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Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas

Nature Physics volume 8, pages 325–330 (2012)Cite this article

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Abstract

The problem of how complex quantum systems eventually come to rest lies at the heart of statistical mechanics. The maximum-entropy principle describes which quantum states can be expected in equilibrium, but not how closed quantum many-body systems dynamically equilibrate. Here, we report the experimental observation of the non-equilibrium dynamics of a density wave of ultracold bosonic atoms in an optical lattice in the regime of strong correlations. Using an optical superlattice, we follow its dynamics in terms of quasi-local densities, currents and coherences—all showing a fast relaxation towards equilibrium values. Numerical calculations based on matrix-product states are in an excellent quantitative agreement with the experimental data. The system fulfills the promise of being a dynamical quantum simulator, in that the controlled dynamics runs for longer times than present classical algorithms can keep track of.

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Figure 1: Relaxation of the density pattern.
Figure 2: Relaxation of the local density for different interaction strengths.
Figure 3: Quasi-local current measurement.
Figure 4: Build-up of short-ranged correlations.

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References

  1. Jaksch, D. & Zoller, P. The cold atom Hubbard toolbox. Ann. Phys. 315, 52–79 (2005).

    Article  ADS  Google Scholar 

  2. Lewenstein, M. et al. Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond. Adv. Phys. 56, 243–379 (2007).

    Article  ADS  Google Scholar 

  3. Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008).

    Article  ADS  Google Scholar 

  4. Chen, Y-A., Huber, S. D., Trotzky, S., Bloch, I. & Altman, E. Many-body Landau–Zener dynamics in coupled one-dimensional Bose liquids. Nature Phys. 7, 61–67 (2011).

    ADS  Google Scholar 

  5. Polkovnikov, A., Sengupta, K., Silva, A. & Vengalattore, M. Colloquium: Nonequilibrium dynamics of closed interacting quantum systems. Rev. Mod. Phys. 83, 863–883 (2011).

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. 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 

  8. Will, S. et al. Time-resolved observation of coherent multi-body interactions in quantum phase revivals. Nature 465, 197–201 (2010).

    Article  ADS  Google Scholar 

  9. Tuchman, A. K., Orzel, C., Polkovnikov, A. & Kasevich, M. A. Nonequilibrium coherence dynamics of a soft boson lattice. Phys. Rev. A 74, 051601(R) (2006).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. Sadler, L. E., Higbie, J. M., Leslie, S. R., Vengalattore, M. & Stamper-Kurn, D. M. Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose–Einstein condensate. Nature 443, 312–315 (2006).

    Article  ADS  Google Scholar 

  12. Hofferberth, S., Lesanovsky, 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 

  13. Sebby-Strabley, J., Anderlini, M., Jessen, P. S. & Porto, J. V. Lattice of double wells for manipulating pairs of cold atoms. Phys. Rev. A 73, 033605 (2006).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. Schollwöck, U. The density-matrix renormalization group. Rev. Mod. Phys. 77, 259–315 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  16. Schollwöck, U. The density-matrix renormalization group in the age of matrix product states. Ann. Phys. 326, 96–192 (2011).

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. Flesch, A., Cramer, M., McCulloch, I. P., Schollwöck, U. & Eisert, J. Probing local relaxation of cold atoms in optical superlattices. Phys. Rev. A 78, 033608 (2008).

    Article  ADS  Google Scholar 

  19. 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  Google Scholar 

  20. Peil, S. et al. Patterned loading of a Bose–Einstein condensate into an optical lattice. Phys. Rev. A 67, 051603(R) (2003).

    Article  ADS  Google Scholar 

  21. Hastings, M. B. & Levitov, L. S. Synchronization and dephasing of many-body states in optical lattices. Preprint at http://arxiv.org/abs/0806.4283v1 (2008).

  22. 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 

  23. Cramer, M. & Eisert, J. A quantum central limit theorem for non-equilibrium systems: Exact local relaxation of correlated states. New J. Phys. 12, 055020 (2010).

    Article  ADS  Google Scholar 

  24. Calabrese, P. & Cardy, J. Evolution of entanglement entropy in one-dimensional systems. J. Stat. Mech. P04010 (2005).

  25. Osborne, T. J. Efficient approximation of the dynamics of one-dimensional quantum spin systems. Phys. Rev. Lett. 97, 157202 (2006).

    Article  ADS  Google Scholar 

  26. Weiss, D. S. et al. Another way to approach zero entropy for a finite system of atoms. Phys. Rev. A 70, 040302 (2004).

    Article  ADS  Google Scholar 

  27. Zhang, C., Rolston, S. L. & Das Sarma, S. Manipulation of single neutral atoms in optical lattices. Phys. Rev. A 74, 042316 (2006).

    Article  ADS  Google Scholar 

  28. Weitenberg, C. et al. Single-spin addressing in an atomic Mott insulator. Nature 471, 319–324 (2011).

    Article  ADS  Google Scholar 

  29. Bakr, W. S., Gillen, J. I., Peng, A., Fölling, S. & Greiner, M. A. A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice. Nature 462, 74–77 (2009).

    Article  ADS  Google Scholar 

  30. Sherson, J. F. et al. Single-atom-resolved fluorescence imaging of an atomic Mott insulator. Nature 467, 68–72 (2010).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge stimulating discussions with B. Paredes, M. Cramer and C. Gogolin. This work was supported by the Deutsche Forschungsgemeinschaft (FOR 635, FOR 801), the European Union (NAMEQUAM, QESSENCE, MINOS, COMPAS), the European Young Investigator Awards (EURYI), and Defense Advanced Research Projects Agency (DARPA) Optical Lattice Emulator (OLE) program.

Author information

Authors and Affiliations

  1. Fakultät für Physik, Ludwig-Maximilians-Universität, 80798 München, Germany

    S. Trotzky, Y-A. Chen, U. Schollwöck & I. Bloch

  2. Max-Planck Institut für Quantenoptik, 85748 Garching, Germany

    S. Trotzky, Y-A. Chen & I. Bloch

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

    S. Trotzky, Y-A. Chen & I. Bloch

  4. Institute for Advanced Simulation and JARA, Forschungszentrum Jülich, 52425 Jülich, Germany

    A. Flesch

  5. School of Physical Sciences, The University of Queensland, Brisbane, Queensland 4072, Australia

    I. P. McCulloch

  6. Institute for Advanced Study Berlin, 14193 Berlin, Germany

    U. Schollwöck & J. Eisert

  7. Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany

    J. Eisert

  8. Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany

    J. Eisert

Authors
  1. S. Trotzky
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  2. Y-A. Chen
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  4. I. P. McCulloch
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  5. U. Schollwöck
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  6. J. Eisert
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  7. I. Bloch
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Contributions

J.E., U.S. and I.B. conceived the research. S.T. and Y-A.C. performed the experiments and evaluated the data. A.F., U.S. and I.P.McC. set up the t-DMRG code and carried out the time-dependent numerical simulations. J.E. performed the analytical calculations and the analysis of mean-field and Markovian approaches. A.F. and S.T. carried out the perturbative calculations. All authors discussed the results and wrote the manuscript.

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Correspondence to S. Trotzky or A. Flesch.

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The authors declare no competing financial interests.

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Trotzky, S., Chen, YA., Flesch, A. et al. Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas. Nature Phys 8, 325–330 (2012). https://doi.org/10.1038/nphys2232

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