Realizing Exactly Solvable SU(N) Magnets with Thermal Atoms
  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. 
Michael E. Beverland, Gorjan Alagic, Michael J. Martin, Andrew P.   Koller, Ana M. Rey, Alexey V. Gorshkov
cond-mat.quant-gas cond-mat.str-el physics.atom-ph quant-ph