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arXiv:2104.13625

Observation of Anomalous Moiré Patterns

Omer Amit, Or Dobkowski, Zhifan Zhou, Yair Margalit, Yonathan Japha, S. Moukouri, Yigal Meir, B. Horovitz, R. Folman

Published Apr 28, 2021• 0 citations
arXivHTMLPDF

Abstract

Moiré patterns are omnipresent. They are important for any overlapping periodic phenomenon, from vibrational and electromagnetic, to condensed matter. Here we show, both theoretically and via experimental simulations by ultracold atoms, that for one-dimensional finite-size periodic systems, moiré patterns give rise to anomalous features in both classical and quantum systems. In contrast to the standard moiré phenomenon, in which the pattern periodicity is a result of a beat-note between its constituents, we demonstrate moiré patterns formed from constituents with the same periodicity. Surprisingly, we observe, in addition, rigidity and singularities. We furthermore uncover universal properties in the frequency domain, which might serve as a novel probe of emitters. These one-dimensional effects could be relevant to a wide range of periodic phenomena.

DOI
10.48550/arxiv.2104.13625

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Moiré patterns are omnipresent. They are important for any overlapping periodic phenomenon, from vibrational and electromagnetic, to condensed matter. Here we show, both theoretically and via experimental simulations by ultracold atoms, that for one-dimensional finite-size periodic systems, moiré patterns give rise to anomalous features in both classical and quantum systems. In contrast to the standard moiré phenomenon, in which the pattern periodicity is a result of a beat-note between its constituents, we demonstrate moiré patterns formed from constituents with the same periodicity. Surprisingly, we observe, in addition, rigidity and singularities. We furthermore uncover universal properties in the frequency domain, which might serve as a novel probe of emitters. These one-dimensional effects could be relevant to a wide range of periodic phenomena.
Abstract Interference between overlapping periodic patterns gives rise to important phenomena, such as Moiré fringes, appearing when the patterns have different periods or orientations. Here we present a novel phenomenon, applicable to both the classical and quantum regimes, where two one-dimensional localized periodic patterns with the same period interfere to create fringes with anomalous periodicity. We analyze the effect theoretically and demonstrate it with atomic matter waves. When a central parameter of the system is scanned continuously, we observe a discontinuous but piecewise-rigid periodicity of the resulting fringes. We show that this is a universal phenomenon that emerges from a superposition of two spatially shifted localized periodic patterns of any source or nature when they interfere with a global phase difference. The rigidity of the spectrum becomes even more robust for a coherent superposition of non-overlapping wavepackets, although the conventional interferometric visibility drops to zero. The effect is expected to appear in space and time, as well as in the momentum distribution of quantum particles.
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.
Abstract Recent advances in spin-dependent optical lattices [ Meng et al . 2023 Nature 615 , 231 ] have enabled the experimental implementation of two superimposed three-dimensional lattices, presenting new opportunities to investigate 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.
Moiré patterns are produced when two periodic structures with different spatial frequencies are superposed. The transmission of the resulting structure gives rise to spatial beatings which are called moiré fringes. In classical optics, the interest in moiré fringes comes from the fact that the spatial beating given by the frequency difference gives information about details (high spatial frequency) of a given spatial structure. We show that moiré fringes can also arise in the spatial distribution of the coincidence count rate of twin photons from the parametric down-conversion, when spatial structures with different frequencies are placed in the path of each one of the twin beams. In other words, we demonstrate how moiré fringes can arise from quantum images.
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.
Electromagnetically induced optical (or photonic) lattices via atomic coherence in atomic ensembles have recently received great theoretical and experimental interest. We here conceive a way to generate electromagnetically induced moiré optical lattices — a twisted periodic pattern when two identical periodic patterns (lattices) are overlapped in a twisted angle ( θ ) — in a three-level coherent atomic gas working under electromagnetically induced transparency. We show that, changing the twisted angle and relative strength between the two constitutive sublattices, the moiré Bloch bands that are extremely flattened can always appear, resembling the typical flat-band and moiré physics found in other contexts. Dynamics of light propagation in the induced periodic structures demonstrating the unique linear localization and delocalization properties are also revealed. Our scheme can be implemented in a Rubidium atomic medium, where the predicted moiré optical lattices and flattened bands are naturally observable.