Realizing Exactly Solvable SU(N) Magnets with Thermal Atoms

Abstract

We show that $n$ thermal fermionic alkaline-earth atoms in a flat-bottom trap allow one to robustly implement a spin model displaying two symmetries: the $S_n$ symmetry that permutes atoms occupying different vibrational levels of the trap and the SU($N$) symmetry associated with $N$ nuclear spin states. The high symmetry makes the model exactly solvable, which, in turn, enables the analytic study of dynamical processes such as spin diffusion in this SU($N$) system. We also show how to use this system to generate entangled states that allow for Heisenberg-limited metrology. This highly symmetric spin model should be experimentally realizable even when the vibrational levels are occupied according to a high-temperature thermal or an arbitrary non-thermal distribution.

12 pages, 5 figures (including supplemental materials)

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Cited by in corpus (20)

• Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap
• One-dimensional mixtures of several ultracold atoms: a review
• High-momentum tails as magnetic structure probes for strongly-correlated $SU(\kappa )$ fermionic mixtures in one-dimensional traps
• Subwavelength-width optical tunnel junctions for ultracold atoms
• SU(N) Fermions in a One-Dimensional Harmonic Trap
• Dynamics of interacting fermions in spin-dependent potentials
• Infinite Barriers and Symmetries for a Few Trapped Particles in One Dimension
• Nematic Spin Liquid Phase in a Frustrated Spin-1 System on the Square Lattice
• Exact ordering of energy levels for one-dimensional interacting Fermi gases with $SU(n)$ symmetry
• Engineering infinite-range SU($n$) interactions with spin-orbit-coupled fermions in an optical lattice
• Suppression and Control of Pre-thermalization in Multi-component Fermi Gases Following a Quantum Quench
• Haldane Gap of the Three-Box Symmetric $\mathrm{SU}(3)$ Chain
• The bilinear-biquadratic model on the complete graph
• Spectrum estimation of density operators with alkaline-earth atoms
• Entanglement properties of the two-dimensional SU(3) AKLT state
• Quantum phases of collective SU(3) spin systems with bipartite symmetry
• Bipartite Sachdev-Ye Models with Read-Saleur Symmetries
• Momentum distribution and tunneling density of states of one-dimensional Fermonic SU(N) Hubbard model
• Ground state separability and criticality in interacting many-particle systems
• Degenerate Rabi spectroscopy of the Floquet engineered optical lattice clock