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

TL;DR

This work demonstrates that Floquet engineering of intralayer interactions in spin-dependent, twisted bilayer hexagonal lattices can generate moiré quasicrystal density-wave patterns in ultracold Bose gases without external quasiperiodic potentials. By solving coupled Gross-Pitaevskii equations with time-periodic scattering length and controllable interlayer coupling, the authors identify four dynamical stages of pattern formation and reveal a robust $D_{12}$ moiré quasicrystal under specific $a_m$ and $\omega$ parameters, with momentum-space distributions showing corresponding high rotational symmetry. The analysis connects real-space and momentum-space patterns and demonstrates the sensitivity of pattern formation to driving frequency and amplitude, consistent with Mathieu equation stability tongues. The findings establish a new quantum platform for studying quasicrystals, their symmetry properties, and dynamical phase transitions in driven bosonic systems, with potential implications for topological and exotic quasiparticle physics.

Abstract

We investigate the formation of moiré quasicrystal patterns in Bose gases confined in twisted bilayer optical lattices via Floquet-engineered intralayer atomic interactions. Dynamical evolutions of the inverse participation ratio and the density wave amplitude reveal the stage for the emergence of moiré quasicrystal patterns, whose symmetry 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.

Figures (7)

• Figure 1: Cold atomic system in spin-dependent twisted bilayer hexagonal lattice. The system is loaded into a 2D harmonic trap in the x-y plane and tightly confined in the z direction, which reduces the dynamics of the system to quasi-2D.
• Figure 2: IPR of the system. (a) IPR of ground DW with different lattice depth $V_0$ and interlayer coupling $\Omega$, where the red star denotes the parameters employed in our following Floquet engineering. (b) IPR of dynamical DW with $\omega=200$ Hz and $a_m=50a_0$.
• Figure 3: The DW amplitude and patterns with $\omega=200$ Hz and $a_m=50a_0$. (a) Four evolution stages divided by DW amplitude (blue curve) and energy (brown curve). (b) The real-space patterns at $t=10, 50, 64, 100$ ms (top) and the corresponding momentum-space patterns amplified by logarithm (bottom). The red triangles in (a) mark the four selected temporal nodes displayed in (b).
• Figure 4: The dynamical evolution of real-space patterns with different modulation frequencies. (a) The patterns with $a_m=50a_0$ and $\omega=200$ Hz (top), $\omega=252$ Hz (middle) and $\omega=300$ Hz (bottom). (b) The corresponding DW amplitudes of (a).
• Figure 5: The dynamical evolution of real-space patterns with different modulation amplitudes. The patterns with $\omega=200$ Hz and (a) $a_m=75a_0$, (b) $a_m=100a_0$. (c) $D_{12}$ moiré quasicrystal patterns comparison: simulations (left), twisted bilayer graphene atomic structure (middle) and graphene quasicrystal (right) graphenequasicrystal1.