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.

  • Article
  • Published:

Many-body Landau–Zener dynamics in coupled one-dimensional Bose liquids

Nature Physics volume 7, pages 61–67 (2011)Cite this article

Abstract

The Landau–Zener model of a quantum mechanical two-level system driven with a linearly time-dependent detuning has served over decades as a textbook model of quantum dynamics. In their seminal work, Landau and Zener derived a non-perturbative prediction for the transition probability between two states, which often serves as a reference point for the analysis of more complex systems. A particularly intriguing question is whether that framework can be extended to describe many-body quantum dynamics. Here we report an experimental and theoretical study of a system of ultracold atoms, offering a direct many-body generalization of the Landau–Zener problem. In a system of pairwise tunnel-coupled one-dimensional (1D) Bose liquids we show how tuning the correlations of the 1D gases and the tunnel coupling between the tubes strongly modify the original Landau–Zener picture. The results are explained using a mean-field description of the inter-tube condensate wavefunction, coupled to the low-energy phonons of the 1D Bose liquid.

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: LZ sweeps in a quantum ladder.
Figure 2: Influence of interactions and correlations on the characteristic sweep rate.
Figure 3: Adiabaticity breakdown in the inverse LZ sweep.
Figure 4: Influence of intra-tube correlations on the adiabaticity breakdown.
Figure 5: Changing the loop size: influence of intra-tube correlations on transfer efficiency.

Similar content being viewed by others

References

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Syassen, N. et al. Strong dissipation inhibits losses and induces correlations in cold molecular gases. Science 320, 1329–1331 (2008).

    Article  ADS  Google Scholar 

  4. Haller, E. et al. Realization of an excited, strongly correlated quantum gas phase. Science 325, 1224–1227 (2009).

    Article  ADS  Google Scholar 

  5. Stöferle, T., Moritz, H., Schori, C., Köhl, M. & Esslinger, T. Transition from a strongly interacting 1D superfluid to a Mott insulator. Phys. Rev. Lett. 92, 130403 (2004).

    Article  ADS  Google Scholar 

  6. Laburthe Tolra, B., O’Hara, K. M., Huckans, J. H., Phillips, W. D. & Porto, J. V. Observation of reduced three-body recombination in a correlated 1D degenerate Bose gas. Phys. Rev. Lett. 92, 190401 (2004).

    Article  Google Scholar 

  7. 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 

  8. Fertig, C. D. et al. Strongly inhibited transport of a 1D bose gas in a lattice. Phys. Rev. Lett. 94, 120403 (2005).

    Article  ADS  Google Scholar 

  9. Calabrese, P. & Cardy, J. Time dependence of correlation functions following a quantum quench. Phys. Rev. Lett. 96, 136801 (2006).

    Article  ADS  Google Scholar 

  10. Kollath, C., Läuchli, A. M. & Altman, E. Quench dynamics and nonequilibrium phase diagram of the Bose–Hubbard model. Phys. Rev. Lett. 98, 180601 (2007).

    Article  ADS  Google Scholar 

  11. Manmana, S. R., Wessel, S., Noack, R. M. & Muramatsu, A. Strongly correlated fermions after a quantum quench. Phys. Rev. Lett. 98, 210405 (2007).

    Article  ADS  Google Scholar 

  12. Rigol, M., Dunjko, V. & Olshanii, M. Thermalization and its mechanism for generic isolated quantum systems. Nature 452, 854–858 (2008).

    Article  ADS  Google Scholar 

  13. Gritsev, V., Barmettler, P. & Demler, E. Scaling approach to quantum non-equilibrium dynamics of many-body systems. Preprint at http://arxiv.org/abs/0912.2744 (2009).

  14. Cramer, M., Dawson, C. M., Eisert, J. & Osborne, T. J. Exact relaxation in a class of nonequilibrium quantum lattice systems. Phys. Rev. Lett. 100, 030602 (2008).

    Article  ADS  Google Scholar 

  15. Cramer, M., Flesch, A., McCulloch, I. P., Schollwöck, U. & Eisert, J. Exploring local quantum many-body relaxation by atom in optical superlattices. Phys. Rev. Lett. 101, 063001 (2008).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. Greiner, M., Mandel, O., Hänsch, T. W. & Bloch, I. Collapse and revival of the macroscopic wave function of a Bose–Einstein condensate. Nature 419, 51–54 (2002).

    Article  ADS  Google Scholar 

  18. Hofferberth, S., Lesanovski, I., Fischer, B., Schumm, T. & Schmiedmayer, J. Non-equilibrium coherence dynamics in one-dimensional Bose gases. Nature 449, 324–327 (2007).

    Article  ADS  Google Scholar 

  19. Widera, A. et al. Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases. Phys. Rev. Lett. 100, 140401 (2008).

    Article  ADS  Google Scholar 

  20. Polkovnikov, A. Universal adiabatic dynamics in the vicinity of a quantum critical point. Phys. Rev. B 72, 161201(R) (2005).

    Article  ADS  Google Scholar 

  21. Zurek, W. H., Dorner, U. & Zoller, P. Dynamics of a quantum phase transition. Phys. Rev. Lett. 96, 050503 (2006).

    Article  MathSciNet  Google Scholar 

  22. Polkovnikov, A. & Gritsev, V. Breakdown of the adiabatic limit in low-dimensional gapless systems. Nature Phys. 4, 477–481 (2008).

