Interaction induced reentrance of Bose glass and quench dynamics of Bose gases in twisted bilayer and quasicrystal optical lattices

We investigate the ground state and dynamical properties of ultracold gases in optical lattices with an aperiodic external potential-a scenario motivated by recent experiments on twisted bilayer optical lattices and optical quasicrystals. Our study reveals that the interplay between on-site repulsive interactions and a quasiperiodic potential gives rise to rich physics. At low filling factors, increasing the interaction strength induces a delocalization effect that transforms a Bose glass (BG) phase, characterized by disconnected superfluid (SF) regions, into a SF phase with a percolated network of SF clusters. This transition is quantitatively characterized by monitoring the percolation probability. At higher filling factors, we uncover a reentrant behavior: as the on-site interaction increases, the system initially transitions from BG to SF, but further increase restores the BG phase. This reentrance is ascribed to an interaction-driven rearrangement of particles, where a once percolated SF network fragments into isolated SF islands as repulsive interactions dominate. Furthermore, our analysis of quench dynamics demonstrates distinct transient behaviors. Intra-phase quenches yield minimal variations in both the percolation probability and the inverse participation ratio (IPR) of the particle density distribution. In contrast, inter-phase quenches produce pronounced effects; for instance, a quench from the SF to BG phase is marked by an abrupt loss of global SF connectivity, while a BG-to-SF quench features oscillatory changes in the percolation probability and a gradual decrease in the IPR, eventually stabilizing the SF phase. Our findings unveil the complex interplay between disorder and interaction in ultracold Bose gases, offering valuable insights that are highly pertinent to current experimental efforts employing twisted bilayer and quasicrystalline optical lattice platforms.