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

## TL;DR

This paper demonstrates how Floquet engineering can induce and manipulate moire quasicrystal patterns in ultracold Bose gases within twisted bilayer optical lattices, revealing new symmetry properties and collective modes.

## Contribution

It introduces a method to generate and control moire quasicrystal patterns in ultracold gases using Floquet modulation, a novel approach in quantum simulation.

## Key findings

- Emergence of twelve-fold quasicrystal pattern under specific parameters
- Pattern symmetry can be tuned by modulation frequencies and amplitudes
- High rotational symmetry observed in momentum-space distributions

## Abstract

We investigate the formation of moire quasicrystal patterns in Bose gasses confined in twisted bilayer optical lattices via Floquet-engineered intralayer atomic interactions. Dynamical evolutions of the total density wave amplitude exhibit the stage for the emergence of moire 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 moire 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.