Correlations and Universality in Ultracold Alkaline Earth Atoms

Ultracold alkaline-earth fermions in an optical lattice realize the famous Hubbard model from solid-state physics, but with spins tunable to be as large as $S=9/2$, instead of the usual $S=1/2$. Although $S$ can be large, the system remains non-classical due to an enlarged SU($N$) interaction symmetry that protects quantum fluctuations and leads to new phases of matter. However, just as for the $N=2$ Hubbard model, it has remained an outstanding challenge for cold atoms experiments to achieve temperatures low enough to observe phenomena such as superconductivity and magnetic order. I will describe how enlarging SU(2) to SU($N$) not only enriches the physics, but lowers the temperature and increases magnetic correlations, as recently observed by the Kyoto group [1] in 1D, 2D, and 3D. Our calculations agree with the measurements in broad regimes. This allows thermometry, showing that the experiments in 1D have produced the coldest fermions ever achieved. The calculations also reveal surprising universality in the equations of state, pointing to simple underlying physics. Finally, I will describe important future directions for understanding longer range correlations and dynamics.