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# Metallic and Insulating Phases of Repulsively Interacting Fermions in a 3D Optical Lattice

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### Abstract

The fermionic Hubbard model plays a fundamental role in the description of strongly correlated materials. Here we report on the realization of this Hamiltonian using a repulsively interacting spin mixture of ultracold $$^{40}$$K atoms in a 3D optical lattice. We have implemented a new method to directly measure the compressibility of the quantum gas in the trap using in-situ imaging and independent control of external confinement and lattice depth. Together with a comparison to ab-initio Dynamical Mean Field Theory calculations, we show how the system evolves for increasing confinement from a compressible dilute metal over a strongly-interacting Fermi liquid into a band insulating state. For strong interactions, we find evidence for an emergent incompressible Mott insulating phase.

### Most cited references6

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### Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

(1996)
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### Creation of ultracold molecules from a Fermi gas of atoms

(2003)
Since the realization of Bose-Einstein condensates (BEC) in atomic gases an experimental challenge has been the production of molecular gases in the quantum regime. A promising approach is to create the molecular gas directly from an ultracold atomic gas; for example, atoms in a BEC have been coupled to electronic ground-state molecules through photoassociation as well as through a magnetic-field Feshbach resonance. The availability of atomic Fermi gases provides the exciting prospect of coupling fermionic atoms to bosonic molecules, and thus altering the quantum statistics of the system. This Fermi-Bose coupling is closely related to the pairing mechanism for a novel fermionic superfluid proposed to occur near a Feshbach resonance. Here we report the creation and quantitative characterization of exotic, ultracold $$^{40}$$K$$_2$$ molecules. Starting with a quantum degenerate Fermi gas of atoms at T < 150 nanoKelvin we scan over a Feshbach resonance to adiabatically create over a quarter million trapped molecules, which we can convert back to atoms by reversing the scan. The small binding energy of the molecules is controlled by detuning from the Feshbach resonance and can be varied over a wide range. We directly detect these weakly bound molecules through rf photodissociation spectra that probe the molecular wavefunction and yield binding energies that are consistent with theory.
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### Finite temperature numerical renormalization group study of the Mott-transition

(2000)
Wilson's numerical renormalization group (NRG) method for the calculation of dynamic properties of impurity models is generalized to investigate the effective impurity model of the dynamical mean field theory at finite temperatures. We calculate the spectral function and self-energy for the Hubbard model on a Bethe lattice with infinite coordination number directly on the real frequency axis and investigate the phase diagram for the Mott-Hubbard metal-insulator transition. While for T T_c there is a smooth crossover from metallic-like to insulating-like solutions.
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### Author and article information

###### Journal
08 September 2008
0809.1464
10.1126/science.1165449