Quantum simulation of the Hubbard model with ultracold fermions in optical lattices

TL;DR

This paper reviews recent progress in using ultracold fermionic atoms in optical lattices to simulate the Fermi-Hubbard model, highlighting experimental achievements and future challenges in understanding strongly correlated quantum systems.

Contribution

It provides a comprehensive overview of the experimental realization and study of the Fermi-Hubbard model with ultracold atoms, emphasizing recent landmark results and future directions.

Findings

Observation of quantum degeneracy and superfluidity in ultracold fermions

Demonstration of the Mott insulator regime in optical lattices

Emergence of long-range anti-ferromagnetic order

Abstract

Ultracold atomic gases provide a fantastic platform to implement quantum simulators and investigate a variety of models initially introduced in condensed matter physics or other areas. One of the most promising applications of quantum simulation is the study of strongly-correlated Fermi gases, for which exact theoretical results are not always possible with state-of-the-art approaches. Here, we review recent progress of the quantum simulation of the emblematic Fermi-Hubbard model with ultracold atoms. After introducing the Fermi-Hubbard model in the context of condensed matter, its implementation in ultracold atom systems, and its phase diagram, we review landmark experimental achievements, from the early observation of the onset of quantum degeneracy and superfluidity to demonstration of the Mott insulator regime and the emergence of long-range anti-ferromagnetic order. We conclude by discussing future challenges, including the possible observation of high-Tc superconductivity, transport properties, and the interplay of strong correlations and disorder or topology.