The Hubbard model contains only the essential ingredients to describe the behavior of strongly interacting electrons moving in a periodic lattice. It describes particles that can tunnel between sites in the lattice and that acquire an on-site interaction energy when two of them occupy the same lattice site. This simple model is a prominent example of how strongly correlated phases emerge from simple Hamiltonians. It gives rise to a Mott-metal insulator transition, and at a density of one particle per site shows an antiferromagnetic ground state. It is also considered to contain the essence of high-temperature superconductivity as observed in the cuprates, a question that remains open due to the difficulty in numerically accessing the solutions of the model at densities different than one particle per site.

In this work we have realized the Hubbard model with a spin mixture of ultracold atoms in a simple cubic optical lattice. Atoms in lattices have emerged in the last decade as promising systems in which to perform quantum simulations of condensed matter Hamiltonians. In the laboratory we can create defect-free optical lattice potentials with laser light, and we can control the interactions between the atoms using a magnetic Feshbach resonance.

For this work we implemented a novel compensated optical lattice setup, which allows us to control the density of the sample and mitigate the non-adiabaticity in the lattice loading process which often leads to heating of the sample or to out of equilibrium distributions. Using the compensated optical lattice we are able to get closer to the ground state of the Hubbard model than anybody before us has been able to do so with ultracold atoms.

To demonstrate this achievement we use spin-sensitive Bragg scattering of light to measure the spin-structure factor, a measure of the antiferromagnetic correlations in the collection of spins. Measurements of the spin-structure factor are compared to theoretical calculations to establish precise thermometry of the atoms in the lattice. We have also studied the in-situ density distribution of the system, which confirms that the temperature of our sample is in a regime where most of the remaining entropy in the system resides in the spin degree of freedom. The results presented here represent an important step in the field of quantum simulation with ultracold atoms. In the future, we expect to further explore and exploit the experimental possibilities opened up by the compensated lattice potential and by light scattering thermometry, with the ultimate goal of addressing the existence of d-wave superfluidity in the Hubbard model.