Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions

TL;DR

This paper reviews recent theoretical and experimental advances in understanding the many-body physics of ultracold alkaline-earth atoms with SU(N) symmetry, emphasizing their unique properties and potential for quantum simulation.

Contribution

It provides a comprehensive review of the thermodynamics, collective modes, and lattice models of SU(N) symmetric ultracold atom systems, highlighting new experimental achievements and theoretical insights.

Findings

Enhanced interaction effects with increasing N

Experimental realization of SU(N) Fermi-Hubbard models

Progress in understanding SU(N) lattice models

Abstract

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 large $N$. Intriguingly however, in recent years, ultracold alkaline-earth-atom (AEA) quantum simulators have paved the path to realize SU($N$)-symmetric many-body models, where $N$ is 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 as $N$ increases. 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.