Abstract

We describe our recent progress on the investigation of two-species Bose-Einstein condensation. From a theoretical analysis we show that there is a new rich phenomenology associated with two-species Bose-Einstein condensates which does not exist in a single-species condensate. We then describe results of a numerical model of the evaporative cooling process of a trapped two-species gas.

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  1. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, "Observations of Bose-Einstein condensation in a dilute atomic vapor," Science 269, 198 (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 (1995).
    [CrossRef] [PubMed]
  3. C. C. Bradley, C. A. Sackett, J. J. Tollett, and R. G. Hulet, "Evidence of Bose-Einstein condensation in an atomic gas with attractive interactions," Phys. Rev. Lett. 75, 1687 (1995).
    [CrossRef] [PubMed]
  4. C. J. Myatt, E. A. Burt, R. W. Ghrist, E. A. Cornell, and C. E. Wieman, "Production of two overlapping Bose-Einstein condensates by sympathetic cooling," Phys. Rev. Lett. 78, 586 (1997).
    [CrossRef]
  5. Tin-Lun Ho and V. B. Shenoy, "Binary mixtures of Bose condensates of alkali atoms," Phys. Rev. Lett. 77, 3276 (1996).
    [CrossRef] [PubMed]
  6. B. D. Esry, Chris H. Greene, James P. Burke, Jr., and John L. Bohn, "Hartree-Fock theory for double condensates," Phys. Rev. Lett. 78, 3594 (1995).
    [CrossRef]
  7. Elena V. Goldstein and Pierre Meystre, "Quasiparticle instabilities in multicomponent atomic condensates," Phys. Rev. A, 55, 2935 (1997).
    [CrossRef]
  8. Th. Busch, J. I. Cirac, V. M. Perez-Garcia, and P. Zoller, "Stability and collective excitations of a two-component Bose-Einstein condensed gas: a moment approach," Phys. Rev. A, 56, 2978 (1997).
    [CrossRef]
  9. C. K. Law, H. Pu, N. P. Bigelow, and J. H. Eberly, "Stability signature in two-species dilute Bose-Einstein condensates," Phys. Rev. Lett. 79, 3105 (1997).
    [CrossRef]
  10. H. Pu and N. P. Bigelow, "Properties of two-species Bose condensates," Phys. Rev. Lett. 80 1130 (1998).
    [CrossRef]
  11. H. Pu and N. P. Bigelow, "Collective excitations, metastability and nonlinear response of a trapped two-species Bose-Einstein condensate," Phys. Rev. Lett. 80 1134 (1998).
    [CrossRef]
  12. C. K. Law, H. Pu, N. P. Bigelow, and J. H. Eberly, "Quantum phase diffusion of a two-component dilute Bose-Einstein condensate," accepted by Phys. Rev. A.
  13. J. Shaffer and N. P. Bigelow, "Two-species trap experiments," Opt. Photonics News Supp. 6:7, 47 (1995).
  14. D. S. Jin, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, "Collective Excitations of a Bose-Einstein condensate in a dilute gas," Phys. Rev. Lett. 77, 420 (1996).
    [CrossRef] [PubMed]
  15. M. -O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, "Collective excitations of a Bose-Einstein condensate in a magnetic trap," Phys. Rev. Lett. 77, 988 (1996).
    [CrossRef] [PubMed]
  16. Mark Edwards, P. A. Ruprecht, K. Burnett, R. J. Dodd, and Charles W. Clark, "Collective excitations of atomic Bose-Einstein condensates," Phys. Rev. Lett. 77, 1671 (1996).
    [CrossRef] [PubMed]
  17. S. Stringari, "Collective excitations of a trapped Bose-condensed gas," Phys. Rev. Lett. 77, 2360 (1996).
    [CrossRef] [PubMed]
  18. Y. Castin and R. Dum, "Bose-Einstein condensates in time dependent traps," Phys. Rev. Lett. 77, 5315 (1996).
    [CrossRef] [PubMed]
  19. V. M. Perez-Garcia, H. Michinel, J. I. Cirac, M. Lewenstein, and P. Zoller, "Low energy excitations of a Bose-Einstein condensate: a time-dependent variational analysis," Phys. Rev. Lett. 77, 5320 (1996).
    [CrossRef] [PubMed]
  20. A. L. Fetter, "Nonuniform states of an imperfect Bose gas," Ann. Phys. (N.Y.) 70, 67 (1972).
    [CrossRef]
  21. Patrik Oehberg and Stig Stenholm,"Hartree-Fock treatment of the two-component Bose-Einstein condensate," Phys. Rev. A 57, 1272 (1998).
    [CrossRef]
  22. S. Inouye, M. R. Andrews, J. Stenger, H. -J. Meisner, D. M. Stamper-Kurn, and W. Ketterle, "Observation of Feshback resonance in a Bose-Einstein condensate," Nature 392, 151 (1998).
    [CrossRef]
  23. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press Inc., New York, 1989).
  24. D. S. Rokhsar, "Vortex stability and persistent currentsin trapped Bose gases," Phys. Rev. Lett. 79, 2164 (1997).
    [CrossRef]
  25. M. Lewenstein and L. You, "Quantum phase diffusion of a Bose-Einstein condensate," Phys. Rev. Lett. 77, 3489 (1996).
    [CrossRef] [PubMed]
  26. R. Ejnisman, Y. E. Young, P. Rudy and N. P. Bigelow, to be submitted.
  27. We have recently learned that V.Bagnato's group in S~ao Carlos, Brazil, has also been investigating a Na-Rb MOT.
  28. G.A.Bird, "Molecular Gas Dynamics," Claredon Press, Oxford, (1976).
  29. H. Wu, E. Arimondo and C. J. Foot, "Dynamics of evaporative cooling for Bose-Einstein condensation," Phys. Rev. A 56, 560 (1997).
    [CrossRef]

