes 460MWcm-2. With the same substitutions, the lifetime would be about 20 s. However, as the frequency of the CO2 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 162~300. It is clear that spontaneous emission is not an issue with CO2 laser excitation.

Up to this point we have only considered photoassociation with one molecular state, the triplet state with vibrational quantum number 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

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

, 26

26. R. Côté and A. Dalgarno, “Mechanism for the production of 6Li2 and 7Li2 ultracold molecules,” J. Mol. Spect. 195, 236–245 (1999). [CrossRef]

, 27

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

]. We have at our disposal the photoassociation rates to all singlet and triplet vibrational states Fig. 7 of Ref. [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]

]), which are proportional to the dipole transition strengths. We may thus conclude that the 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 CO2 laser example the intensity simply gets multiplied by 0.07 and becomes 30 MW cm-2.

It is, in principle, possible to tailor the scattering length by off-resonant photoassociation, and thereby effect the BCS transition in a low-temperature Fermi gas of, say Li vapor. The required laser intensities, however, are high. As in the case of coherent photoassociation [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]

], the problem is not so much that the matrix elements for photoassociation are weak, but that the primarily photoassociated molecules tend to decay spontaneously and the sample is lost. To avoid spontaneous emission, one has to go very far off resonance, which leads to challenging requirements on laser intensity. In pursuit of the BCS transition by means of off-resonant photoassociation, it might be worthwhile to try and look for other ways of getting around the spontaneous emission.

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 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 6Li,” 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 6Li 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 474114–4122 (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]

16.

S. L. Cornish, N. R. Claussen, J. L. Roberts, E. A. Cornell, and C. E. Wieman, “Stable 85Rb 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]

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. 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 6Li2 and 7Li2 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 (2π)5.

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

  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]
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  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 .

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