Moiré physics has transcended spatial dimensions, extending into synthetic domains and enabling novel quantum phenomena. We propose a theoretical model for a two-dimensional (2D) moiré time crystal formed by ultracold atoms, induced by periodic perturbations applied to a nonlattice trap. Our analysis reveals the emergence of regional superfluid states exhibiting moiré-scale quantum coherence across temporal, spatial, and spatiotemporal domains. This Letter provides fundamental insights into temporal moiré phenomena and presents an alternative pathway to engineer spatial moiré phases without requiring twisted multilayer lattices.
Moiré physics has transcended spatial dimensions, extending into synthetic domains and enabling novel quantum phenomena. We propose a theoretical model for a two-dimensional (2D) moiré time crystal formed by ultracold atoms, induced by periodic perturbations applied to a nonlattice trap. Our analysis reveals the emergence of regional superfluid states exhibiting moiré-scale quantum coherence across temporal, spatial, and spatiotemporal domains. This Letter provides fundamental insights into temporal moiré phenomena and presents an alternative pathway to engineer spatial moiré phases without requiring twisted multilayer lattices.
The work intends to extend the moiré physics to three dimensions. Three-dimensional moiré patterns can be realized in ultracold atomic gases by coupling two spin states in spin-dependent optical lattices with a relative twist, a structure currently unachievable in solid-state materials. We give the commensurate conditions under which the three-dimensional moiré pattern features a periodic structure termed a three-dimensional moiré crystal. We emphasize a key distinction of three-dimensional moiré physics: In three dimensions, the twist operation generically does not commute with the rotational symmetry of the original lattice, unlike in two dimensions, where these two always commute. Consequently, the moiré crystal can exhibit a crystalline structure that differs from the original underlying lattice. We demonstrate that twisting a simple cubic lattice can generate various crystal structures. This capability of altering crystal structures by twisting offers a broad range of tunability for three-dimensional band structures.
A Moiré time crystal is a non-equilibrium quantum phase emerging from the coherent interference of two distinct frequencies, at least one being the intrinsic oscillation of a symmetry-broken time crystal. Its hallmark is an ultra-long beat period, reflecting a time-domain mapping of the Moiré fringes that arise from mismatched spatial lattices. However, to date, no experimental realization of such a Moiré time crystal has been reported. In this work, by applying a bichromatic driving field with two distinct frequencies, we demonstrate that the interplay between long-range Rydberg interactions and dissipation gives rise to a unique comb-like Moiré pattern characterized by a beat-note comb, which superimposes subharmonic periodicity and fundamental frequencies. This Moiré pattern formed by two mismatched drives is staggered in the spectrum as the frequency of one driver changes. We experimentally map the phase diagram of the system and identify a robust region where the Moiré temporal order persists against perturbations in laser detuning. The reported Moiré time crystal not only provides a controllable platform for exploring emergent slow-fast dynamics and synthetic space-time symmetries but also opens avenues for engineering complex temporal order in driven quantum many-body systems.
Moiré superlattices, a twisted functional structure crossing the periodic and nonperiodic potentials, have recently attracted great interest in multidisciplinary fields, including optics and ultracold atoms, because of their unique band structures, physical properties, and potential implications. Driven by recent experiments on quantum phenomena of bosonic gases, the atomic Bose–Einstein condensates in moiré optical lattices, by which other quantum gases such as ultracold fermionic atoms are trapped, could be readily achieved in ultracold atom laboratories, whereas the associated nonlinear localization mechanism remains unexploited. Here, we report the nonlinear localization theory of ultracold atomic Fermi gases in two-dimensional moiré optical lattices. The linear Bloch-wave spectrum of such a twisted structure exhibits rich nontrivial flat bands, which are separated by different finite bandgaps wherein the existence, properties, and dynamics of localized superfluid Fermi gas structures of two types, gap solitons and gap vortices (topological modes) with vortex charge S=1, are studied numerically. Our results demonstrate the wide stability regions and robustness of these localized structures, opening up a new avenue for studying soliton physics and moiré physics in ultracold atoms beyond bosonic gases.
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.
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.
Recent advances in spin-dependent optical lattices [Meng et al., Nature \textbf{615}, 231 (2023)] have enabled the experimental implementation of two superimposed three-dimensional lattices, presenting new opportunities to investigate \textit{three-dimensional moiré physics} in ultracold atomic gases. This work studies the moiré physics of atoms within a spin-dependent cubic lattice with relative twists along different directions. It is discovered that dimensionality significantly influences the low-energy moiré physics. From a geometric perspective, this manifests in the observation that moiré patterns, generated by rotating lattices along different axes, can exhibit either periodic or quasi-periodic behavior--a feature not present in two-dimensional systems. We develop a low-energy effective theory applicable to systems with arbitrary rotation axes and small rotation angles. This theory elucidates the emergence of quasi-periodicity in three dimensions and demonstrates its correlation with the arithmetic properties of the rotation axes. Numerical analyses reveal that these quasi-periodic moiré potentials can lead to distinctive dimensional localization behaviors of atoms, manifesting as localized wave functions in planar or linear configurations.