Engineering infinite-range <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>SU</mml:mi><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> interactions with spin-orbit-coupled fermions in an optical lattice
Michael A. Perlin, Diego Barberena, Mikhail Mamaev, Bhuvanesh Sundar, Robert J. Lewis-Swan, Ana María Rey
Abstract
We study multilevel fermions in an optical lattice described by the Hubbard model with on-site $\mathrm{SU}(n)$-symmetric interactions. We show that in an appropriate parameter regime this system can be mapped onto a spin model with all-to-all $\mathrm{SU}(n)$-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 $\mathrm{SU}(n)$ 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 intraspin coherences. Our predictions are readily testable in current experiments with ultracold alkaline-earth-metal(-like) atoms.