Engineering infinite-range SU($n$) interactions with spin-orbit-coupled fermions in an optical lattice

TL;DR

This paper explores how to engineer infinite-range SU(n) interactions in optical lattices using spin-orbit-coupled fermions, revealing complex dynamical phases and initial state sensitivities relevant for ultracold atom experiments.

Contribution

It demonstrates a method to realize all-to-all SU(n) symmetric interactions with spin-orbit coupling in optical lattices and analyzes the resulting dynamical phase diagram.

Findings

Identification of two dynamical phases obeying scaling with n

Sensitivity of dynamics to initial intra-spin coherences for n>2

Feasibility of experimental realization with ultracold atoms

Abstract

We study multilevel fermions in an optical lattice described by the Hubbard model with on site SU($n$)-symmetric interactions. We show that in an appropriate parameter regime this system can be mapped onto a spin model with all-to-all SU($n$)-symmetric couplings. Raman pulses that address internal spin states modify the atomic dispersion relation and induce spin-orbit coupling, which can act as a synthetic inhomogeneous magnetic field that competes with the SU($n$) exchange interactions. We investigate the mean-field dynamical phase diagram of the resulting model as a function of $n$ and different initial configurations that are accessible with Raman pulses. Consistent with previous studies for $n=2$, we find that for some initial states the spin model exhibits two distinct dynamical phases that obey simple scaling relations with $n$. Moreover, for $n>2$ we find that dynamical behavior can be highly sensitive to initial intra-spin coherences. Our predictions are readily testable in current experiments with ultracold alkaline-earth(-like) atoms.