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Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms


Transport properties are among the defining characteristics of many important phases in condensed-matter physics. In the presence of strong correlations they are difficult to predict, even for model systems such as the Hubbard model. In real materials, additional complications arise owing to impurities, lattice defects or multi-band effects. Ultracold atoms in contrast offer the possibility to study transport and out-of-equilibrium phenomena in a clean and well-controlled environment and can therefore act as a quantum simulator for condensed-matter systems. Here we studied the expansion of an initially confined fermionic quantum gas in the lowest band of a homogeneous optical lattice. For non-interacting atoms, we observe ballistic transport, but even small interactions render the expansion almost bimodal, with a dramatically reduced expansion velocity. The dynamics is independent of the sign of the interaction, revealing a novel, dynamic symmetry of the Hubbard model.

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Figure 1: Expansion of fermionic atoms after a quench of the trapping potential.
Figure 2: Expansion of non-interacting fermions.
Figure 3: Expansion of interacting fermions.
Figure 4: Core-expansion velocities.

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We thank M. Moreno-Cardoner, F. Heidrich-Meisner, D. Pekker and R. Sensarma, B. Kawohl, C. Kiefer, J. Krug and M. Zirnbauer for stimulating and insightful discussions.

This work was supported by the Deutsche Forschungsgemeinschaft (FOR801, SFB TR 12, SFB 608, Gottfried Wilhelm Leibniz Prize), the European Union (Integrated Project SCALA), EuroQUAM (L.H.), the US Defense Advanced Research Projects Agency (Optical Lattice Emulator program), the US Air Force Office of Scientific Research (Quantum Simulation MURI (E.D.)), the National Science Foundation (DMR-07-05472) (E.D.), the Harvard-MIT CUA (E.D.), MATCOR (S.W.), the Gutenberg Akademie (S.W.) and the German National Academic Foundation (S.M.).

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Authors and Affiliations



U.S., L.H. and J.P.R. carried out the measurements, U.S. performed the data analysis with contributions from L.H. and J.P.R.. I.B. supervised the measurements. S.M. and D.R. performed the numerical calculations supervised by A.R.. E.D., U.S. and A.R. constructed the analytical proof of the dynamical symmetry. U.S. and A.R. wrote the manuscript with substantial contributions by I.B. and all authors.

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Correspondence to Ulrich Schneider.

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Schneider, U., Hackermüller, L., Ronzheimer, J. et al. Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms. Nature Phys 8, 213–218 (2012).

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