Floquet-engineered moire quasicrystal patterns of ultracold atoms in twisted bilayer optical lattices

Abstract: We obtain moire quasicrystal patterns via Floquet-engineering intralayer-atomic interactions in twisted bilayer hexagonal optical lattices of ultracold atoms. By tracking the density wave amplitude, we partition the dynamical evolution into four distinct stages and verify the pattern changes of each stage in both real and momentum space. The spatial symmetry of the patterns is intimately tied to the modulation amplitudes and frequencies. Consequently, appropriately reducing the modulation frequency and increasing the amplitude will facilitate lattice symmetry breaking and the subsequent emergence of rotational symmetry. Most notably, at specific parameters, a twelve-fold (D12) moire quasicrystal pattern emerges which closely resembles that observed in twisted bilayer graphene. The momentum-space patterns likewise exhibit pronounced rotational symmetry, with those in real space showing good agreement at specific instants. The patterns obtained exhibit remarkable sensitivity to the modulation frequency, suggesting that this frequency-dependent pattern formation could be exploited for quantum precision measurement. Our findings introduce a new paradigm for investigating the quasicrystals and their associated symmetries in ultracold atomic system.