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:

Non-equilibrium coherence dynamics in one-dimensional Bose gases

Nature volume 449, pages 324–327 (2007)Cite this article

Abstract

Low-dimensional systems provide beautiful examples of many-body quantum physics1. For one-dimensional (1D) systems2, the Luttinger liquid approach3 provides insight into universal properties. Much is known of the equilibrium state, both in the weakly4,5,6,7 and strongly8,9 interacting regimes. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached10. Here we present a direct experimental study of the coherence dynamics in both isolated and coupled degenerate 1D Bose gases. Dynamic splitting is used to create two 1D systems in a phase coherent state11. The time evolution of the coherence is revealed through local phase shifts of the subsequently observed interference patterns. Completely isolated 1D Bose gases are observed to exhibit universal sub-exponential coherence decay, in excellent agreement with recent predictions12. For two coupled 1D Bose gases, the coherence factor is observed to approach a non-zero equilibrium value, as predicted by a Bogoliubov approach13. This coupled-system decay to finite coherence is the matter wave equivalent of phase-locking two lasers by injection. The non-equilibrium dynamics of superfluids has an important role in a wide range of physical systems, such as superconductors, quantum Hall systems, superfluid helium and spin systems14,15,16. Our experiments studying coherence dynamics show that 1D Bose gases are ideally suited for investigating this class of phenomena.

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: Schematic of the experiment.
Figure 2: Direct observation of the phase dynamics through interference.
Figure 3: Time evolution of the coherence factor for uncoupled 1D quasi-condensates.
Figure 4: Time evolution of the coherence factor for coupled 1D quasi-condensates.

Similar content being viewed by others

References

  1. Popov, V. N. Functional Integrals in Quantum Field Theory and Statistical Physics (Reidel, Dordrecht, 1983)

    Book  MATH  Google Scholar 

  2. Giamarchi, T. Quantum Physics in One Dimension (Oxford Univ. Press, Oxford, 2003)

    Book  MATH  Google Scholar 

  3. Haldane, F. Effective harmonic-fluid approach to low-energy properties of one-dimensional quantum fluids. Phys. Rev. Lett. 47, 1840–1843 (1981)

    Article  CAS  ADS  Google Scholar 

  4. Petrov, D. S., Shlyapnikov, G. V. & Walraven, J. T. M. Regimes of quantum degeneracy in trapped 1D gases. Phys. Rev. Lett. 85, 3745–3749 (2000)

    Article  CAS  ADS  PubMed  Google Scholar 

  5. Dettmer, S. et al. Observation of phase fluctuations in elongated Bose-Einstein condensates. Phys. Rev. Lett. 87, 160406 (2001)

    Article  CAS  ADS  PubMed  Google Scholar 

  6. Richard, S. et al. Momentum spectroscopy of 1D phase fluctuations in Bose-Einstein condensates. Phys. Rev. Lett. 91, 010405 (2003)

    Article  CAS  ADS  PubMed  Google Scholar 

  7. Pricoupenko, L., Perrin, H. & Olshanii, M. Quantum Gases in Low Dimensions (Journal de Physique IV Proceedings, Vol. 116, EDP Sciences, 2004)

    Google Scholar 

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

    Article  CAS  ADS  PubMed  Google Scholar 

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

    Article  CAS  ADS  PubMed  Google Scholar 

  10. Kinoshita, T., Wenger, T. R. & Weiss, D. S. A quantum Newton’s cradle. Nature 440, 900–903 (2006)

    Article  CAS  ADS  PubMed  Google Scholar 

  11. Schumm, T. et al. Matter wave interferometry in a double well on an atom chip. Nature Phys. 1, 57–62 (2005)

    Article  CAS  ADS  Google Scholar 

  12. Burkov, A. A., Lukin, M. D. & Demler, E. Decoherence dynamics in low-dimensional cold atoms interferometers. Phys. Rev. Lett. 98, 200404 (2007)

    Article  CAS  ADS  PubMed  Google Scholar 

  13. Whitlock, N. K. & Bouchoule, I. Relative phase fluctuations of two coupled one-dimensional condensates. Phys. Rev. A 68, 053609 (2003)

