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

We investigate the formation of novel moiré quasicrystal patterns in Bose gases confined in twisted bilayer optical lattices via Floquet-engineered intralayer-atomic interactions. By introducing the density wave amplitude, we divide the dynamical evolution into four distinct stages and verify the pattern changes at each stage. The spatial symmetry of the patterns is closely linked to the modulation amplitudes and frequencies. Consequently, appropriately reducing the modulation frequency and increasing the amplitude 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, consistent with the real-space patterns at specific evolution times. The patterns exhibit remarkable sensitivity to the modulation frequency, suggesting potential applications of this strongly frequency-dependent pattern formation in quantum precision measurement. Our findings establish a new quantum platform for exploring quasicrystals and their symmetry properties in ultracold bosonic systems.