Strong interactions between electrons in a solid material can lead to surprising properties. A prime example is the Mott insulator, in which suppression of conductivity occurs as a result of interactions rather than a filled Bloch band. Proximity to the Mott insulating phase in fermionic systems is the origin of many intriguing phenomena in condensed matter physics, most notably high-temperature superconductivity. The Hubbard model, which encompasses the essential physics of the Mott insulator, also applies to quantum gases trapped in an optical lattice. It is therefore now possible to access this regime with tools developed in atomic physics. However, an atomic Mott insulator has so far been realized only with a gas of bosons, which lack the rich and peculiar nature of fermions. Here we report the formation of a Mott insulator of a repulsively interacting two-component Fermi gas in an optical lattice. It is identified by three features: a drastic suppression of doubly occupied lattice sites, a strong reduction of the compressibility inferred from the response of double occupancy to an increase in atom number, and the appearance of a gapped mode in the excitation spectrum. Direct control of the interaction strength allows us to compare the Mott insulating regime and the non-interacting regime without changing tunnel-coupling or confinement. Our results pave the way for further studies of the Mott insulator, including spin-ordering and ultimately the question of d-wave superfluidity.

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We perform a quantitative simulation of the repulsive Fermi-Hubbard model using an ultracold gas trapped in an optical lattice. The entropy of the system is determined by comparing accurate measurements of the equilibrium double occupancy with theoretical calculations over a wide range of parameters. We demonstrate the applicability of both high-temperature series and dynamical mean-field theory to obtain quantitative agreement with the experimental data. The reliability of the entropy determination is confirmed by a comprehensive analysis of all systematic errors. In the center of the Mott insulating cloud we obtain an entropy per atom as low as 0:77k B which is about twice as large as the entropy at the Néel transition. The corresponding temperature depends on the atom number and for small fillings reaches values on the order of the tunneling energy. Experimental progress in the field of atomic quantum gases has led to a new approach to quantum many-body physics. In particular, the combination of quantum degenerate and strongly interacting Fermi gases [1,2] with optically induced lattice potentials [3] now allows the study of a centerpiece of quantum condensed matter physics, the Fermi-Hubbard model [4]. The high level of control over the atomic systems has led to the concept of quantum simulation, which for the case of the Fermi-Hubbard model is expected to provide answers to intriguing open questions of frustrated magnetism and d-wave superfluidity [5]. Recent experiments [6,7] have indeed demonstrated that the strongly correlated regime of the repulsive FermiHubbard model is experimentally accessible and the emergence of a Mott insulating state has been observed. In this Letter, we succeed in performing a quantitative simulation of the Fermi-Hubbard model using cold atoms. The level of precision of the experiment enables us to determine the entropy and the temperature of the system, and thereby to quantify the approach to the low temperature phases.The main challenge for the quantum simulation of the Fermi-Hubbard model is a further reduction in temperature. Here the lack of a quantitative thermometry method in the lattice is a key obstacle. For strongly correlated bosonic systems thermometry has recently been demonstrated by direct comparison with quantum Monte Carlo simulations [8] or by using the boundary of two spin polarized clouds [9]. In the fermionic case, previous methods to determine the temperature could be used only in limiting regimes of the Hubbard model, namely, the noninteracting [10,11] and zero-tunneling [6,12] regimes. However, intermediate interactions are most interesting for quantum simulation of the Fermi-Hubbard model and no reliable thermometry method has been available up to now.In both the metallic and Mott insulating regimes an accurate measurement of the double occupancy provides direct access to thermal excitations. We analyze the crossover from thermal creation of double occupancies to thermal depletion which is unique to a trapped system (see Fig. 1). The variability of the d...

We explore the transport properties of an interacting Fermi gas in a three-dimensional optical lattice. The center of mass dynamics of the atoms after a sudden displacement of the trap minimum is monitored for different interaction strengths and lattice fillings. With increasingly strong attractive interactions the weakly damped oscillation, observed for the noninteracting case, turns into a slow relaxational drift. Tuning the interaction strength during the evolution allows us to dynamically control the transport behavior. Strong attraction between the atoms leads to the formation of local pairs with a reduced tunneling rate. The interpretation in terms of pair formation is supported by a measurement of the number of doubly occupied lattice sites. This quantity also allows us to determine the temperature of the noninteracting gas in the lattice to be as low as (27+/-2)% of the Fermi temperature.