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Coherent spinor dynamics in a spin-1 Bose condensate

Abstract

Collisions in a thermal gas are perceived as random or incoherent as a consequence of the large numbers of initial and final quantum states accessible to the system. In a quantum gas, for example, a Bose–Einstein condensate or a degenerate Fermi gas, the phase space accessible to low-energy collisions is so restricted that collisions become coherent and reversible. Here, we report the observation of coherent spin-changing collisions in a gas of spin-1 bosons. Starting with condensates occupying two spin states, a condensate in the third spin state is coherently and reversibly created by atomic collisions. The observed dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter–wave four-wave mixing. The spin-dependent scattering length is determined from these oscillations to be −1.45(32) bohr. Finally, we demonstrate coherent control of the evolution of the system by applying differential phase shifts to the spin states using magnetic fields.

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Figure 1: Coherent spin mixing of spin-1 Bose condensate in an optical trap.
Figure 2: Coherent spin mixing versus magnetic field.
Figure 3: Coherent control of spinor dynamics.

References

  1. Nozières, P. & James, D. S. Particle vs pair condensation in attractive Bose liquids. J. Phys. 43, 1133–1148 (1982).

    Article  Google Scholar 

  2. Ensher, J. R., Jin, D. S., Matthews, M. R., Wieman, C. E. & Cornell, E. A. Bose-Einstein condensation in a dilute gas: Measurement of energy and ground-state occupation. Phys. Rev. Lett. 77, 4984–4987 (1996).

    Article  ADS  Google Scholar 

  3. Burt, E. A. et al. Coherence, correlations, and collisions: What one learns about Bose-Einstein condensates from their decay. Phys. Rev. Lett. 79, 337–340 (1997).

    Article  ADS  Google Scholar 

  4. Andrews, M. R. et al. Observation of interference between two Bose condensates. Science 275, 637–641 (1997).

    Article  Google Scholar 

  5. Madison, K. W., Chevy, F., Wohlleben, W. & Dalibard, J. Vortex formation in a stirred Bose-Einstein condensate. Phys. Rev. Lett. 84, 806–809 (2000).

    Article  ADS  Google Scholar 

  6. Matthews, M. R. et al. Vortices in a Bose-Einstein condensate. Phys. Rev. Lett. 83, 2498–2501 (1999).

    Article  ADS  Google Scholar 

  7. Abo-Shaeer, J. R., Raman, C., Vogels, J. M. & Ketterle, W. Observation of vortex lattices in Bose-Einstein condensates. Science 292, 476–479 (2001).

    Article  ADS  Google Scholar 

  8. Donley, E. A., Claussen, N. R., Thompson, S. T. & Wieman, C. E. Atom-molecule coherence in a Bose-Einstein condensate. Nature 417, 529–533 (2002).

    Article  ADS  Google Scholar 

  9. Greiner, M., Regal, C. A. & Jin, D. S. Emergence of a molecular Bose-Einstein condensate from a Fermi gas. Nature 426, 537–540 (2003).

    Article  ADS  Google Scholar 

  10. Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002).

    Article  ADS  Google Scholar 

  11. Anderson, B. P. & Kasevich, M. A. Macroscopic quantum interference from atomic tunnel arrays. Science 282, 1686–1689 (1998).

    Article  ADS  Google Scholar 

  12. Ho, T. L. Spinor Bose condensates in optical traps. Phys. Rev. Lett. 81, 742–745 (1998).

    Article  ADS  Google Scholar 

  13. Ohmi, T. & Machida, K. Bose-Einstein condensation with internal degrees of freedom in alkali atom gases. J. Phys. Soc. Jpn 67, 1822–1825 (1998).

    Article  ADS  Google Scholar 

  14. Hall, D. S., Matthews, M. R., Wieman, C. E. & Cornell, E. A. Measurements of relative phase in two-component Bose-Einstein condensates. Phys. Rev. Lett. 81, 1543–1546 (1998).