    Article  ADS  CAS  Google Scholar 

  14. Blatter, G., Feigelman, M., Geshkenbein, V., Larkin, A. & Vinokur, V. Vortices in high-temperature superconductors. Rev. Mod. Phys. 66, 1125–1388 (1994)

    Article  CAS  ADS  Google Scholar 

  15. Shimshoni, E., Auerbach, A. & Kapitulnik, A. Transport through quantum melts. Phys. Rev. Lett. 80, 3352–3355 (1998)

    Article  CAS  ADS  Google Scholar 

  16. Forte, S. Quantum mechanics and field theory with fractional spin and statistics. Rev. Mod. Phys. 64, 193–236 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  17. Folman, R., Krüger, P., Schmiedmayer, J., Denschlag, J. & Henkel, C. Microscopic atom optics: From wires to an atom chip. Adv. At. Mol. Opt. Phys. 48, 263–356 (2002)

    Article  CAS  ADS  Google Scholar 

  18. Fortagh, J. & Zimmermann, C. Magnetic microtraps for ultracold atoms. Rev. Mod. Phys. 79, 235 (2007)

    Article  CAS  ADS  Google Scholar 

  19. Bouchoule, I., Kheruntsyan, K. V. & Shlyapnikov, G. V. Interaction-induced crossover versus finite-size condensation in a weakly interacting trapped one-dimensional Bose gas. Phys. Rev. A 75, 031606(R) (2007)

    Article  ADS  CAS  Google Scholar 

  20. Hofferberth, S., Lesanovsky, I., Fischer, B., Verdu, J. & Schmiedmayer, J. Radio-frequency dressed state potentials for neutral atoms. Nature Phys. 2, 710–716 (2006)

    Article  CAS  ADS  Google Scholar 

  21. Jo, G. B. et al. Matter-wave interferometry with phase fluctuating Bose-Einstein condensates. Preprint at 〈http://arxiv.org/abs/0706.4041v3〉 (2007)

  22. Spietz, L., Lehnert, K. W., Siddiqi, I. & Schoelkopf, R. J. Primary electronic thermometry using the shot noise of a tunnel junction. Science 300, 1929–1932 (2003)

    Article  CAS  ADS  PubMed  Google Scholar 

  23. Gati, R., Hemmerling, B., Fölling, J., Albiez, M. & Oberthaler, M. K. Noise thermometry with two weakly coupled Bose-Einstein condensates. Phys. Rev. Lett. 96, 130404 (2006)

    Article  ADS  CAS  PubMed  Google Scholar 

  24. Bistritzer, R. & Altman, E. Intrinsic dephasing in one dimensional ultracold atom interferometers. Proc. Natl Acad. Sci. USA 104, 9955–9959 (2007)

    Article  CAS  ADS  PubMed  Google Scholar 

  25. Andreev, A. F. The hydrodynamics of two-dimensional and one-dimensional fluids. Sov. Phys. JETP 51, 1038–1040 (1980)

    ADS  Google Scholar 

  26. Rigol, M., Dunjko, V., Yurovsky, V. & Olshanii, M. Relaxation in a completely integrable many-body quantum system: An ab initio study of the dynamics of the highly excited states of 1d lattice hard-core bosons. Phys. Rev. Lett. 98, 050405 (2007)

    Article  ADS  CAS  PubMed  Google Scholar 

  27. Cazalilla, M. Bosonizing one-dimensional cold atomic gases. J. Phys. B 37, S1–S47 (2004)

    Article  CAS  ADS  Google Scholar 

  28. Ananikian, D. & Bergeman, T. The Gross-Pitaevskii equation for Bose particles in a double well potential: Two mode models and beyond. Phys. Rev. A 73, 013604 (2006)

    Article  ADS  CAS  Google Scholar 

  29. Bouchoule, I. Modulational instabilities in Josephson oscillations of elongated coupled condensates. Eur. Phys. J. D 35, 147–154 (2005)

