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arXiv:1409.8348 · Physical Review Letters

Compressibility of a Fermionic Mott Insulator of Ultracold Atoms

Pedro M. Duarte, Russell Hart, Tsung‐Lin Yang, Xinxing Liu, Thereza Paiva, Ehsan Khatami, Richard T. Scalettar, Nandini Trivedi, Randall G. Hulet

Published Feb 20, 2015• 71 citations

Abstract

We characterize the Mott insulating regime of a repulsively interacting Fermi gas of ultracold atoms in a three-dimensional optical lattice. We use in situ imaging to extract the central density of the gas and to determine its local compressibility. For intermediate to strong interactions, we observe the emergence of a plateau in the density as a function of atom number, and a reduction of the compressibility at a density of one atom per site, indicating the formation of a Mott insulator. Comparisons to state-of-the-art numerical simulations of the Hubbard model over a wide range of interactions reveal that the temperature of the gas is of the order of, or below, the tunneling energy scale. Our results hold great promise for the exploration of many-body phenomena with ultracold atoms, where the local compressibility can be a useful tool to detect signatures of different phases or phase boundaries at specific values of the filling.

DOI: 10.1103/physrevlett.114.070403

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Ultracold mixtures of different atomic species have great promise for realizing novel many-body phenomena. In a binary mixture of femions with a large mass difference and repulsive interspecies interactions, a disordered Mott insulator phase can occur. This phase displays an incompressible total density, although the relative density remain compressible. We use strong-coupling and Monte Carlo calculations to show that this phase exists for a broad parameter region for ultracold gases confined in a harmonic trap on a three-dimensional optical lattice, for experimentally accessible values of the trap parameters.

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The subtle interplay between kinetic energy, interactions, and dimensionality challenges our comprehension of strongly correlated physics observed, for example, in the solid state.In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics.Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions 0 ≲ U=t ≲ 20 and temperatures, down to k B T=t ¼ 0.63ð2Þ using highresolution imaging of ultracold fermionic atoms in optical lattices.We show density profiles, compressibilities, and double occupancies over the whole doping range, and, hence, our results constitute benchmarks for state-of-the-art theoretical approaches.