    Article  ADS  Google Scholar 

  15. Stenger, J. et al. Spin domains in ground-state Bose-Einstein condensates. Nature 396, 345–348 (1998).

    Article  ADS  Google Scholar 

  16. Barrett, M. D., Sauer, J. A. & Chapman, M. S. All-optical formation of an atomic Bose-Einstein condensate. Phys. Rev. Lett. 87, 010404 (2001).

    Article  ADS  Google Scholar 

  17. Gorlitz, A. et al. Sodium Bose-Einstein condensates in the F=2 state in a large-volume optical trap. Phys. Rev. Lett. 90, 090401 (2003).

    Article  ADS  Google Scholar 

  18. Schmaljohann, H. et al. Dynamics of F=2 spinor Bose-Einstein condensates. Phys. Rev. Lett. 92, 040402 (2004).

    Article  ADS  Google Scholar 

  19. Chang, M. S. et al. Observation of spinor dynamics in optically trapped Rb-87 Bose-Einstein condensates. Phys. Rev. Lett. 92, 140403 (2004).

    Article  ADS  Google Scholar 

  20. Koashi, M. & Ueda, M. Exact eigenstates and magnetic response of spin-1 and spin-2 Bose-Einstein condensates. Phys. Rev. Lett. 84, 1066–1069 (2000).

    Article  ADS  Google Scholar 

  21. Law, C. K., Pu, H. & Bigelow, N. P. Quantum spins mixing in spinor Bose-Einstein condensates. Phys. Rev. Lett. 81, 5257–5261 (1998).

    Article  ADS  Google Scholar 

  22. Goldstein, E. V. & Meystre, P. Quantum theory of atomic four-wave mixing in Bose-Einstein condensates. Phys. Rev. A 59, 3896–3901 (1999).

    Article  ADS  Google Scholar 

  23. Pu, H., Law, C. K., Raghavan, S., Eberly, J. H. & Bigelow, N. P. Spin-mixing dynamics of a spinor Bose-Einstein condensate. Phys. Rev. A 60, 1463–1470 (1999).

    Article  ADS  Google Scholar 

  24. Burke, J. P., Julienne, P. S., Williams, C. J., Band, Y. B. & Trippenbach, M. Four-wave mixing in Bose-Einstein condensate systems with multiple spin states. Phys. Rev. A 70, 033606 (2004).

    Article  ADS  Google Scholar 

  25. Romano, D. R. & de Passos, E. J. V. Population and phase dynamics of F=1 spinor condensates in an external magnetic field. Phys. Rev. A 70, 043614 (2004).

    Article  ADS  Google Scholar 

  26. Zhang, W., Zhou, D. L., Chang, M. -S., Chapman, M. S. & You, L. Coherent spin mixing dynamics in a spin-1 atomic condensate. Phys. Rev. A 72, 013602 (2005).

    Article  ADS  Google Scholar 

  27. Barone, A. & Paterno, G. Physics and Applications of the Josephson Effect (Wiley, New York, 1982).

    Book  Google Scholar 

  28. Hall, D. S., Matthews, M. R., Ensher, J. R., Wieman, C. E. & Cornell, E. A. Dynamics of component separation in a binary mixture of Bose-Einstein condensates. Phys. Rev. Lett. 81, 1539–1542 (1998).

    Article  ADS  Google Scholar 

  29. Zhang, W. X., Yi, S. & You, L. Mean field ground state of a spin-1 condensate in a magnetic field. New J. Phys. 5, 77 (2003).

    Article  ADS  Google Scholar 

  30. Leanhardt, A. E., Shin, Y., Kielpinski, D., Pritchard, D. E. & Ketterle, W. Coreless vortex formation in a spinor Bose-Einstein condensate. Phys. Rev. Lett. 90, 140403 (2003).

    Article  ADS  Google Scholar 

  31. Kuwamoto, T., Araki, K., Eno, T. & Hirano, T. Magnetic field dependence of the dynamics of Rb-87 spin-2 Bose-Einstein condensates. Phys. Rev. A 69, 063604 (2004).

