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arXiv:2412.14731 · Frontiers of Physics

Ground state phases and topological excitations of spin-1 Bose−Einstein condensate in twisted optical lattices

Tian-Tian Li, Ze-Hong Guo, Xiao-Ning Wang, Qizhong Zhu

Published Jan 1, 2025• 2 citations
arXivHTMLPDF

Abstract

Recently, the simulation of moiré physics using cold atom platforms has gained significant attention. These platforms provide an opportunity to explore novel aspects of moiré physics that go beyond the limits of traditional condensed matter systems. Building on recent experimental advancements in creating twisted bilayer spin-dependent optical lattices for pseudospin-1/2 Bose gases, we extend this concept to a trilayer optical lattice for spin-1 Bose gases. Unlike conventional moiré patterns, which are typically induced by interlayer tunneling or interspin coupling, the moiré pattern in this trilayer system arises from inter-species atomic interactions. We investigate the ground state of Bose-Einstein condensates loaded in this spin-1 twisted optical lattice under both ferromagnetic and antiferromagnetic interactions. We find that the ground state forms a periodic pattern of distinct phases in the homogeneous case, including ferromagnetic, antiferromagnetic, polar, and broken axial symmetry phases. Additionally, by quenching the optical lattice potential strength, we examine the quench dynamics of the system above the ground state and observe the emergence of topological excitations such as vortex pairs. This study provides a pathway for exploring the rich physics of spin-1 twisted optical lattices and expands our understanding of moiré systems in synthetic quantum platforms.

DOI
10.15302/frontphys.2025.042201

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Recently, the simulation of moiré physics using cold atom platforms has gained significant attention. These platforms provide an opportunity to explore novel aspects of moiré physics that go beyond the limits of traditional condensed matter systems. Building on recent experimental advancements in creating twisted bilayer spin-dependent optical lattices for pseudospin-1/2 Bose gases, we extend this concept to a trilayer optical lattice for spin-1 Bose gases. Unlike conventional moiré patterns, which are typically induced by interlayer tunneling or interspin coupling, the moiré pattern in this trilayer system arises from inter-species atomic interactions. We investigate the ground state of Bose-Einstein condensates loaded in this spin-1 twisted optical lattice under both ferromagnetic and antiferromagnetic interactions. We find that the ground state forms a periodic pattern of distinct phases in the homogeneous case, including ferromagnetic, antiferromagnetic, polar, and broken axial symmetry phases. Additionally, by quenching the optical lattice potential strength, we examine the quench dynamics of the system above the ground state and observe the emergence of topological excitations such as vortex pairs. This study provides a pathway for exploring the rich physics of spin-1 twisted optical lattices and expands our understanding of moiré systems in synthetic quantum platforms.
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Moiré superlattices, classified as a supercell periodic structure configured from a periodic lattice overlaps with its twisted counterpart, have been demonstrated to exhibit many emergent linear and nonlinear phenomena like moiré induced flat bands, unconventional superconductivity, unique linear classical wave localization and nonlinear localized modes. Recent studies are, however, mainly focused on twisted bilayer structures, the static and nonequilibrium physics of trilayer moiré superlattices have remained largely unknown. We here consider trilayer moiré optical lattices by which Bose−Einstein condensates are trapped, and demonstrate theoretically the emergent flat bands and nonlinear phenomena — localized gap modes in form of gap solitons and vortices with a topological charge s=1. We give a unified picture for constructing optimal (largest) photonic forbidden gaps in such trilayer moiré superlattices and reveal nonlinear localization mechanism therein. Computational studies demonstrated the robustness of these localized modes, enabling insightful inspections of moiré physics and exploring ongoing moiré photonics applications in twisted trilayer superlattices in optics and ultracold atoms.
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Twisted bilayer materials provide a versatile platform for realizing correlated topological states. Motivated by the recent experimental realization of atomic Bose-Einstein condensates in twisted bilayer optical lattices, we investigate the emergence of fractional topological phases in such systems. For experimentally realistic parameters, the single-particle spectrum hosts a pair of quasi-degenerate nearly flat moiré bands. We show using self-consistent Hartree-Fock calculations that atomic interactions spontaneously break time-reversal symmetry, lift the quasi-degeneracy, and generate an isolated nearly flat band with a nonzero Chern number. At fractional filling, exact diagonalization of the Hamiltonian projected to this band reveals a threefold degenerate ground-state manifold and a characteristic particle entanglement spectrum, providing strong evidence for a fractional Chern insulator. The resulting many-body gap is of order 10−3ER10^{-3}E_R10−3ER​, corresponding to a nanokelvin energy scale accessible to state-of-the-art cold-atom experiments. Our scheme requires neither spin-orbit coupling, as in transition metal dichalcogenides, nor a finite magnetic field, as in existing twisted-bilayer-graphene experiments, providing a highly tunable route to strongly correlated topological phases in twisted bilayer optical lattices.
Creating crystal bilayers twisted with respect to each other would lead to large periodic supercell structures, which can support a wide range of novel electron correlated phenomena, where the full understanding is still under debate. Here, we propose a scheme to realize an interaction-induced twisted-bilayer lattice in an atomic Bose-Einstein condensate (BEC). The key idea here is to utilize the intrinsic atomic interaction to couple different layers and dynamically induce a supercell structure, distinct from the conventional wisdom to achieve the static twisted-bilayer lattices. To illustrate that, we study the dynamics of a two-component BEC and show that the intrinsic interaction effect arising from interacting bosonic ultracold atoms can dynamically induce both periodic (commensurable) and aperiodic (incommensurable) moir\'e structures. One of the interesting moir\'e-physics effects, i.e., the flat-band physics, is shown through investigating the dynamics of a wave packet of the BEC. Our proposal can be implemented using available state-of-the-art experimental techniques and leads to an alternative way to study twistronics in cold atom quantum simulators.