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

TL;DR

The paper addresses whether quasicrystalline order can arise spontaneously in a binary BEC without externally imposed aperiodic lattices. It analyzes a two-component 2D BEC in spin-dependent square lattices twisted by $\theta=\pi/4$ using coupled Gross-Pitaevskii equations, exploring ground states and real-time dynamics for balanced and imbalanced mixtures as the intercomponent coupling $g_{12}$ and lattice depth $U$ vary. The main results show a progression from four lattice-induced momentum peaks to eightfold symmetry via secondary peaks, a global immiscible phase that can suppress QC order, and a metastable, locally phase-separated regime where eightfold order re-emerges; an inner ring of peaks at smaller wave vectors signals a crossover to longer-wavelength density modulations. For imbalanced mixtures, QC order exists only at intermediate coupling and is lost after global phase separation, emphasizing population balance as a key stabilizer of quantum quasicrystals. The work demonstrates emergent QC phases in binary condensates without explicit aperiodic confinement, offering a tunable platform for studying QC physics and potential quantum simulation applications.

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.

Figures (8)

• Figure 1: (a) Schematic illustration of two independent periodic optical lattice potentials, $V_1$ for component 1 and $V_2$ for component 2. Panels (b) and (c) show the corresponding spatial profiles of $V_1$ and $V_2$ along the $x$ and $y$ directions, highlighting the relative orientation of the square lattices. This configuration enables independent manipulation of atoms in different spin components via spin-dependent optical lattices.
• Figure 2: Ground-state density distributions of components 1 and 2 in a balanced binary BEC. The intra-component interactions are fixed at $g_{11} = g_{22} \equiv g = 15$, with lattice depth $U = 1.2$. The circular box trap parameters are $V_0 = 50$, $R_t = 15\pi$, and $w_t = 2$. The middle panels show line profiles along $y = 0$, $|\Psi_j(x, y=0)|^2$, while the bottom panels display the corresponding momentum-space distributions. Panels (a)–(f) correspond to intercomponent interaction strengths $g_{12} = 1.5$, $6$, $10.5$, $15.15$, $15.25$, $15.35$, and $15.65$, respectively. Each real-space panel spans a spatial domain of $(32\pi)^2$, and each momentum-space panel spans $(3\pi)^2$.
• Figure 3: Energies of the ground and metastable states as a function of the intercomponent interaction strength $g_{12}$ for the balanced mixture. Solid lines indicate the energies of the respective states. Insets show the real-space density distribution of component 1 for each case. Other parameters are the same as in Fig. \ref{['fig:fig3']}. Real-space densities are plotted over a spatial domain of $(32\pi)^2$, and the corresponding momentum-space distribution for the case shown in panel (f) is displayed in panel (g), spanning $(2\pi)^2$.
• Figure 4: Ground-state density distributions of an imbalanced binary BEC in a spin-dependent periodic lattice. Panels (a)–(c) show the system for increasing intercomponent interactions $g_{12} = 15.15$, $15.3$, and $15.9$, respectively. The bottom panels display line profiles along $y=0$, $|\Psi_j(x, y=0)|^2$, and the corresponding momentum-space distributions. For moderate $g_{12}$ in panels (a) and (b), the condensates form partially miscible quasicrystalline density clusters with eightfold rotational symmetry, whereas for stronger $g_{12}$ in panel (c), the components undergo global phase separation and the quasicrystalline signature disappears. Other parameters are the same as in Fig. \ref{['fig:fig3']}. ach real-space panel spans a spatial domain of $(32\pi)^2$, and each momentum-space panel spans $(3\pi)^2$.
• Figure 5: Phase diagram of the balanced binary BEC in the $(g_{12}, U)$ plane, obtained from the overlap parameter $\mathcal{O}$ defined in Eq. \ref{['eq:overlap']}. The black square marks the parameters of Fig. \ref{['fig:fig3']}(e), corresponding to a quasicrystalline phase (QC I) where the system begins to segregate into large spatial domains while retaining eightfold symmetry in momentum space. The black star indicates the globally immiscible phase shown in Fig. \ref{['fig:fig3']}(f), where $\mathcal{O}=0$ and quasicrystalline order is lost. The black circle denotes the metastable quasicrystalline regime (QC II) of Fig. \ref{['fig:meta_stable']}(f), where density modulations re-emerge and the momentum distribution recovers eightfold rotational symmetry despite local phase separation.