Other (29)

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, "Observations of Bose-Einstein condensation in a dilute atomic vapor," Science 269, 198 (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 (1995).
[CrossRef] [PubMed]

C. C. Bradley, C. A. Sackett, J. J. Tollett, and R. G. Hulet, "Evidence of Bose-Einstein condensation in an atomic gas with attractive interactions," Phys. Rev. Lett. 75, 1687 (1995).
[CrossRef] [PubMed]

C. J. Myatt, E. A. Burt, R. W. Ghrist, E. A. Cornell, and C. E. Wieman, "Production of two overlapping Bose-Einstein condensates by sympathetic cooling," Phys. Rev. Lett. 78, 586 (1997).
[CrossRef]

Tin-Lun Ho and V. B. Shenoy, "Binary mixtures of Bose condensates of alkali atoms," Phys. Rev. Lett. 77, 3276 (1996).
[CrossRef] [PubMed]

B. D. Esry, Chris H. Greene, James P. Burke, Jr., and John L. Bohn, "Hartree-Fock theory for double condensates," Phys. Rev. Lett. 78, 3594 (1995).
[CrossRef]

Elena V. Goldstein and Pierre Meystre, "Quasiparticle instabilities in multicomponent atomic condensates," Phys. Rev. A, 55, 2935 (1997).
[CrossRef]

Th. Busch, J. I. Cirac, V. M. Perez-Garcia, and P. Zoller, "Stability and collective excitations of a two-component Bose-Einstein condensed gas: a moment approach," Phys. Rev. A, 56, 2978 (1997).
[CrossRef]

C. K. Law, H. Pu, N. P. Bigelow, and J. H. Eberly, "Stability signature in two-species dilute Bose-Einstein condensates," Phys. Rev. Lett. 79, 3105 (1997).
[CrossRef]

H. Pu and N. P. Bigelow, "Properties of two-species Bose condensates," Phys. Rev. Lett. 80 1130 (1998).
[CrossRef]

H. Pu and N. P. Bigelow, "Collective excitations, metastability and nonlinear response of a trapped two-species Bose-Einstein condensate," Phys. Rev. Lett. 80 1134 (1998).
[CrossRef]

C. K. Law, H. Pu, N. P. Bigelow, and J. H. Eberly, "Quantum phase diffusion of a two-component dilute Bose-Einstein condensate," accepted by Phys. Rev. A.

J. Shaffer and N. P. Bigelow, "Two-species trap experiments," Opt. Photonics News Supp. 6:7, 47 (1995).

D. S. Jin, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, "Collective Excitations of a Bose-Einstein condensate in a dilute gas," Phys. Rev. Lett. 77, 420 (1996).
[CrossRef] [PubMed]

M. -O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, "Collective excitations of a Bose-Einstein condensate in a magnetic trap," Phys. Rev. Lett. 77, 988 (1996).
[CrossRef] [PubMed]

Mark Edwards, P. A. Ruprecht, K. Burnett, R. J. Dodd, and Charles W. Clark, "Collective excitations of atomic Bose-Einstein condensates," Phys. Rev. Lett. 77, 1671 (1996).
[CrossRef] [PubMed]

