Realizing Exactly Solvable SU(N) Magnets with Thermal Atoms

TL;DR

This paper proposes a method to realize exactly solvable SU(N) spin models using thermal fermionic alkaline-earth atoms in traps, enabling analytic studies of dynamics and entanglement for quantum metrology.

Contribution

It introduces a high-symmetry, exactly solvable SU(N) spin model using thermal atoms, facilitating new analytical insights and applications in quantum metrology.

Findings

Model displays both $S_n$ and SU($N$) symmetries.

System allows analytic study of spin diffusion.

Potential for Heisenberg-limited metrology.

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.