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Atom–molecule coherence in a Bose–Einstein condensate

Nature volume 417, pages 529–533 (2002)Cite this article

Abstract

Recent advances in the precise control of ultracold atomic systems have led to the realisation of Bose–Einstein condensates (BECs) and degenerate Fermi gases. An important challenge is to extend this level of control to more complicated molecular systems. One route for producing ultracold molecules is to form them from the atoms in a BEC. For example, a two-photon stimulated Raman transition in a 87Rb BEC has been used to produce 87Rb2 molecules in a single rotational-vibrational state1, and ultracold molecules have also been formed2 through photoassociation of a sodium BEC. Although the coherence properties of such systems have not hitherto been probed, the prospect of creating a superposition of atomic and molecular condensates has initiated much theoretical work3,4,5,6,7. Here we make use of a time-varying magnetic field near a Feshbach resonance8,9,10,11,12 to produce coherent coupling between atoms and molecules in a 85Rb BEC. A mixture of atomic and molecular states is created and probed by sudden changes in the magnetic field, which lead to oscillations in the number of atoms that remain in the condensate. The oscillation frequency, measured over a large range of magnetic fields, is in excellent agreement with the theoretical molecular binding energy, indicating that we have created a quantum superposition of atoms and diatomic molecules—two chemically different species.

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Figure 1: Feshbach resonance bound-state energy and scattering length.
Figure 2: Magnetic field pulse shape.
Figure 3: An absorption image taken after the fast magnetic-field pulse sequence and the mean-field expansion.
Figure 4: Nremnant versus tevolve for n0 = 5.4 × 1013 cm-3.
Figure 5: Oscillation frequency versus magnetic field.
Figure 6: Number versus tevolve for n0 = 1.1 × 1013 cm-3.

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References

  1. Wynar, R. H., Freeland, R. S., Han, D. J., Ryu, C. & Heinzen, D. J. Molecules in a Bose-Einstein condensate. Science 287, 1016–1019 (2000)

    Article  ADS  CAS  Google Scholar 

  2. McKenzie, C. et al. Photoassociation of sodium in a Bose-Einstein condensate. Phys. Rev. Lett. 88, 120403-1–120403-4 (2001)

    Google Scholar 

  3. Anglin, J. R. & Vardi, A. Dynamics of a two-mode Bose-Einstein condensate beyond mean-field theory. Phys. Rev. A 64, 013605-1–013605-9 (2001)

    ADS  Google Scholar 

  4. Cusack, B. J., Alexander, T. J., Ostrovskaya, E. A. & Kivshar, Y. S. Existence and stability of coupled atomic-molecular Bose-Einstein condensates. Phys. Rev. A 65, 013609-1–013609-4 (2001)

    Article  ADS  Google Scholar 

  5. Calsamiglia, J., Mackie, M. & Suominen, K. Superposition of macroscopic numbers of atoms and molecules. Phys. Rev. Lett. 87, 160403-1–160403-4 (2001)

    Article  ADS  Google Scholar 

  6. Drummond, P. D., Kheruntsyan, K. V., Heinzen, D. J. & Wynar, R. H. Stimulated Raman adiabatic passage from an atomic to a molecular Bose-Einstein condensate. Preprint cond-mat/0110578 at 〈http://xxx.lanl.gov〉 (2002).

  7. Heinzen, D. J., Wynar, R., Drummond, P. D. & Kheruntsyan, K. V. Superchemistry: dynamics of coupled atomic and molecular Bose-Einstein condensates. Phys. Rev. Lett. 84, 5029–5033 (2000)

    Article  ADS  CAS  Google Scholar 

  8. Tiesinga, E., Moerdijk, A., Verhaar, B. J. & Stoof, H. T. C. Conditions for Bose-Einstein condensation in magnetically trapped atomic cesium. Phys. Rev. A 46, R1167–R1170 (1992)

    Article  ADS  CAS  Google Scholar 

  9. Tiesinga, E., Verhaar, B. J. & Stoof, H. T. C. Threshold and resonance phenomena in ultracold ground-state collisions. Phys. Rev. A 47, 4114–4122 (1993)

    Article  ADS  CAS  Google Scholar 

  10. Moerdijk, A. J., Verhaar, B. J. & Axelson, A. Resonances in ultracold collisions of 6Li, 7Li, and 23Na. Phys. Rev. A 51, 4852–4861 (1995)

    Article  ADS  CAS  Google Scholar 

  11. van Abeelen, F. A. & Verhaar, B. J. Time-dependent Feshbach resonance scattering and anomalous decay of a Na Bose-Einstein condensate. Phys. Rev. Lett. 83, 1550–1553 (1999)

    Article  ADS  CAS  Google Scholar 

  12. Mies, F. H., Tiesinga, E. & Julienne, P. S. Manipulation of Feshbach resonances in ultracold atomic collisions using time-dependent magnetic fields. Phys. Rev. A 61, 022721-1–022721-17 (2000)

    Article  ADS  Google Scholar 

  13. van Abeelen, F. A., Heinzen, D. J. & Verhaar, B. J. Photoassociation as a probe of Feshbach resonances in cold-atom scattering. Phys. Rev. A 57, R4102–R4105 (1998)

