Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Collapse and revival of the matter wave field of a Bose–Einstein condensate

Abstract

A Bose–Einstein condensate represents the most ‘classical’ form of a matter wave, just as an optical laser emits the most classical form of an electromagnetic wave. Nevertheless, the matter wave field has a quantized structure owing to the granularity of the discrete underlying atoms. Although such a field is usually assumed to be intrinsically stable (apart from incoherent loss processes), this is no longer true when the condensate is in a coherent superposition of different atom number states1,2,3,4,5,6. For example, in a Bose–Einstein condensate confined by a three-dimensional optical lattice, each potential well can be prepared in a coherent superposition of different atom number states, with constant relative phases between neighbouring lattice sites. It is then natural to ask how the individual matter wave fields and their relative phases evolve. Here we use such a set-up to investigate these questions experimentally, observing that the matter wave field of the Bose–Einstein condensate undergoes a periodic series of collapses and revivals; this behaviour is directly demonstrated in the dynamical evolution of the multiple matter wave interference pattern. We attribute the oscillations to the quantized structure of the matter wave field and the collisions between individual atoms.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Quantum dynamics of a coherent state owing to cold collisions.
Figure 2: Dynamical evolution of the multiple matter wave interference pattern observed after jumping from a potential depth VA = 8 Er to a potential depth VB = 22 Er and a subsequent variable hold time t.
Figure 3: Number of coherent atoms relative to the total number of atoms monitored over time for the same experimental sequence as in Fig. 2.
Figure 4: Revival period in the dynamical evolution of the interference pattern after jumping to different potential depths VB from a potential depth of VA = 5.5 Er.
Figure 5: Influence of the atom number statistics on the collapse time.

References

  1. Wright, E. M., Walls, D. F. & Garrison, J. C. Collapses and revivals of Bose-Einstein condensates formed in small atomic samples. Phys. Rev. Lett. 77, 2158–2161 (1996)

    ADS  CAS  Article  Google Scholar 

  2. Wright, E. M., Wong, T., Collett, M. J., Tan, S. M. & Walls, D. F. Collapses and revivals in the interference between two Bose-Einstein condensates formed in small atomic samples. Phys. Rev. A 56, 591–602 (1997)

    ADS  CAS  Article  Google Scholar 

  3. Imamoglu, A., Lewenstein, M. & You, L. Inhibition of coherence in trapped Bose-Einstein condensates. Phys. Rev. Lett. 78, 2511–2514 (1997)

    ADS  CAS  Article  Google Scholar 

  4. Castin, Y. & Dalibard, J. Relative phase of two Bose-Einstein condensates. Phys. Rev. A 55, 4330–4337 (1997)

    ADS  CAS  Article  Google Scholar 

  5. Dunningham, J. A., Collett, M. J. & Walls, D. F. Quantum state of a trapped Bose-Einstein condensate. Phys. Lett. A 245, 49–54 (1998)

    ADS  CAS  Article  Google Scholar 

  6. Zhang, W. & Walls, D. F. Bosonic-degeneracy-induced quantum correlation in a nonlinear atomic beam splitter. Phys. Rev. A 52, 4696–4703 (1995)

    ADS  CAS  Article  Google Scholar 

  7. Walls, D. F. & Milburn, G. J. Quantum Optics (Springer, Berlin, 1994)

    Book  Google Scholar 

  8. Milburn, G. J. & Holmes, C. A. Dissipative quantum and classical Liouville mechanics of the anharmonic oscillator. Phys. Rev. Lett. 56, 2237–2240 (1986)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  9. Daniel, D. J. & Milburn, G. J. Destruction of quantum coherence in a nonlinear oscillator via attenuation and amplification. Phys. Rev. A 39, 4628–4640 (1989)

    ADS  CAS  Article  Google Scholar 

  10. Orzel, C., Tuchman, A. K., Fenselau, M. L., Yasuda, M. & Kasevich, M. A. Squeezed states in a Bose-Einstein condensate. Science 291, 2386–2389 (2001)

    ADS  CAS  Article  Google Scholar 

  11. 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)

    ADS  CAS  Article  Google Scholar 

  12. Fisher, M. P. A., Weichman, P. B., Grinstein, G. & Fisher, D. S. Boson localization and the superfluid-insulator transition. Phys. Rev. B 40, 546–570 (1989)

    ADS  CAS  Article  Google Scholar 

  13. Jaksch, D., Bruder, C., Cirac, J. I., Gardiner, C. W. & Zoller, P. Cold bosonic atoms in optical lattices. Phys. Rev. Lett. 81, 3108–3111 (1998)

    ADS  CAS  Article  Google Scholar 

  14. Greiner, M., Bloch, I., Mandel, O., Hänsch, T. W. & Esslinger, T. Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Phys. Rev. Lett. 87, 160405-1–160405-4 (2001)

    ADS  Google Scholar 

  15. Greiner, M., Bloch, I., Hänsch, T. W. & Esslinger, T. Magnetic transport of trapped cold atoms over a large distance. Phys. Rev. A 63, 031401-1–031401-4 (2001)

    ADS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  17. Rokhsar, D. S. & Kotliar, B. G. Gutzwiller projection for bosons. Phys. Rev. B 44, 10328–10332 (1991)

    ADS  CAS  Article  Google Scholar 

  18. Jaksch, D., Briegel, H. J., Cirac, J. I., Gardiner, C. W. & Zoller, P. Entanglement of atoms via cold controlled collisions. Phys. Rev. Lett. 82, 1975–1978 (1999)

    ADS  CAS  Article  Google Scholar 

  19. Briegel, H. J., Calarco, T., Jaksch, D., Cirac, J. I. & Zoller, P. Quantum computing with neutral atoms. J. Mod. Opt. 47, 415–451 (2000)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  20. Briegel, H. J. & Raussendorf, R. Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910–913 (2001)

    ADS  CAS  Article  Google Scholar 

  21. Raussendorf, R. & Briegel, H. J. A one-way quantum computer. Phys. Rev. Lett. 86, 5188–5191 (2001)

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

We thank W. Zwerger, T. Esslinger, A. Görlitz, H. Briegel, E. Wright and I. Cirac for discussions, and A. Altmeyer for help in the final stages of the experiment. This work was supported by the DFG.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Immanuel Bloch.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Greiner, M., Mandel, O., Hänsch, T. et al. Collapse and revival of the matter wave field of a Bose–Einstein condensate. Nature 419, 51–54 (2002). https://doi.org/10.1038/nature00968

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature00968

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing