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



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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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.

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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).

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