    Article  ADS  CAS  Google Scholar 

  14. Timmermans, E., Tommasini, P., Hussein, M. & Kerman, A. Feshbach resonances in atomic Bose-Einstein condensates. Phys. Rep. 315, 199–230 (1999)

    Article  ADS  CAS  Google Scholar 

  15. Timmermans, E., Tommasini, P., Côté, R., Hussein, M. & Kerman, A. Rarified liquid properties of hybrid atomic-molecular Bose-Einstein condensates. Phys. Rev. Lett. 83, 2691–2691 (1999)

    Article  ADS  CAS  Google Scholar 

  16. Drummond, P. D., Kheruntsyan, K. V. & He, H. Coherent molecular solitons in Bose-Einstein condensates. Phys. Rev. Lett. 81, 3055–3058 (1998)

    Article  ADS  CAS  Google Scholar 

  17. Holland, M., Park, J. & Walser, R. Formation of pairing fields in resonantly coupled atomic and molecular Bose-Einstein condensates. Phys. Rev. Lett. 86, 1915–1918 (2001)

    Article  ADS  CAS  Google Scholar 

  18. Góral, K., Gajda, M. & Rza¸żewski, K. Multimode dynamics of a coupled ultracold atomic-molecular system. Phys. Rev. Lett. 86, 1397–1401 (2001)

    Article  ADS  Google Scholar 

  19. Vardi, A., Yurovsky, V. A. & Anglin, J. R. Quantum effects on the dynamics of a two-mode atom-molecule Bose-Einstein condensate. Phys. Rev. A 64, 063611-1–063611-5 (2001)

    Article  ADS  Google Scholar 

  20. Stenger, J. et al. Strongly enhanced inelastic collisions in a Bose-Einstein condensate near Feshbach resonances. Phys. Rev. Lett. 82, 2422–2425 (1999)

    Article  ADS  CAS  Google Scholar 

  21. Cornish, S. L., Claussen, N. R., Roberts, J. L., Cornell, E. A. & Wieman, C. E. Stable 85Rb Bose-Einstein condensates with widely tunable interactions. Phys. Rev. Lett. 85, 1795–1798 (2000)

    Article  ADS  CAS  Google Scholar 

  22. Claussen, N. R., Cornish, S. L., Roberts, J. L., Cornell, E. A. & Wieman, C. E. in Atomic Physics 17 (eds Arimondo, E., DeNatale, P. & Inguscio, M.) 325–336 (American Institute of Physics, New York, 2001)

    Google Scholar 

  23. Claussen, N. R., Donley, E. A., Thompson, S. T. & Wieman, C. E. Microscopic dynamics in a strongly interacting Bose-Einstein condensate. Phys. Rev. Lett. (submitted); preprint cond-mat/0201400 at 〈http://xxx.lanl.gov〉 (2002).

  24. Roberts, J. L. et al. Controlled collapse of a Bose-Einstein condensate. Phys. Rev. Lett. 86, 4211–4214 (2001)

    Article  ADS  CAS  Google Scholar 

  25. Pérez-García, V. M., Michinel, H., Cirac, J. I., Lewenstein, M. & Zoller, P. Dynamics of Bose-Einstein condensates: variational solutions of the Gross-Pitaevskii equations. Phys. Rev. A 56, 1424–1432 (1997)

    Article  ADS  Google Scholar 

  26. Donley, E. A. et al. Dynamics of collapsing and exploding Bose-Einstein condensates. Nature 412, 295–299 (2001)

    Article  ADS  CAS  Google Scholar 

  27. Sakurai, J. J. Modern Quantum Mechanics 410–416 (Addison-Wesley, Reading, Massachusetts, 1994)

    Google Scholar 

  28. Roberts, J. L. et al. Improved characterization of elastic scattering near a Feshbach resonance in 85Rb. Phys. Rev. A 64, 024702-1–024702-3 (2001)

    ADS  Google Scholar 

  29. van Kempen, E. G. M., Kokkelmans, S. J. J. M. F., Heinzen, D. J. & Verhaar, B. J. Interisotope determination of ultracold rubidium interactions from three high-precision experiments. Phys. Rev. Lett. 88, 093201-1–093201-4 (2002)

    Article  ADS  Google Scholar 

  30. Ramsey, N. F. A molecular beam resonance method with separated oscillating fields. Phys. Rev. 78, 695–699 (1950)

    Article  ADS  CAS  Google Scholar 

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Acknowledgements

We acknowledge contributions from E. A. Cornell and the JILA quantum gas collaboration. We are grateful to C. H. Greene and S. J. J. M. F. Kokkelmans for providing the coupled-channels scattering calculations presented in Fig. 5 and to L. Pitaevskii for numerous discussions. S.T.T. acknowledges the support of an ARO-MURI Fellowship. This work was also supported by ONR and NSF.

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Authors and Affiliations

  1. JILA, University of Colorado and National Institute of Standards and Technology, Boulder, Colorado, 80309-0440, USA

    Elizabeth A. Donley, Neil R. Claussen, Sarah T. Thompson & Carl E. Wieman

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  1. Elizabeth A. Donley
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Correspondence to Neil R. Claussen.

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Donley, E., Claussen, N., Thompson, S. et al. Atom–molecule coherence in a Bose–Einstein condensate. Nature 417, 529–533 (2002). https://doi.org/10.1038/417529a

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