    Article  ADS  Google Scholar 

  23. Landau, L. D. Zur Theorie der Energieübertragung ii. Phys. Z. Sowjet. 2, 46–51 (1932).

    MATH  Google Scholar 

  24. Zener, C. Non-adiabatic crossing of energy levels. Proc. R. Soc. Lond. A 137, 692–702 (1932).

    Article  ADS  Google Scholar 

  25. Dobrescu, B. & Pokrovsky, V. Production efficiency of Feshbach molecules in fermion systems. Phys. Lett. A 350, 154–158 (2006).

    Article  ADS  Google Scholar 

  26. Tikhonenkov, I., Pazy, E., Band, Y. B., Fleischhauer, M. & Vardi, A. Many-body effects on adiabatic passage through Feshbach resonances. Phys. Rev. A 73, 043605 (2006).

    Article  ADS  Google Scholar 

  27. Gurarie, V. Feshbach molecule production in fermionic atomic gases. Phys. Rev. A 80, 023626 (2009).

    Article  ADS  Google Scholar 

  28. Gefen, Y. & Thouless, D. J. Zener transitions and energy dissipation in small driven systems. Phys. Rev. Lett. 59, 1752–1755 (1987).

    Article  ADS  Google Scholar 

  29. Ao, P. & Rammer, J. Influence of dissipation on the Landau–Zener transition. Phys. Rev. Lett. 62, 3004–3007 (1989).

    Article  ADS  Google Scholar 

  30. Fölling, S. et al. Direct observation of second-order atom tunnelling. Nature 448, 1029–1032 (2007).

    Article  ADS  Google Scholar 

  31. Trotzky, S. et al. Time-resolved observation and control of superexchange interactions with ultracold atoms in optical lattices. Science 319, 295–299 (2008).

    Article  ADS  Google Scholar 

  32. Sebby-Strabley, J. et al. Preparing and probing atomic number states with an atom interferometer. Phys. Rev. Lett. 98, 200405 (2007).

    Article  ADS  Google Scholar 

  33. Cheinet, P. et al. Counting atoms using interaction blockade in an optical superlattice. Phys. Rev. Lett. 101, 090404 (2008).

    Article  ADS  Google Scholar 

  34. Venumadhav, T., Haque, M. & Moessner, R. Finite-rate quenches of site bias in the Bose–Hubbard dimer. Phys. Rev. B 81, 054305 (2010).

    Article  ADS  Google Scholar 

  35. Danshita, I., Williams, J. E., Sá de Melo, C. A. R. & Clark, C. W. Quantum phases of bosons in double-well optical lattices. Phys. Rev. A 76, 043606 (2007).

    Article  ADS  Google Scholar 

  36. Wu, B. & Niu, Q. Nonlinear Landau–Zener tunneling. Phys. Rev. A 61, 023402 (2000).

    Article  ADS  Google Scholar 

  37. Liu, J. et al. Theory of nonlinear Landau–Zener tunneling. Phys. Rev. A 66, 023404 (2002).

    Article  ADS  Google Scholar 

  38. Jona-Lasinio, M. et al. Asymmetric Landau–Zener tunneling in a periodic potential. Phys. Rev. Lett. 91, 230406 (2003).

    Article  ADS  Google Scholar 

  39. Boson, Gerbier F. Mott insulators at finite temperatures. Phys. Rev. Lett. 99, 120405 (2007).

    Article  Google Scholar 

  40. Huber, S. D. & Altman, E. Universal dephasing of many-body Rabi oscillations of atoms in one-dimensional traps. Phys. Rev. Lett. 103, 160402 (2009).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  42. Hipolito, R. & Polkovnikov, A. Breakdown of macroscopic quantum self-trapping in coupled mesoscopic one-dimensional Bose gases. Phys. Rev. A 81, 013621 (2010).

    Article  ADS  Google Scholar 

  43. Barmettler, P., Punk, M., Gritsev, V., Demler, E. & Altman, E. Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench. Phys. Rev. Lett. 102, 130603 (2009).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We would like to thank A. Polkovnikov, G. Orso, C. Kasztelan and U. Schollwöck for stimulating discussions. This work was supported by the DFG, the EU (STREP NAMEQUAM), DARPA (OLE program), AFOSR, DIP (E.A. and I.B.) and the ISF (E.A.).

Author information

Author notes

  1. Yu-Ao Chen and Sebastian D. Huber: These authors contributed equally to this work

Authors and Affiliations

  1. Fakultät für Physik, Ludwig-Maximilian-Universität, Schellingstrasse 4, 80798 München, Germany

    Yu-Ao Chen, Stefan Trotzky & Immanuel Bloch

  2. Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany

    Yu-Ao Chen, Stefan Trotzky & Immanuel Bloch

  3. Institut für Physik, Johannes Gutenberg-Universität, Staudingerweg 7, 54099 Mainz, Germany

    Yu-Ao Chen, Stefan Trotzky & Immanuel Bloch

  4. Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot, 76100, Israel

    Sebastian D. Huber & Ehud Altman

Authors
  1. Yu-Ao Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sebastian D. Huber
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stefan Trotzky
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Immanuel Bloch
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ehud Altman
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

I.B. and E.A. conceived the research. Y-A.C. and S.T. carried out the experiment and analysed the data. S.D.H. and E.A. performed the calculations. I.B. and E.A. supervised the whole project. All authors discussed the experimental results and co-wrote the manuscript.

Corresponding authors

Correspondence to Yu-Ao Chen or Ehud Altman.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 454 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, YA., Huber, S., Trotzky, S. et al. Many-body Landau–Zener dynamics in coupled one-dimensional Bose liquids. Nature Phys 7, 61–67 (2011). https://doi.org/10.1038/nphys1801

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys1801

This article is cited by

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