Emergent aperiodicity in Bose-Bose mixtures induced by spin-dependent periodic potentials

TL;DR

This paper investigates how spin-dependent periodic potentials induce emergent aperiodic and quasicrystalline phases in binary Bose-Einstein condensates, revealing conditions for their stability and experimental realization.

Contribution

It demonstrates that quasicrystalline order can arise in binary condensates without aperiodic lattices, highlighting population balance as crucial for stabilization.

Findings

Emergence of eightfold symmetric quasicrystalline patterns at certain interaction strengths.

Metastable long-lived phases with restored eightfold symmetry at strong coupling.

Dynamical stability and experimental accessibility of aperiodic structures.

Abstract

We study the ground-state and low-lying metastable phases of repulsive binary Bose-Einstein condensates confined in twisted, spin-dependent periodic optical lattices. For balanced mixtures, weak intercomponent interactions yield a fourfold momentum-space symmetry dictated by the lattice geometry. Increasing the coupling strength leads to the emergence of additional momentum peaks that combine with the lattice-induced structure to produce an eightfold rotationally symmetric pattern, signaling quasicrystalline order. At intermediate interactions, global phase separation suppresses this quasicrystalline state; however, at stronger coupling, local phase separation gives rise to a long-lived metastable phase in which the eightfold symmetry is restored. In this regime, a secondary ring of dominant momentum peaks appears at smaller wave vectors, indicating longer-wavelength density modulations and a crossover from lattice-dominated to interaction-driven quasicrystalline order. In contrast, imbalanced mixtures form partially miscible density clusters with eightfold-symmetric aperiodic patterns only at intermediate coupling, while stronger interactions drive global phase separation and permanently destroy quasicrystalline order. Real-time simulations demonstrate that these aperiodic structures are dynamically stable and experimentally accessible. Our results show that quasicrystalline order can emerge in binary condensates without explicitly aperiodic lattices and reveal population balance as a key ingredient for stabilizing quantum quasicrystals.