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Frontiers of Physics

Efficient and tunable photoinduced moiré lattice in an atomic ensemble

Muhua Zhai, Feng Wen, Shaowei Zhang, Huapeng Ye, Zhenkun Wu, Dong Zhong, Yang Lei, Yangxin Gu, Wei Wang, Minghui Zhang, Yanpeng Zhang, Hongxing Wang

Published Jan 1, 2025• 6 citations
Publisher

Abstract

Photonic moiré lattices (PMLs), with unique twisted periodic patterns, provide a valuable platform for investigating strongly correlated materials, unconventional superconductivity, and the localization−delocalization transition. However, PMLs created either by the misorientation between lattice layers or by twisted van der Waals materials are typically non-tunable and inherently possess immutable refractive indices. Unlike those in the moiré lattices of twisted two-dimensional materials, our work reports a moiré lattice formed by overlapping two identical sublattices with twisted angles in an ultracold atomic ensemble. This photoinduced moiré lattice with two twisted sublattices exhibits high flexibility and rich periodicity through adjustable twisted angles. Our results indicate that both the absorption/dispersion coefficients and the transmission of the photoinduced moiré lattices can be effectively tuned by photon detuning and Rabi frequency, resulting in amplitude- and phase-type moiré lattices. Based on the Fraunhofer diffraction theory, we have demonstrated that the far-field diffraction efficiency can be adjusted via altering photon detuning, and the rotation angle serves as a control knob for modulating the diffracted intensity distribution, thereby optimizing the performance of the photonic lattice. It is also found that the operation domains of the moiré lattices with different rotation angles remain consistent, allowing for seamless conversion between various moiré period structures. Furthermore, a moiré lattice composed of three twisted sublattices is investigated, revealing that the diffraction energy is uniformly dispersed in a circular distribution, which provides excellent agility in the design of optical devices. Such tunable PML offer a powerful tool for studying light propagation control and the intriguing physics of twisted systems in atomic media.