    Article  ADS  Google Scholar 

  32. Klausen, N. N., Bohn, J. L. & Greene, C. H. Nature of spinor Bose-Einstein condensates in rubidium. Phys. Rev. A 64, 053602 (2001).

    Article  ADS  Google Scholar 

  33. 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 (2002).

    Article  ADS  Google Scholar 

  34. Burke, J. P., Greene, C. H. & Bohn, J. L. Multichannel cold collisions: Simple dependences on energy and magnetic field. Phys. Rev. Lett. 81, 3355–3358 (1998).

    Article  ADS  Google Scholar 

  35. Duan, L. M., Cirac, J. I. & Zoller, P. Quantum entanglement in spinor Bose-Einstein condensates. Phys. Rev. A 65, 033619 (2002).

    Article  ADS  Google Scholar 

  36. Pu, H., Raghavan, S. & Bigelow, N. P. Manipulating spinor condensates with magnetic fields: Stochastization, metastability, and dynamical spin localization. Phys. Rev. A 61, 023602 (2000).

    Article  ADS  Google Scholar 

  37. Miesner, H. J. et al. Observation of metastable states in spinor Bose-Einstein condensates. Phys. Rev. Lett. 82, 2228–2231 (1999).

    Article  ADS  Google Scholar 

  38. Matthews, M. R. et al. Watching a superfluid untwist itself: Recurrence of rabi oscillations in a Bose-Einstein condensate. Phys. Rev. Lett. 83, 3358–3361 (1999).

    Article  ADS  Google Scholar 

  39. Leggett, A. J. Theoretical description of new phases of liquid-He-3. Rev. Mod. Phys. 47, 331–414 (1975).

    Article  ADS  Google Scholar 

  40. Wheatley, J. C. Experimental properties of superfluid He-3. Rev. Mod. Phys. 47, 415–470 (1975).

    Article  ADS  Google Scholar 

  41. Davis, J. C. & Packard, R. E. Superfluid 3He weak links. Rev. Mod. Phys. 74, 741–773 (2001).

    Article  ADS  Google Scholar 

  42. Javanainen, J. Oscillatory exchange of atoms between traps containing Bose condensates. Phys. Rev. Lett. 57, 3164–3166 (1986).

    Article  ADS  Google Scholar 

  43. Smerzi, A., Fantoni, S., Giovanazzi, S. & Shenoy, S. R. Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates. Phys. Rev. Lett. 79, 4950–4953 (1997).

    Article  ADS  Google Scholar 

  44. Cataliotti, F. S. et al. Josephson junction arrays with Bose-Einstein condensates. Science 293, 843–846 (2001).

    Article  ADS  Google Scholar 

  45. Cennini, G. et al. All-optical realization of an atom laser. Phys. Rev. Lett. 91, 240408 (2003).

    Article  ADS  Google Scholar 

  46. Shapiro, S. Josephson currents in superconducting tunneling: the effect of microwaves and other observations. Phys. Rev. Lett. 11, 80–82 (1963).

    Article  ADS  Google Scholar 

  47. Deng, L. et al. Four-wave mixing with matter waves. Nature 398, 218–220 (1999).

    Article  ADS  Google Scholar 

  48. Widera, A. et al. Coherent collisional spin dynamics in optical lattices. Phys. Rev. Lett. (in the press); preprint at < http://arxiv.org/abs/cond-mat/0505492> (2005).

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Acknowledgements

This work was supported by NSF-PHYS 0303013 and NASA-NAG3-2893. We would like to thank C. D. Hamley, K. M. Fortier, J. A. Sauer and other members of the Georgia Tech Atomic Physics and Quantum Optics Group for their assistance, and H. Pu for valuable discussions.

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Correspondence to Michael S. Chapman.

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Chang, MS., Qin, Q., Zhang, W. et al. Coherent spinor dynamics in a spin-1 Bose condensate. Nature Phys 1, 111–116 (2005). https://doi.org/10.1038/nphys153

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