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

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.

State Preparation in the Heisenberg Model through Adiabatic Spiraling

“…While a quantum advantage has yet to be established for a scientific application, including quantum field theories, there are substantial efforts underway to perform quantum simulations that can be compared with experiment, or impact future experiments, and impressive progress has been made toward these objectives in the last decade. This includes the development of techniques to simulate abelian gauge theories , non-abelian gauge theories , fermionic field theories [98][99][100][101], and scalar field theories [102][103][104][105][106][107][108]. There has also been the development of techniques to extract observables of interest to nuclear physics [109][110][111][112][113][114][115], scattering processes in high energy physics [116][117][118][119][120][121][122][123] and methods to mitigate errors on noisy quantum hardware [124][125][126][127][128][129].…”