Ultracold Fermi Gases with Emergent SU(N) Symmetry

Abstract

We review recent experimental and theoretical progress on ultracold alkaline-earth Fermi gases with emergent SU$(N)$ symmetry. Emphasis is placed on describing the ground-breaking experimental achievements of recent years. The latter include the cooling to below quantum degeneracy of various isotopes of ytterbium and strontium, the demonstration of optical Feshbach resonances and the optical Stern-Gerlach effect, the realization of a Mott insulator of ${}^{173}$Yb atoms, the creation of various kinds of Fermi-Bose mixtures and the observation of many-body physics in optical lattice clocks. On the theory side, we survey the zoo of phases that have been predicted for both gases in a trap and loaded into an optical lattice, focusing on two and three-dimensional systems. We also discuss some of the challenges that lie ahead for the realization of such phases, such as reaching the temperature scale required to observe magnetic and more exotic quantum orders, and dealing with collisional relaxation of excited electronic levels.

Review article (43 pages, 7 figures); comments are welcome

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• Entropy dependence of correlations in one-dimensional SU(N) antiferromagnets
• Adiabatic loading of one-dimensional SU(N) alkaline earth fermions in optical lattices
• Nagaoka states in the SU($n$) Hubbard model
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• Flat band induced non-Fermi liquid behavior of multicomponent fermions
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• Quantum spin liquid phases in the bilinear-biquadratic two-SU(4)-fermion Hamiltonian on the square lattice
• Suppression and Control of Pre-thermalization in Multi-component Fermi Gases Following a Quantum Quench
• Trion states and quantum criticality of attractive SU(3) Dirac fermions
• Two-leg SU(2n) spin ladder: A low-energy effective field theory approach
• Topological terms of (2+1)d flag-manifold sigma models
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue
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• Achieving spin-squeezed states by quench dynamics in a quantum chain
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• Flat-band-induced superconductivity in synthetic bilayer optical lattices
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• Chemical reactions of ultracold alkaline-earth-metal diatomic molecules
• Fluctuation effects in rotating Bose-Einstein condensates with broken $\mathrm{SU}(2)$ and $\mathrm{U}(1)\times \mathrm{U}(1)$ symmetries in the presence of intercomponent density-density interactions
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• Thermodynamics of one-dimensional SU(4) and SU(6) fermions with attractive interactions
• Coherent control over the high-dimensional space of the nuclear spin of alkaline-earth atoms
• A generalized effective spin-chain formalism for strongly interacting spinor gases in optical lattice
• Engineering of a Low-Entropy Quantum Simulator for Strongly Correlated Electrons Using SU($\mathcal{N}$)-Symmetric Cold Atom Mixtures
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• Exact one-particle density matrix for SU($N$) fermionic matter-waves in the strong repulsive limit
• Beyond universality in repulsive SU(N) Fermi gases
• Phase transitions in the decomposition of $SU(N)$ representations
• Dipolar ordering transitions in many-body quantum optics: Analytical diagrammatic approach to equilibrium quantum spins
• Stabilization of the chiral phase of the SU($6m$) Heisenberg model on the honeycomb lattice with $m$ particles per site for $m$ larger than 1
• Localization of Lindbladian Fermions
• Projective symmetry group classification of $Z_3$ parafermion spin liquids on a honeycomb lattice
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