Fate of moiré flat bands for a weakly repulsive Bose-Einstein condensate in one-dimensional PT-symmetric bichromatic optical lattices

This paper investigates how non-Hermitian parity-time (PT) symmetry and weak repulsive interactions influence the band structure of a Bose-Einstein condensate (BEC) in a one-dimensional moiré optical lattice. By tuning the ratio of the lattice constants (the moiré ratio), the authors examine how the interplay between dissipation (modeled by an imaginary potential) and interaction (modeled by the Gross-Pitaevskii equation) modulates the flatness of the lowest energy band.

The study reveals a fundamental distinction between moiré lattices with even and odd denominators. In the non-interacting regime, even-denominator ratios lead to a monotonic broadening of the lowest band as the imaginary potential strength increases, driven by direct PT-symmetry breaking between the lowest two bands. Conversely, odd-denominator ratios exhibit nonmonotonic behavior. In these cases, the presence of a self-conjugate center minimum in the potential delays PT-symmetry breaking in the lowest band, shifting the instability to higher bands and allowing for a nonmonotonic response where the band flatness can be enhanced or reduced.

When weak repulsive interactions are introduced, the authors find that the interaction and the imaginary potential work in tandem to further modulate the band structure. For even parities, the interaction consistently diminishes band flattening. For odd parities, the imaginary potential can either enhance or reduce the degree of flattening, depending on the specific interaction strength. These results provide a theoretical framework for understanding how dissipation and nonlinearity compete to control band flatness in synthetic quantum systems.