Many-body physics of ultracold alkaline-earth atoms with SU(N)-symmetric interactions

Symmetries play a crucial role in understanding phases of matter and the transitions between them. Theoretical investigations of quantum models with SU(N) symmetry have provided important insights into many-body phenomena. However, these models have generally remained a theoretical idealization, since it is very difficult to exactly realize the SU(N) symmetry in conventional quantum materials for largeN. Intriguingly however, in recent years, ultracold alkaline-earth-atom (AEA) quantum simulators have paved the path to realize SU(N)-symmetric many-body models, whereNis tunable and can be as large as 10. This symmetry emerges due to the closed shell structure of AEAs, thereby leading to a perfect decoupling of the electronic degrees of freedom from the nuclear spin. In this work, we provide a systematic review of recent theoretical and experimental work on the many-body physics of these systems. We first discuss the thermodynamic properties and collective modes of trapped Fermi gases, highlighting the enhanced interaction effects that appear asNincreases. We then discuss the properties of the SU(N) Fermi-Hubbard model, focusing on some of the major experimental achievements in this area. We conclude with a compendium highlighting some of the significant theoretical progress on SU(N) lattice models and a discussion of some exciting directions for future research.