The recent experimental realization of clock-laser-induced synthetic gauge fields and one-dimensional spin-orbit coupling in ultracold alkaline-earth(-like) atoms provides a new way to explore topological quantum states with suppressed heating effects. Here, we propose a scheme for realizing a synthetic quantum Hall tube and ribbon in an optical lattice clock system with multiple optical clock transition couplings. The legs of the synthetic Hall system are composed of the atomic ground and metastable orbital states, and the couplings between the legs are generated by clock lasers, resulting in a synthetic gauge flux. We investigate the band structure and topological phase diagram under various conditions and demonstrate the phase transition. The momentum-resolved quench dynamics of the synthetic Hall system is analyzed to demonstrate the presence of gauge flux on plaquettes and reveal the critical point of the phase transition. The hyperfine spin can serve as an additional synthetic dimension, allowing a two-component Hall system to be realized in synthetic dimensions. A size-enlarged Hall system could be realized by coupling the magnetic sublevels and orbital states simultaneously. Our scheme is within reach of existing optical lattice clocks and thus provides a realistic method to achieve topological quantum Hall systems with ultracold alkaline-earth(-like) atoms. This study paves the way for realizing quantum spin Hall states with hyperfine spins and has the potential to explore more interesting topological phases.
The ``synthetic dimension'' proposal [A. Celi et al., Phys. Rev. Lett. 112, 043001 (2014)] uses atoms with
M internal states (``flavors'') in a one-dimensional (1D) optical lattice, to realize a hopping Hamiltonian equivalent to the Hofstadter model (tight-binding model with a given magnetic flux per plaquette) on an
M-sites-wide square lattice strip. We investigate the physics of
SU(M) symmetric interactions in the synthetic dimension system. We show that this system is equivalent to particles [with
SU(M) symmetric interactions] experiencing an
SU(M) Zeeman field at each lattice site and a non-Abelian
SU(M) gauge potential that affects their hopping. This equivalence brings out the possibility of generating nonlocal interactions between particles at different sites of the optical lattice. In addition, the gauge field induces a flavor-orbital coupling, which mitigates the ``baryon breaking'' effect of the Zeeman field. For
M particles, concomitantly, the
SU(M) singlet baryon which is site localized in the usual 1D optical lattice, is deformed to a nonlocal object (``squished baryon''). We conclusively demonstrate this effect by analytical arguments and exact (numerical) diagonalization studies. Our study promises a rich many-body phase diagram for this system. It also uncovers the possibility of using the synthetic dimension system to laboratory realize condensed-matter models such as the
SU(M) random flux model, inconceivable in conventional experimental systems.
Abstract Synthetic gauge fields in synthetic dimensions are now of great interest. This concept provides a convenient manner for exploring topological phases of matter. Here, we report on the first experimental realization of an atom-optically synthetic gauge field based on the synthetic momentum-state lattice of a Bose gas of 133Cs atoms, where magnetically controlled Feshbach resonance is used to tune the interacting lattice into noninteracting regime. Specifically, we engineer a noninteracting one-dimensional lattice into a two-leg ladder with tunable synthetic gauge fields. We observe the flux-dependent populations of atoms and measure the gauge field-induced chiral currents in the two legs. We also show that an inhomogeneous gauge field could control the atomic transport in the ladder. Our results lay the groundwork for using a clean noninteracting synthetic momentum-state lattice to study the gauge field-induced topological physics.