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.

  • Review Article
  • Published:

Nonlinear and quantum atom optics

Abstract

Coherent matter waves in the form of Bose–Einstein condensates have led to the development of nonlinear and quantum atom optics — the de Broglie wave analogues of nonlinear and quantum optics with light. In nonlinear atom optics, four-wave mixing of matter waves and mixing of combinations of light and matter waves have been observed; such progress culminated in the demonstration of phase-coherent matter-wave amplification. Solitons represent another active area in nonlinear atom optics: these non-dispersing propagating modes of the equation that governs Bose–Einstein condensates have been created experimentally, and observed subsequently to break up into vortices. Quantum atom optics is concerned with the statistical properties and correlations of matter-wave fields. A first step in this area is the measurement of reduced number fluctuations in a Bose–Einstein condensate partitioned into a series of optical potential wells.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: The fundamental process of momentum transfer between laser fields and atoms involved in Bragg scattering.
Figure 2: Results of four-wave mixing of atomic de Broglie waves18.
Figure 3: Matter-wave amplification11.
Figure 4: Dark solitons produced in a BEC with phase imprinting28.
Figure 5: Loss of phase coherence as the atom-number distribution is squeezed in an optical lattice34.

Similar content being viewed by others

References

  1. Anderson, M. H. et al. Observation of Bose-Einstein condensation in a dilute atomic vapor. Science 269, 198–201 (1995).

    Article  ADS  CAS  Google Scholar 

  2. Inguscio, M., Stringari, S. & Wieman, C. (eds) Bose-Einstein Condensation in Atomic Gases(Int. School Phys. “Enrico Fermi” Course 140) (IOS Press, Amsterdam, 1999).

    Google Scholar 

  3. Franken, P. A., Hill, A. E., Peters, C. W. & Weinreich, G. Generation of optical harmonics. Phys. Rev. Lett. 7, 118–119 (1961).

    Article  ADS  Google Scholar 

  4. Evans, M. & Kielich, S. Modern Nonlinear Optics Vols 1–3 (Wiley, New York, 1997).

    Google Scholar 

  5. Migdall, A. Correlated-photon metrology without absolute standards. Phys. Today 52, 41–46 (1999).

    Article  ADS  CAS  Google Scholar 

  6. 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  CAS  Google Scholar 

  7. Kozuma, M. et al. Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction. Phys. Rev. Lett. 82, 871–875 (1999).

    Article  ADS  CAS  Google Scholar 

  8. Martin, P. J., Oldaker, B. G., Miklich, A. H. & Pritchard, D. E. Bragg scattering of atoms from a standing light wave. Phys. Rev. Lett. 60, 515–518 (1988).

    Article  ADS  CAS  Google Scholar 

  9. Ovchinnikov, Y. B. et al. Diffraction of a released Bose-Einstein condensate by a pulsed standing light wave. Phys. Rev. Lett. 83, 284–287 (1999).

    Article  ADS  CAS  Google Scholar 

  10. Simsarian, J. E. et al. Imaging the phase of an evolving Bose-Einstein condensate wave function. Phys. Rev. Lett. 85, 2040–2043 (2000).

    Article  ADS  CAS  Google Scholar 

  11. Kozuma, M. et al. Phase-coherent amplification of matter waves. Science 286, 2309–2312 (1999).

    Article  CAS  Google Scholar 

  12. Inouye, S. et al. Phase-coherent amplification of atomic matter waves. Nature 402, 641–644 (1999).

    Article  ADS  CAS  Google Scholar 

  13. Hagley, E. W. et al. Measurement of the coherence of a Bose-Einstein condensate. Phys. Rev. Lett. 83, 3112–3115 (1999).

    Article  ADS  CAS  Google Scholar 

  14. Stenger, J. et al. Bragg spectroscopy of a Bose-Einstein condensate. Phys. Rev. Lett. 82, 4569–4572 (1999).

    Article  ADS  CAS  Google Scholar 

  15. Shen, Y. R. The Principles of Nonlinear Optics (Wiley-Interscience, New York, 1984).

    Google Scholar 

  16. Lens, G., Meystre, P. & Wright, E. W. Nonlinear atom optics. Phys. Rev. Lett. 71, 3271–3274 (1993).

    Article  ADS  Google Scholar 

  17. Trippenbach, M., Band, Y. B. & Julienne, P. S. Four wave mixing in the scattering of Bose-Einstein condensates. Opt. Express 3, 530–537 (1998).