    Article  CAS  ADS  Google Scholar 

  30. Gritsev, V., Polkovnikov, A. & Demler, E. Linear response theory for a pair of coupled one-dimensional condensates of interacting atoms. Phys. Rev. B 75, 174511 (2007)

    Article  ADS  CAS  Google Scholar 

  31. Gritsev, V., Demler, E., Lukin, M. & Polkovnikov, A. Analysis of quench dynamics of coupled one dimensional condensates using quantum sine Gordon model. Preprint at 〈http://arxiv.org/cond-mat/0702343〉

  32. Wildermuth, S. et al. Optimized magneto-optical trap for experiments with ultracold atoms near surfaces. Phys. Rev. A 69, 030901 (2004)

    Article  ADS  CAS  Google Scholar 

  33. Groth, S. et al. Atom chips: Fabrication and thermal properties. Appl. Phys. Lett. 85, 2980–2982 (2004)

    Article  CAS  ADS  Google Scholar 

  34. Krüger, P. et al. Disorder potentials near lithographically fabricated atom chips. Preprint at 〈http://arxiv.org/cond-mat/0504686〉 (2004)

  35. Wildermuth, S. et al. Sensing electric and magnetic fields with Bose-Einstein condensates. Appl. Phys. Lett. 88, 264103 (2006)

    Article  ADS  CAS  Google Scholar 

  36. Lesanovsky, I. et al. Adiabatic radio frequency potentials for the coherent manipulation of matter waves. Phys. Rev. A 73, 033619 (2006)

    Article  ADS  CAS  Google Scholar 

  37. Hofferberth, S., Fischer, B., Schumm, T., Schmiedmayer, J. & Lesanovsky, I. Ultracold atoms in radio-frequency dressed potentials beyond the rotating-wave approximation. Phys. Rev. A 76, 013401 (2007)

    Article  ADS  CAS  Google Scholar 

  38. Hadzibabic, Z., Krüger, P., Cheneau, M., Battelier, B. & Dalibard, J. Berezinskii-Kosterlitz-Thouless crossover in a trapped atomic gas. Nature 441, 1118–1121 (2006)

    Article  CAS  ADS  PubMed  Google Scholar 

  39. Gerbier, F. Quasi-1d Bose-Einstein condensates in the dimensional crossover regime. Europhys. Lett. 66, 771–777 (2004)

    Article  CAS  ADS  Google Scholar 

  40. 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  CAS  ADS  Google Scholar 

  41. Röhrl, A., Naraschewski, M., Schenzle, A. & Wallis, H. Transition from phase locking to the interference of independent Bose condensates: Theory versus experiment. Phys. Rev. Lett. 78, 4143–4146 (1997)

    Article  ADS  Google Scholar 

  42. Fisher, N. I. Statistical Analysis of Circular Data (Cambridge Univ. Press, Cambridge, UK, 1993)

    Book  MATH  Google Scholar 

Download references

Acknowledgements

We thank A Burkov, V. Gritsev, E. Demler, R. Bistritzer and E. Altman for discussions. We also thank S. Groth for fabricating the atom chip used in the experiments. We acknowledge financial support from the Wittgenstein Prize and the European Union, through Atom Chips and FET/QIPC SCALA projects.

Author information

Authors and Affiliations

  1. Physikalisches Institut, Universität Heidelberg, Philosophenweg 12, D-69120 Heidelberg, Germany,

    S. Hofferberth, B. Fischer & J. Schmiedmayer

  2. Atominstitut der Österreichischen Universitäten, TU-Wien, Stadionallee 2, A-1020 Vienna, Austria,

    S. Hofferberth, T. Schumm & J. Schmiedmayer

  3. Institut für Theoretische Physik, Universität Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria,

    I. Lesanovsky

Authors
  1. S. Hofferberth
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. Lesanovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. Fischer
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. T. Schumm
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. J. Schmiedmayer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Schmiedmayer.

Ethics declarations

Competing interests

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

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hofferberth, S., Lesanovsky, I., Fischer, B. et al. Non-equilibrium coherence dynamics in one-dimensional Bose gases. Nature 449, 324–327 (2007). https://doi.org/10.1038/nature06149

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature06149

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