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arXiv:2405.20732 · Physical Review A

Interaction-induced moiré systems in twisted bilayer optical lattices

Jian-Hua Zeng, Qizhong Zhu, Liang He

Published Jun 3, 2025• 9 citations
arXivHTMLPDF

Abstract

Moiré related physics in twisted bilayer two-dimensional (2D) materials has attracted widespread interest in condensed matter physics. Simulation of moiré related physics in cold atom platform is expected to outperform the 2D materials thanks to its advantage of higher tunablility. Here, we demonstrate that, the cold atom platform enables a new mechanism of moiré lattice formation, induced by interlayer interaction with intrinsic "dynamical" character, in contrast to conventional moiré lattice induced by "static" ways such as single-particle interlayer tunneling. Specifically, we consider a twisted bilayer Bose-Hubbard model with vanishing interlayer tunneling, and the bilayer is solely coupled through interlayer interaction that originates from contact interaction of atoms. We find that this system hosts a plethora of novel phases unique to this dynamical lattice, including a variety of Mott insulator (MI) and superfluid (SF) phases either preserving or breaking moiré lattice symmetry, phases with one layer in SF and the other in MI, "interlocked" MI, and self-localized phases at commensurate twist angles, which exhibits the characteristics of Bose glass and quasi-many-body localization in the absence of (quasi)disorder or quasicrystalline lattices. Our prediction can be readily observed in current experimental setup of twisted bilayer optical lattices, opening up new avenues for exploring the rich physics of interaction induced moiré systems in cold atoms.

DOI
10.1103/zpqd-ryjm

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Moiré related physics in twisted bilayer two-dimensional (2D) materials has attracted widespread interest in condensed matter physics. Simulation of moiré related physics in cold atom platform is expected to outperform the 2D materials thanks to its advantage of higher tunablility. Here, we demonstrate that, the cold atom platform enables a new mechanism of moiré lattice formation, induced by interlayer interaction with intrinsic "dynamical" character, in contrast to conventional moiré lattice induced by "static" ways such as single-particle interlayer tunneling. Specifically, we consider a twisted bilayer Bose-Hubbard model with vanishing interlayer tunneling, and the bilayer is solely coupled through interlayer interaction that originates from contact interaction of atoms. We find that this system hosts a plethora of novel phases unique to this dynamical lattice, including a variety of Mott insulator (MI) and superfluid (SF) phases either preserving or breaking moiré lattice symmetry, phases with one layer in SF and the other in MI, "interlocked" MI, and self-localized phases at commensurate twist angles, which exhibits the characteristics of Bose glass and quasi-many-body localization in the absence of (quasi)disorder or quasicrystalline lattices. Our prediction can be readily observed in current experimental setup of twisted bilayer optical lattices, opening up new avenues for exploring the rich physics of interaction induced moiré systems in cold atoms.
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.
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 new scheme to realize a nonlinearity-induced dynamical self-organized twisted-bilayer lattice in an atomic Bose-Einstein condensate (BEC). The key idea here is to utilize the nonlinear effect from the intrinsic atomic interactions to couple different layers and induce a dynamical self-organized supercell structure, dramatically 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 nonlinear interaction effect naturally emerged in the Gross-Pitaevskii equation of interacting bosonic ultracold atoms can dynamically induce both periodic (commensurable) and aperiodic (incommensurable) moiré structures. One of the interesting moiré phenomena, i.e., the flat-band physics, is shown through investigating the dynamics of the wave packet of BEC. Our proposal can be implemented using available state-of-the-art experimental techniques and reveal a profound connection between the nonlinearity and twistronics in cold atom quantum simulators.
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.
Abstract Observation of strong correlations and superconductivity in twisted-bilayer-graphene have stimulated tremendous interest in fundamental and applied physics. In this system, the superposition of two twisted honeycomb lattices, generating a Moire pattern, is the key to the observed flat electronic bands, slow electron velocity and large density of states. Despite these observations, a full understanding of the emerging superconductivity from the coupled layers and the appearance of a small magic angle remain a hot topic of research. Here, we demonstrate a quantum simulation platform to study superfluids in twisted bilayer lattices based on Bose-Einstein condensates loaded into spin-dependent optical lattices. The lattices are made of two sets of laser beams that independently address atoms in different spin states, which form the synthetic dimension accommodating the two layers. The twisted angle of the two lattices is controlled by the relative angle of the laser beams. We show that atoms in each spin state only feel one set of the lattice and the interlayer coupling can be controlled by microwave coupling between the spin states. Our system allows for flexible control of both the inter- and intralayer couplings. Furthermore we directly observe the spatial Moire pattern and the momentum diffraction, which confirm the presence of atomic superfluid in the bilayer lattices. Our system constitutes a powerful platform to investigate the physics underlying the superconductivity in twisted-bilayer-graphene and to explore other novel quantum phenomena difficult to realize in materials.
Moiré superlattices in twisted bilayer graphene and transition-metal dichalcogenides have emerged as a powerful tool for engineering novel band structures and quantum phases of two-dimensional quantum materials. Here we investigate Moiré physics emerging from twisting two independent hexagonal optical lattices of atomic (pseudo-)spin states (instead of bilayers) that exhibit remarkably different physics from twisted bilayer graphene. We employ a momentum-space tight-binding calculation that includes all range real-space tunnelings and show that all twist angles θ≲6° can become magic and support gapped flat bands. Because of the greatly enhanced density of states near the flat bands, the system can be driven to superfluidity by weak attractive interaction. Strikingly, the superfluid phase corresponds to a Larkin-Ovchinnikov state with finite momentum pairing that results from the interplay between flat bands and interspin interactions in the unique single-layer spin-twisted lattice. Our work may pave the way for exploring novel quantum phases and twistronics in cold atomic systems.
Moiré lattices formed by superimposing rotated two-dimensional (2D) periodic sublattices, such as twisted bilayer graphene, can exhibit fascinating properties not observed in their individual constituent layers. Despite extensive research on 2D moiré lattices, the physics of three-dimensional (3D) moiré lattices—formed by superimposing rotated 3D periodic sub-lattices with crystallographic symmetries, which exhibit unique 3D potentials determined by twisting angles—remains largely unexplored. In this work, we demonstrate that depending on the choice of rotation angles, moiré potentials composed of two cubic sub-lattices can exhibit three different phases: they can be fully 3D incommensurate, incommensurate in only one spatial direction (while remaining periodic in the orthogonal plane), or fully periodic. These incommensurate potentials, which can be created for condensates of non-interacting atoms using judiciously combined laser beams, are shown to support compact states of three distinct types: fully localized in space, confined to a line, or confined to a specific plane. Our findings establish a foundation for controlling wave localization in incommensurate 3D moiré systems, with potential applications in cold atom systems, optics, and beyond. 3D moiré lattices can exhibit distinct incommensurate phases depending on twist angles. Here, authors demonstrate phase-controlled emergence of fully localized, line-localized, and plane-localized states, enabling tunable 3D transport in cold atom and optical systems.