S. Stringari, "Collective excitations of a trapped Bose-condensed gas," Phys. Rev. Lett. 77, 2360 (1996).
[CrossRef] [PubMed]

Y. Castin and R. Dum, "Bose-Einstein condensates in time dependent traps," Phys. Rev. Lett. 77, 5315 (1996).
[CrossRef] [PubMed]

V. M. Perez-Garcia, H. Michinel, J. I. Cirac, M. Lewenstein, and P. Zoller, "Low energy excitations of a Bose-Einstein condensate: a time-dependent variational analysis," Phys. Rev. Lett. 77, 5320 (1996).
[CrossRef] [PubMed]

A. L. Fetter, "Nonuniform states of an imperfect Bose gas," Ann. Phys. (N.Y.) 70, 67 (1972).
[CrossRef]

Patrik Oehberg and Stig Stenholm,"Hartree-Fock treatment of the two-component Bose-Einstein condensate," Phys. Rev. A 57, 1272 (1998).
[CrossRef]

S. Inouye, M. R. Andrews, J. Stenger, H. -J. Meisner, D. M. Stamper-Kurn, and W. Ketterle, "Observation of Feshback resonance in a Bose-Einstein condensate," Nature 392, 151 (1998).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press Inc., New York, 1989).

D. S. Rokhsar, "Vortex stability and persistent currentsin trapped Bose gases," Phys. Rev. Lett. 79, 2164 (1997).
[CrossRef]

M. Lewenstein and L. You, "Quantum phase diffusion of a Bose-Einstein condensate," Phys. Rev. Lett. 77, 3489 (1996).
[CrossRef] [PubMed]

R. Ejnisman, Y. E. Young, P. Rudy and N. P. Bigelow, to be submitted.

We have recently learned that V.Bagnato's group in S~ao Carlos, Brazil, has also been investigating a Na-Rb MOT.

G.A.Bird, "Molecular Gas Dynamics," Claredon Press, Oxford, (1976).

H. Wu, E. Arimondo and C. J. Foot, "Dynamics of evaporative cooling for Bose-Einstein condensation," Phys. Rev. A 56, 560 (1997).
[CrossRef]

Supplementary Material (2)

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Figures (5)

Figure 1.
Figure 1.

Density distribution of a Na-Rb TBEC for different values of a 12. In our calculations, we take 87Rb as species 1 and 23Naas species 2, with scattering lengths 6 and 3 nm, respectively. N 1 = N 2 = 103. The trapping frequencies are: ω 1 = 2π × 160 Hz and ω 2 = 2π × 310 Hz. [Media 1]

Figure 2.
Figure 2.

Density at the center of the trap as functions of time under a sinusoid modulation of the trapping potential. The units for time, length and density are: 1 ω 1 , ξ = ħ 2 m 1 ω 1 and ξ -3, respectively. a 12 = 9.6 nm. Other parameters are the same as in Fig. 1. A macroscopic quantum jump occurs at about t=25.

Figure 3.
Figure 3.

Thermal relaxation of a mixture of Na and Rb atoms. Trap frequencies for Na: ωx = ωy = 2×ωz = 100×2πrad/s; for Rb: : ωx = ωy = 2×ωz = 52×2πrad/s. Other parameters are: densities nRb = nNa = 8 × 108 cm-3, intra-species cross-sections σNa = 2 × 10-12 cm2, σRb = 9 × 10-12 cm2.

Figure 4.
Figure 4.

Evaporative cooling of a sample containing initially an equal number of Na and Rb atoms. (a) Fraction of atoms remaining as the evaporation takes place; (b) evolution temperature of the Na and Rb atoms; (c) average radius of the samples together with the cut-off imposed by the RF-field; (d) phase space density (nλdB3) for each sample. The dashed line indicates the BEC border. Inter-species cross-section σNa-Rb = 1.8×10-12 cm2. Other parameters are the same as in Fig. 3.

Figure 5.
Figure 5.

Evolution of the Na and Rb samples in phase space (density vs. temperature). The lines indicate the BEC boundary for Na and Rb. Parameters are the same as in Fig. 4. [Media 2]

Equations (2)

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ψ 1 r t t = [ ħ 2 2 m 1 2 + 1 2 m 1 ω 1 2 r 2 + N 1 U 1 ψ 1 2 + N 2 U 12 ψ 2 2 ] ψ 1 ,
ψ 2 r t t = [ ħ 2 2 m 2 2 + 1 2 m 2 ω 2 2 r 2 + N 2 U 2 ψ 2 2 + N 1 U 12 ψ 1 2 ] ψ 2 ,

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