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.

  • Letter
  • Published:

A quantum Newton's cradle

Nature volume 440, pages 900–903 (2006)Cite this article

Abstract

It is a fundamental assumption of statistical mechanics that a closed system with many degrees of freedom ergodically samples all equal energy points in phase space. To understand the limits of this assumption, it is important to find and study systems that are not ergodic, and thus do not reach thermal equilibrium. A few complex systems have been proposed that are expected not to thermalize because their dynamics are integrable1,2. Some nearly integrable systems of many particles have been studied numerically, and shown not to ergodically sample phase space3. However, there has been no experimental demonstration of such a system with many degrees of freedom that does not approach thermal equilibrium. Here we report the preparation of out-of-equilibrium arrays of trapped one-dimensional (1D) Bose gases, each containing from 40 to 250 87Rb atoms, which do not noticeably equilibrate even after thousands of collisions. Our results are probably explainable by the well-known fact that a homogeneous 1D Bose gas with point-like collisional interactions is integrable. Until now, however, the time evolution of out-of-equilibrium 1D Bose gases has been a theoretically unsettled issue4,5,6, as practical factors such as harmonic trapping and imperfectly point-like interactions may compromise integrability. The absence of damping in 1D Bose gases may lead to potential applications in force sensing and atom interferometry.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Figure 1: Classical and quantum Newton's cradles.
Figure 2: Absorption images in the first oscillation cycle for initial average peak coupling strength γ o = 1.
Figure 3: The expanded momentum distribution, f(pex), for three values of γo.
Figure 4: Projected versus actual f(pex) for various γd, the dephased average peak coupling strength.

Similar content being viewed by others

References

  1. Coleman, S. Quantum sine-Gordon equation as the massive Thirring model. Phys. Rev. D 11, 2088–2097 (1975)

    Article  ADS  Google Scholar 

  2. Tabor, M. Chaos and Integrability in Nonlinear Dynamics (Wiley, New York, 1989)

    MATH  Google Scholar 

  3. Berman, G. P. & Izrailev, F. M. The Fermi-Pasta-Ulam problem: fifty years of progress. Chaos 15, 015104 (2005)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  4. Berman, G. P., Borgonovi, F., Izrailev, F. M. & Smerzi, A. Irregular dynamics in a one-dimensional Bose system. Phys. Rev. Lett. 92, 030404 (2004)

    Article  ADS  CAS  Google Scholar 

  5. Minguzzi, A. & Gangardt, D. M. Exact coherent states of a harmonically confined Tonks-Girardeau gas. Phys. Rev. Lett. 94, 240404 (2005)

    Article  ADS  Google Scholar 

  6. Proukakis, N. P., Schmiedmayer, J. & Stoof, H. T. C. Quasi-condensate growth on an atom chip. Preprint at http://arxiv.org/cond-mat/0509154 (2005).

  7. Herrmann, F. & Schmalzle, P. Simple explanation of a well-known collision experiment. Am. J. Phys. 49, 761–764 (1981)

    Article  ADS  Google Scholar 

  8. Girardeau, M. Relationship between systems of impenetrable bosons and fermions in one dimension. J. Math. Phys. 1, 516–523 (1960)

    Article  ADS  MathSciNet  Google Scholar 

  9. Girardeau, M. D. & Wright, E. M. Measurement of one-particle correlations and momentum distributions for trapped 1D gases. Phys. Rev. Lett. 87, 050403 (2001)

    Article  ADS  CAS  Google Scholar 

  10. Paredes, B. et al. Tonks-Girardeau gas of ultracold atoms in an optical lattice. Nature 429, 277–281 (2004)

    Article  ADS  CAS  Google Scholar 

  11. Kinoshita, T., Wenger, T. & Weiss, D. S. Observation of a one-dimensional Tonks-Girardeau gas. Science 305, 1125–1128 (2004)

    Article  ADS  CAS  Google Scholar 

  12. Rigol, M. & Muramatsu, A. Fermionization in an expanding 1D gas of hard-core bosons. Phys. Rev. Lett. 94, 240403 (2005)

    Article  ADS  Google Scholar 

  13. Pedri, P., Santos, L., Öhberg, P. & Stringari, S. Violation of self-similarity in the expansion of a one-dimensional Bose gas. Phys. Rev. A 68, 043601 (2003)

    Article  ADS  Google Scholar 

  14. Dunjko, V., Lorent, V. & Olshanii, M. Bosons in cigar-shaped traps: Thomas-Fermi regime, Tonks-Girardeau regime, and in between. Phys. Rev. Lett. 86, 5413–5416 (2001)

