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.

12 pages, 8 figures (21 pages, 10 figures with appendices)

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• Adiabatic loading of one-dimensional SU(N) alkaline earth fermions in optical lattices
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Cited by in corpus (13)

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• Crafting the dynamical structure of synchronization by harnessing bosonic multilevel cavity QED
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• State Preparation in the Heisenberg Model through Adiabatic Spiraling
• Preparation for Quantum Simulation of the 1+1D O(3) Non-linear σ-Model using Cold Atoms
• Two emitters coupled to a bath with Kerr-like non-linearity: Exponential decay, fractional populations, and Rabi oscillations
• Intertwining of lasing and superradiance under spintronic pumping
• Spectroscopic evidence for engineered hadron formation in repulsive fermionic $\text{SU}(N)$ Hubbard Models
• Bipartite Sachdev-Ye Models with Read-Saleur Symmetries
• Disentangling Pauli blocking of atomic decay from cooperative radiation and atomic motion in a 2D Fermi gas
• Dark spin-cats as biased qubits
• Effective light-induced Hamiltonian for atoms with large nuclear spin
• Fluctuation-induced first-order superfluid transition in unitary $\mathrm{SU}(N)$ Fermi gases