    Article  ADS  CAS  Google Scholar 

  18. Dalfovo, F., Giorgini, S., Pitaevskii, L. P. & Stringari, S. Theory of Bose-Einstein condensation in trapped gases. Rev. Mod. Phys. 71, 463–512 (1999).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  20. Javanianen, J. & Mackie, M, Coherent photoassociation of a Bose-Einstein condensate. Phys. Rev. A 59, R3186–R3189 (1999).

    Article  ADS  Google Scholar 

  21. Raithel, G., Phillips, W. D. & Rolston, S. L. Collapse and revivals of wave packets in optical lattices. Phys. Rev. Lett. 81, 3615–3618 (1998).

    Article  ADS  CAS  Google Scholar 

  22. Inouye, S. et al. Superradiant Rayleigh scattering from a Bose-Einstein condensate. Science 285, 571–574 (1999).

    Article  CAS  Google Scholar 

  23. Moore, M. G. & Meystre, P. Atomic four-wave mixing: fermions versus bosons. Phys. Rev. Lett. 86, 4199–4202 (2001).

    Article  ADS  CAS  Google Scholar 

  24. Ketterle, W. & Inouye, S. Dose matter wave amplification work for fermions? Phys. Rev. Lett. 86, 4203–4206 (2001).

    Article  ADS  CAS  Google Scholar 

  25. Russell, J. S. Report on waves. Report of the 14th meeting of the British Association for the Advancement of Science 331–390 (1844).

  26. Denschlag, J. et al. Generating solitons by phase engineering of a Bose-Einstein condensate. Science 287, 97–100 (2000).

    Article  ADS  CAS  Google Scholar 

  27. Burger, S. et al. Dark solitons in Bose-Einstein condensates. Phys. Rev. Lett. 83, 5198–5201 (1999).

    Article  ADS  CAS  Google Scholar 

  28. Feder, D. L. et al. Dark-soliton states of Bose-Einstein condensates in anisotropic traps. Phys. Rev. A62, 053606-1–053606-11 (2000).

    ADS  Google Scholar 

  29. Dutton, Z., Budde, M., Stowe, C. & Hau, L. V. Observation of quantum shock waves created with ultra-slow light pulses in a Bose-Einstein condensate. Science 293, 663–668 (2001).

    Article  ADS  CAS  Google Scholar 

  30. Liu, C., Dutton, Z., Behroozi, C. H. & Hau, L. V. Observation of coherent optical information storage in an atomic medium using halted light pulses. Nature 409, 490–493 (2001).

    Article  ADS  CAS  Google Scholar 

  31. Anderson, B. P. et al. Watching dark solitons decay into vortex rings in a Bose-Einstein condensate. Phys. Rev. Lett. 86, 2926–2929 (2001).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  33. 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  CAS  Google Scholar 

  34. Robert, A. et al. A Bose-Einstein condensate of metastable atoms. Science 292, 461–464 (2001).

    Article  ADS  CAS  Google Scholar 

  35. Pereira Dos Santos, F. et al. Bose-Einstein condensation of metastable helium. Phys. Rev. Lett. 86, 3459–3462 (2001).

    Article  ADS  CAS  Google Scholar 

  36. Kitagawa, M. & Ueda, M. Spin squeezed states. Phys. Rev. A 47, 5138–5143 (1993).

    Article  ADS  CAS  Google Scholar 

  37. Sørenson, A. & Mølmer, K. Spin-spin interaction and spin squeezing in an optical lattice. Phys. Rev. Lett. 83, 2274–2277 (1999).

    Article  ADS  Google Scholar 

  38. Sørenson, A., Duan, L. M., Cirac, J. I. & Zoller, P. Many-particle entanglements with Bose–Einstein condensates. Nature 409, 63–66 (2001).

    Article  ADS  Google Scholar 

  39. Helmerson, K. & You, L. Creating massive entanglement of Bose condensed atoms. Phys. Rev. Lett. 87, 170402-1–170402-4 (2001).

    Article  ADS  Google Scholar 

  40. Mewes, M.-O. et al. Output coupler for Bose-Einstein condensed atoms. Phys. Rev. Lett. 78, 582–585 (1997).

    Article  ADS  CAS  Google Scholar 

  41. Bloch, I., Hänsch, T. & Esslinger, T. Atom laser with a cw output coupler. Phys. Rev. Lett. 82, 3008–3011 (1999).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  43. Hagley, E. W. et al. A well-collimated quasi-continuous atom laser. Science 283, 1706–1709 (1999).

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

Work in this area at NIST-Gaithersburg was partly supported by the US Office of Naval Research, NASA and ARDA-NSA.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. L. Rolston.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rolston, S., Phillips, W. Nonlinear and quantum atom optics. Nature 416, 219–224 (2002). https://doi.org/10.1038/416219a

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1038/416219a

This article is cited by

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