Fermi gases in one dimension: From Bethe ansatz to experiments

Abstract

This article reviews theoretical and experimental developments for one-dimensional Fermi gases. Specifically, the experimentally realized two-component delta-function interacting Fermi gasthe 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, spincharge 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.

High-momentum tails as magnetic-structure probes for strongly correlatedSU(κ)fermionic mixtures in one-dimensional traps

“…In the spirit of quantum simulations [5], they now allow to study many important phenomena like for instance superfluidity, integrable models [4], quantum phase transitions and quantum magnetism [6]. In the latter case, multi-component strongly interacting quantum particles, living in continuous space, appear to be a promising alternative to lattice systems where magnetic interaction parameters are hardly tunable [7].…”

“…The recent progresses on the experimental control offered by ultra-cold atoms setups [1][2][3][4] provides new platforms for the theoretical and experimental activity on one dimensional (1D) strongly correlated quantum systems. In the spirit of quantum simulations [5], they now allow to study many important phenomena like for instance superfluidity, integrable models [4], quantum phase transitions and quantum magnetism [6].…”

Repulsive Fermi polarons with negative effective mass

“…This is particularly true for the system of repulsive polaron, since it lies in an excited upper branch of atomic system rather than the ground state. On the other hand, one might be able to gain important insights by studying the counterpart problem in 1D, where the exact solutions can be accessible [21] and effective spin-chain models can be established in strong coupling limit [22][23][24][25][26][27][28]. For 1D fermion system, the ferromagnetic transition has been exactly proved with arbitrary number and arbitrary potential [29], and the polaron problem in continuum has also been exactly solved by McGuire in 1960's [30,31] and recently by Guan [32].…”

Cluster Gutzwiller study of the Bose-Hubbard ladder: Ground-state phase diagram and many-body Landau-Zener dynamics

“…The remarkable cleanness and high tunability of ultracold atomic systems allow one to explore various many-body quantum phenomena in BH models [9][10][11]. For an example, the experimental realization of the one-dimensional (1D) atomic Hubbard model [12] provides new opportunities to exploring quantum statistical effects and strong correlation effects in low-dimensional quantum many-body systems [13]. Quantum dynamics as well as quantum phase transition between superfluid (SF) phase and Mott insulator (MI) phase in BH models are of great interests and have been widely investigated [14][15][16][17][18][19][20][21].…”