Cold atoms in twisted bilayer optical potentials

Abstract

The possibility of creating crystal bilayers twisted with respect to each other has led to the discovery of a wide range of novel electron correlated phenomena whose full understanding is still under debate. Here we propose and analyze a method to simulate twisted bilayers using cold atoms in state-dependent optical lattices. Our proposed setup can be used as an alternative platform to explore twisted bilayers which allows one to control the inter/intra-layer coupling in a more flexible way than in the solid-state realizations. We focus on square geometries but also point how it can be extended to simulate other lattices which show Dirac-like physics. This setup opens a path to observe similar physics, e.g., band narrowing, with larger twist angles, to rule out some of the mechanisms to explain the observed strongly correlated effects, as well as to study other phenomena difficult to realize with crystals. As an example of the latter we explore the quantum optical consequences of letting emitters interact with twisted bilayer reservoirs, and predict the appearance of unconventional radiation patterns and emitter interactions following the emergent Moiré geometry.

12 pages, 6 figures. Comments, suggestions, and constructive criticism are welcome

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• A comprehensive review on developments of synthetic dimensions
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• Pythagoras Superposition Principle for Localized Eigenstates of 2D Moiré Lattices
• Particle dynamics and ergodicity-breaking in twisted-bilayer optical lattices
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• Vacancy-induced tunable Kondo effect in twisted bilayer graphene
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• Self-consistent tensor network method for correlated super-moiré matter beyond one billion sites
• Effective tight-binding models in optical moiré potentials
• Experimental study of tune-out wavelengths for spin-dependent optical lattice in ${}^{87}$Rb Bose-Einstein condensation
• Dissipation-Driven Transition of Particles from Dispersive to Flat Bands
• Fate of Berezinskii-Kosterlitz-Thouless Paired Phase in Coupled $XY$ Models
• Atomic Regional Superfluids in two-dimensional Moiré Time Crystals
• Insulating-to-conducting state transition in the bilayer Hubbard model induced by a perpendicular quench field