Fermi gases in one dimension: From Bethe Ansatz to experiments

TL;DR

This review discusses theoretical models and experimental findings on one-dimensional Fermi gases, highlighting exact solutions like the Bethe ansatz and their relevance to phenomena such as pairing, Luttinger liquids, and quantum criticality.

Contribution

It synthesizes recent advances in understanding 1D Fermi gases through exact models and experiments, emphasizing the connection between theory and real-world systems.

Findings

Exact Bethe ansatz solutions elucidate quantum many-body phenomena.

Experimental realizations confirm theoretical predictions of 1D Fermi physics.

Identification of novel states like trions and FFLO-like pair correlations.

Abstract

This article reviews theoretical and experimental developments for one-dimensional Fermi gases. Specifically, the experimentally realized two-component delta-function interacting Fermi gas -- the Gaudin-Yang model -- and its generalisations to multi-component Fermi systems with larger spin symmetries. The exact results obtained for Bethe ansatz integrable models of this kind enable the study of the nature and microscopic origin of a wide range of quantum many-body phenomena driven by spin population imbalance, dynamical interactions and magnetic fields. This physics includes Bardeen-Cooper-Schrieffer-like pairing, Tomonaga-Luttinger liquids, spin-charge separation, Fulde-Ferrel-Larkin-Ovchinnikov-like pair correlations, quantum criticality and scaling, polarons and the few-body physics of the trimer state (trions). The fascinating interplay between exactly solved models and experimental developments in one dimension promises to yield further insight into the exciting and fundamental physics of interacting Fermi systems.