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.

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

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• Quantum Computing and Quantum Simulation with Group-II Atoms
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• Coherent multi-flavour spin dynamics in a fermionic quantum gas
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• BCS pairing in Fermi systems with several flavors
• p-Wave cold collisions in an optical lattice clock
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• Superfluidity in a Three-flavor Fermi Gas with SU(3) Symmetry
• Steady-state many-body entanglement of hot reactive fermions
• High temperature thermodynamics of fermionic alkaline earth atoms in optical lattices
• Cold collision shift cancelation and inelastic scattering in a Yb optical lattice clock
• Population imbalance and pairing in the BCS-BEC crossover of three-component ultracold fermions
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• Many-body treatment of the collisional frequency shift in fermionic atoms
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• Heavy fermions in an optical lattice
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• Bose-Einstein condensation of 86Sr
• Haldane charge conjecture in one-dimensional multicomponent fermionic cold atoms
• Competing states in the SU(3) Heisenberg model on the honeycomb lattice: Plaquette valence-bond crystal versus dimerized color-ordered state
• Pomeranchuk cooling of the SU($2N$) ultra-cold fermions in optical lattices
• Nagaoka states in the SU($n$) Hubbard model
• Noncommutative Geometry, Extended W(infty) Algebra and Grassmannian Solitons in Multicomponent Quantum Hall Systems
• Cooling of Sr to high phase-space density by laser and sympathetic cooling in isotopic mixtures
• Realizing non-Abelian gauge potentials in optical square lattices: Application to atomic Chern insulators
• Spatially nonuniform phases in the one-dimensional SU(n) Hubbard model for commensurate fillings
• Renormalization group study of interacting electrons
• Resolved atomic interaction sidebands in an optical clock transition
• Ground state phase diagram of the repulsive SU(3) Hubbard model in Gutzwiller approximation
• Exact diagonalization study of the trionic crossover and the trion liquid in the attractive three-component Hubbard model
• Theory of Fermionic superfluid with SU(2)xSU(6) symmetry
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• Quantum Walk in Degenerate Spin Environments
• Unified Phase Diagram of Antiferromagnetic SU(N) Spin Ladders
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• Flag manifold sigma models: spin chains and integrable theories
• Majorana Quasi-Particles Protected by ${\mathbb{Z}}_2$ Angular Momentum Conservation
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