    Article  ADS  CAS  Google Scholar 

  15. Kinoshita, T., Wenger, T. & Weiss, D. S. Local pair correlations in one-dimensional Bose gases. Phys. Rev. Lett. 95, 190406 (2005)

    Article  ADS  Google Scholar 

  16. Gangardt, D. M. & Shlyapnikov, G. V. Stability and phase coherence of trapped 1D Bose gases. Phys. Rev. Lett. 90, 010401 (2003)

    Article  ADS  CAS  Google Scholar 

  17. Tolra, B. L. et al. Observation of reduced three-body recombination in a correlated 1D degenerate Bose gas. Phys. Rev. Lett. 92, 190401 (2004)

    Article  ADS  Google Scholar 

  18. Lieb, E. H. & Liniger, W. Exact analysis of an interacting Bose gas. The general solution and the ground state. Phys. Rev. 130, 1605–1616 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  19. Wu, S., Wang, Y. J., Diot, Q. & Prentiss, M. Splitting matter waves using an optimized standing-wave light-pulse sequence. Phys. Rev. A 71, 043602 (2005)

    Article  ADS  Google Scholar 

  20. Wang, Y. J. et al. Atom Michelson interferometer on a chip using a Bose-Einstein condensate. Phys. Rev. Lett. 94, 090405 (2005)

    Article  ADS  Google Scholar 

  21. Moore, M. G., Bergeman, T. & Olshanii, M. Scattering in tight atom waveguides. J. Phys. IV 116, 69–86 (2004)

    CAS  Google Scholar 

  22. Olshanii, M. Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Phys. Rev. Lett. 81, 938–941 (1998)

    Article  ADS  CAS  Google Scholar 

  23. Wu, H. & Foot, C. J. Direct simulation of evaporative cooling. J. Phys. B 29, L321–L328 (1996)

    Article  ADS  CAS  Google Scholar 

  24. Raman, C. et al. Evidence for a critical velocity in a Bose-Einstein condensed gas. Phys. Rev. Lett. 83, 2502–2505 (1999)

    Article  ADS  CAS  Google Scholar 

  25. Carusotto, I. et al. Sensitive measurement of forces at the micron scale using Bloch oscillations of ultracold atoms. Phys. Rev. Lett. 95, 093202 (2005)

    Article  ADS  CAS  Google Scholar 

  26. Fallani, L. et al. Observation of dynamical instability for a Bose-Einstein condensate in a moving 1D optical lattice. Phys. Rev. Lett. 93, 140406 (2004)

    Article  ADS  CAS  Google Scholar 

  27. Gustavson, T. L., Landragin, A. & Kasevich, M. A. Rotation sensing with a dual atom-interferometer Sagnac gyroscope. Class. Quantum Grav. 17, 2385–2398 (2000)

    Article  ADS  CAS  Google Scholar 

  28. Olshanii, M. & Dunjko, V. Interferometry in dense nonlinear media and interaction-induced loss of contrast in microfabricated atom interferometers. Preprint at http://arxiv.org/cond-mat/0505358 (2005).

  29. Miesner, H.-J. et al. Bosonic stimulation in the formation of a Bose-Einstein condensate. Science 279, 1005–1007 (1998)

    Article  ADS  CAS  Google Scholar 

  30. Kinoshita, T., Wenger, T. & Weiss, D. S. All-optical Bose-Einstein condensation using a compressible crossed dipole trap. Phys. Rev. A 71, 11602(R) (2005)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank M. Olshanii, K. O'Hara, K. Gibble and J. Jain for discussions, and the NSF for support.

Author information

Authors and Affiliations

  1. Department of Physics, The Pennsylvania State University, 104 Davey Laboratory, University Park, Pennsylvania, 16802, USA

    Toshiya Kinoshita, Trevor Wenger & David S. Weiss

Authors
  1. Toshiya Kinoshita
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Trevor Wenger
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. David S. Weiss
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David S. Weiss.

Ethics declarations

Competing interests

Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests.

Supplementary information

Supplementary Data

Contains Supplementary Fig. SI1 and SI2, their legends and notes on the observation of heating, and fine spatial structure. (DOC 381 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kinoshita, T., Wenger, T. & Weiss, D. A quantum Newton's cradle. Nature 440, 900–903 (2006). https://doi.org/10.1038/nature04693

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature04693

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

Advanced 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