Floquet -engineered moiré quasicrystal patterns of ultracold Bose gases in twisted bilayer optical lattices

We investigate the formation of moiré quasicrystal patterns in Bose gasses confined in twisted bilayer optical lattices via Floquet-engineered intralayer atomic interactions. The time evolution of the total density wave amplitude exhibit the stage for the emergence of moiré quasicrystal patterns, where the pattern formation is closely associated with the momenta of collective modes excited by the weak periodic drive. Through analyzing the radial and angular density wave amplitude, we find that these new collective modes are only coupled radially and cannot be decoupled eventually. The symmetry of quasicrystal patterns can be easily manipulated by the modulation frequencies and amplitudes. Reducing the frequencies and increasing the amplitudes can both facilitate lattice symmetry breaking and the subsequent emergence of rotational symmetry. Notably, a twelve-fold quasicrystal pattern emerges under specific parameters, closely resembling the moiré quasicrystal in twisted bilayer graphene. The momentum-space distributions also exhibit high rotational symmetry, which is consistent with the real-space patterns at specific evolution times. Our findings establish a new quantum platform for exploring quasicrystals and their symmetry properties in ultracold bosonic systems.