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Solid state physics with fermionic atomic quantum gases: engineering metals and Mott insulators in an optical lattice

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Strong interactions between electrons in a solid material lead to surprising effects such as the Mott insulator, where a suppression of conductivity occurs due to interactions rather than due to a filled Bloch band. Proximity to the Mott insulating phase is the origin of many intriguing phenomena in condensed matter physics, most notably high-temperature superconductivity. We experimentally implement the Fermi-Hubbard model, which encompasses the physics of the Mott insulator, by trapping a repulsively interacting two-component Fermi gas in an optical lattice. The system is characterized using accurate measurements of the double occupancy. By comparison with ab initio calculations we determine the entropy of the sample and identify metallic as well as Mott insulating states. The unique control over the creation of double occupancies and the high resolution in detecting them also allow us to study dynamic and non-equilibrium properties. Starting with a repulsively interacting gas of fermions, we perturb the sample by modulating the lattice depth and monitor the increase of doublons with time. The observed behavior is captured by linear response theory and is sensitive to temperature and local spin ordering. Additionally, we measure the lifetime of doublons in the isolated many-body system. Over two orders of magnitude, it shows an exponential dependence on the ratio of interaction energy to kinetic energy, in agreement with diagrammatic calculations

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