DOI
10.15302/frontphys.2025.034207

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Photonic moiré lattices (PMLs), with unique twisted periodic patterns, provide a valuable platform for investigating strongly correlated materials, unconventional superconductivity, and the localization−delocalization transition. However, PMLs created either by the misorientation between lattice layers or by twisted van der Waals materials are typically non-tunable and inherently possess immutable refractive indices. Unlike those in the moiré lattices of twisted two-dimensional materials, our work reports a moiré lattice formed by overlapping two identical sublattices with twisted angles in an ultracold atomic ensemble. This photoinduced moiré lattice with two twisted sublattices exhibits high flexibility and rich periodicity through adjustable twisted angles. Our results indicate that both the absorption/dispersion coefficients and the transmission of the photoinduced moiré lattices can be effectively tuned by photon detuning and Rabi frequency, resulting in amplitude- and phase-type moiré lattices. Based on the Fraunhofer diffraction theory, we have demonstrated that the far-field diffraction efficiency can be adjusted via altering photon detuning, and the rotation angle serves as a control knob for modulating the diffracted intensity distribution, thereby optimizing the performance of the photonic lattice. It is also found that the operation domains of the moiré lattices with different rotation angles remain consistent, allowing for seamless conversion between various moiré period structures. Furthermore, a moiré lattice composed of three twisted sublattices is investigated, revealing that the diffraction energy is uniformly dispersed in a circular distribution, which provides excellent agility in the design of optical devices. Such tunable PML offer a powerful tool for studying light propagation control and the intriguing physics of twisted systems in atomic media.
Two-dimensional (2D) photoinduced lattices in atomic ensembles constitute an ideal platform for the systematic investigation of light−matter interactions and controllable diffraction phenomena. Nevertheless, existing research efforts have primarily concentrated on fixed or symmetric lattice configurations, resulting in insufficient exploration of asymmetric diffraction behaviors. Herein, we theoretically propose a 2D phase-controllable photoinduced lattice, which is constructed by overlapping two identical sublattices with independently tunable spatial phases within an atomic ensemble. Spatial phase difference between the two sublattices can be controlled directly by tuning the initial phase of the lattice-forming beams, eliminating the need for complex optical path designs and tedious system optimization. We demonstrate that the absorption, dispersion, and transmission properties of the proposed lattice can be dynamically tuned via photon detuning, leading to the generation of both amplitude- and phase-type lattices. Notably, the amplitude-type lattices exhibit insensitivity to phase variations, whereas the phase-type lattices demonstrate remarkable phase-dependent energy transfer effects and pronounced directional asymmetry. Specifically, a one-dimensional (1D) spatial phase difference between the two identical sublattices induces stripe-like modulation, whereas a 2D spatial phase difference yields reconfigurable anisotropic 2D modulation patterns. Furthermore, we demonstrate that the combined modulation of detuning and spatial phase difference induces periodic asymmetric oscillations in diffraction energy, enabling precisely controllable asymmetric distribution of diffraction. Our work establishes a comprehensive theoretical framework for phase-driven asymmetric diffraction in photoinduced lattices and provides an effective strategy for the development of dynamically reconfigurable all-optical nonreciprocal photonic devices.
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.
Abstract Artificial periodic structures (APS) with controllable optical properties are highly demanded in all‐optical devices and circuits in communication networks. However, APS realized in solid materials are usually non‐tunable and inherently possess immutable photonic bandgap. In this article, a novel honeycomb lattice in an atomic ensemble by utilizing the multi‐beam interference method is reported. Unlike the honeycomb lattice formed in solid materials, the optical properties of this photoinduced honeycomb lattice, such as the absorption/dispersion coefficients and the photonic bandgap can be efficiently tuned by two‐photon detuning and Rabi frequency, resulting in both amplitude‐ and phase‐ type honeycomb lattice. Based on the two‐photon quantum‐imaging method, the near‐field diffraction of the honeycomb lattice is also investigated. It is found that the resolution of the diffraction pattern is tunable by simply adjusting the manner of the two detectors scanning across the imaging beams. In addition, the contrast of the pattern can be greatly enhanced by tuning the optical properties of the lattice. Such an optical honeycomb lattice with tunable properties could find applications in all‐optical switching at the few photons level and paves the way for the generation and manipulation of optical topological insulators.
We investigate the localization-delocalization transition (LDT) in an electromagnetically induced photonic lattice. A four-level tripod-type scheme in atomic ensembles is proposed to generate an effective photonic moir\'e lattice through the electromagnetically induced transparency (EIT) mechanism. By taking advantage of the tunable atomic coherence, we show that both periodic (commensurable) and aperiodic (incommensurable) structure can be created in such a photonic moir\'e lattice via adjusting the twist angle between two superimposed periodic patterns with square primitive. Furthermore, we also find that by tuning the amplitudes of these two superimposed periodic patterns, the localization-delocalization transition occurs for the light propagating in the aperiodic moir\'e lattice. Such localization is shown to link the fact that the flat bands of moir\'e lattice support quasi-nondiffracting localized modes and thus induce the localization of the initially localized beam. It would provide a promising approach to control the light propagation via the electromagnetically induced photonic lattice.
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.
Conventional periodic structures usually have nontunable refractive indices and thus lead to immutable photonic bandgaps. A periodic structure created in an ultracold atoms ensemble by externally controlled light can overcome this disadvantage and enable lots of promising applications. Here, two novel types of optically induced square lattices, i.e., the amplitude and phase lattices, are proposed in an ultracold atoms ensemble by interfering four ordinary plane waves under different parameter conditions. We demonstrate that in the far-field regime, the atomic amplitude lattice with high transmissivity behaves similarly to an ideal pure sinusoidal amplitude lattice, whereas the atomic phase lattices capable of producing phase excursion across a weak probe beam along with high transmissivity remains equally ideal. Moreover, we identify that the quality of Talbot imaging about a phase lattice is greatly improved when compared with an amplitude lattice. Such an atomic lattice could find applications in all-optical switching at the few photons level and paves the way for imaging ultracold atoms or molecules both in the near-field and in the far-field with a nondestructive and lensless approach.