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Moir{e} superlattices in twisted bilayer graphene and transition-metal dichalcogenides have emerged as a powerful tool for engineering novel band structures and quantum phases of two-dimensional quantum materials. Here we investigate Moir{e} physics emerging from twisting two independent hexagonal optical lattices of atomic (pseudo-)spin states (instead of bilayers), which exhibits remarkably different physics from twisted bilayer graphene. We employ a momentum-space tight-binding calculation that includes all range real-space tunnelings, and show that all twist angles $theta lesssim 6^{circ }$ can become magic that support gapped flat bands. Due to greatly enhanced density of states near the flat bands, the system can be driven to superfluid by weak attractive interaction. Strikingly, the superfluid phase corresponds to a Larkin-Ovchinnikov state with finite momentum pairing, resulting from the interplay between flat bands and inter-spin interactions in the unique single-layer spin-twisted lattice. Our work may pave the way for exploring novel quantum phases and twistronics in cold atomic systems.
We study the dynamical behaviour of ultracold fermionic atoms loaded into an optical lattice under the presence of an effective magnetic flux, induced by spin-orbit coupled laser driving. At half filling, the resulting system can emulate a variety of
Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard m
Ultracold atoms in optical lattices offer a great promise to generate entangled states for scalable quantum information processing owing to the inherited long coherence time and controllability over a large number of particles. We report on the gener
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Recently a scheme has been proposed for generating the 2D Rashba-type spin-orbit coupling (SOC) for ultracold atomic bosons in a bilayer geometry [S.-W. Su et al, Phys. Rev. A textbf{93}, 053630 (2016)]. Here we investigate the superfluidity properti