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Showing papers by "Yuri S. Kivshar published in 2020"


Journal ArticleDOI
17 Jan 2020-Science
TL;DR: This work implements a new physical mechanism for suppressing radiative losses of individual nanoscale resonators to engineer special modes with high quality factors: optical bound states in the continuum (BICs), and demonstrates that an individual subwavelength dielectric resonator hosting a BIC mode can boost nonlinear effects increasing second-harmonic generation efficiency.
Abstract: Subwavelength optical resonators made of high-index dielectric materials provide efficient ways to manipulate light at the nanoscale through mode interferences and enhancement of both electric and magnetic fields. Such Mie-resonant dielectric structures have low absorption, and their functionalities are limited predominantly by radiative losses. We implement a new physical mechanism for suppressing radiative losses of individual nanoscale resonators to engineer special modes with high quality factors: optical bound states in the continuum (BICs). We demonstrate that an individual subwavelength dielectric resonator hosting a BIC mode can boost nonlinear effects increasing second-harmonic generation efficiency. Our work suggests a route to use subwavelength high-index dielectric resonators for a strong enhancement of light-matter interactions with applications to nonlinear optics, nanoscale lasers, quantum photonics, and sensors.

543 citations


Journal ArticleDOI
28 Feb 2020-Science
TL;DR: The results provide an approach that breaks the long-standing trade-off between low energy consumption and high-speed nanophotonics, introducing vortex microlasers that are switchable at terahertz frequencies.
Abstract: The development of classical and quantum information–processing technology calls for on-chip integrated sources of structured light. Although integrated vortex microlasers have been previously demonstrated, they remain static and possess relatively high lasing thresholds, making them unsuitable for high-speed optical communication and computing. We introduce perovskite-based vortex microlasers and demonstrate their application to ultrafast all-optical switching at room temperature. By exploiting both mode symmetry and far-field properties, we reveal that the vortex beam lasing can be switched to linearly polarized beam lasing, or vice versa, with switching times of 1 to 1.5 picoseconds and energy consumption that is orders of magnitude lower than in previously demonstrated all-optical switching. Our results provide an approach that breaks the long-standing trade-off between low energy consumption and high-speed nanophotonics, introducing vortex microlasers that are switchable at terahertz frequencies.

414 citations


Journal ArticleDOI
TL;DR: In this paper, the authors introduce the emerging field of nonlinear topological photonics and highlight the recent developments in bridging the physics of topological phases with nonlinear optics.
Abstract: Rapidly growing demands for fast information processing have launched a race for creating compact and highly efficient optical devices that can reliably transmit signals without losses. Recently discovered topological phases of light provide novel opportunities for photonic devices robust against scattering losses and disorder. Combining these topological photonic structures with nonlinear effects will unlock advanced functionalities such as magnet-free nonreciprocity and active tunability. Here, we introduce the emerging field of nonlinear topological photonics and highlight the recent developments in bridging the physics of topological phases with nonlinear optics. This includes the design of novel photonic platforms which combine topological phases of light with appreciable nonlinear response, self-interaction effects leading to edge solitons in topological photonic lattices, frequency conversion, active photonic structures exhibiting lasing from topologically protected modes, and many-body quantum topological phases of light. We also chart future research directions discussing device applications such as mode stabilization in lasers, parametric amplifiers protected against feedback, and ultrafast optical switches employing topological waveguides.

337 citations


Journal ArticleDOI
TL;DR: This work suggests a direct route to boost the resonant field enhancement in plasmonic metasurfaces via combining a small effective mode volume of plAsmonic systems with engineered high-Q resonances provided by the BIC physics, with multiple applications to enhance light-matter interaction for nano-optics and quantum photonics.
Abstract: The concept of optical bound states in the continuum (BICs) currently drives the field of dielectric resonant nanophotonics, providing an important physical mechanism for engineering high-quality (high-Q) optical resonances in high-index dielectric nanoparticles and structured dielectric metasurfaces. For structured metallic metasurfaces, realization of BICs remains a challenge associated with strong dissipative losses of plasmonic materials. Here, we suggest and realize experimentally anisotropic plasmonic metasurfaces supporting high-Q resonances governed by quasi-BIC collective resonant modes. Our metasurfaces are composed of arrays of vertically oriented double-pillar meta-molecules covered by a thin layer of gold. We engineer quasi-BIC modes and observe experimentally sharp resonances in mid-IR reflectance spectra. Our work suggests a direct route to boost the resonant field enhancement in plasmonic metasurfaces via combining a small effective mode volume of plasmonic systems with engineered high-Q resonances provided by the BIC physics, with multiple applications to enhance light-matter interaction for nano-optics and quantum photonics.

159 citations


Journal ArticleDOI
TL;DR: It is demonstrated that rotationally symmetric chiral metasurfaces can support sharp resonances with the maximum optical chirality determined by precise shaping of bound states in the continuum (BICs), and a realization of such chiral BIC metAsurfaces based on pairs of dielectric bars is proposed.
Abstract: We demonstrate that rotationally symmetric chiral metasurfaces can support sharp resonances with the maximum optical chirality determined by precise shaping of bound states in the continuum (BICs) Being uncoupled from one circular polarization of light and resonantly coupled to its counterpart, a metasurface hosting the chiral BIC resonance exhibits a narrow peak in the circular dichroism spectrum with the quality factor limited by weak dissipation losses We propose a realization of such chiral BIC metasurfaces based on pairs of dielectric bars and validate the concept of maximum chirality by numerical simulations

148 citations


Journal ArticleDOI
TL;DR: This work boosts the effective nonlinear susceptibility of a TMD monolayer by integrating it with a resonant dielectric metasurface, which supports pronounced optical resonances with high quality factors: bound states in the continuum (BICs).
Abstract: Atomically thin monolayers of transition metal dichalcogenides (TMDs) have emerged as a promising class of novel materials for optoelectronics and nonlinear optics. However, the intrinsic nonlinearity of TMD monolayers is weak, limiting their functionalities for nonlinear optical processes such as frequency conversion. Here we boost the effective nonlinear susceptibility of a TMD monolayer by integrating it with a resonant dielectric metasurface that supports pronounced optical resonances with high quality factors: bound states in the continuum (BICs). We demonstrate that a WS2 monolayer combined with a silicon metasurface hosting BICs exhibits enhanced second-harmonic intensity by more than 3 orders of magnitude relative to a WS2 monolayer on top of a flat silicon film of the same thickness. Our work suggests a pathway to employ high-index dielectric metasurfaces as hybrid structures for enhancement of TMD nonlinearities with applications in nonlinear microscopy, optoelectronics, and signal processing.

145 citations


Journal ArticleDOI
TL;DR: This work demonstrates lasing action of corner states in nanophotonic topological structures and identifies several multipole corner modes with distinct emission profiles via hyperspectral imaging and discern signatures of non-Hermitian radiative coupling of leaky topological states.
Abstract: Topological photonics provides a fundamental framework for robust manipulation of light, including directional transport and localization with built-in immunity to disorder. Combined with an optical gain, active topological cavities hold special promise for a design of light-emitting devices. Most studies to date have focused on lasing at topological edges of finite systems or domain walls. Recently discovered higher-order topological phases enable strong high-quality confinement of light at the corners. Here, we demonstrate lasing action of corner states in nanophotonic topological structures. We identify several multipole corner modes with distinct emission profiles via hyperspectral imaging and discern signatures of non-Hermitian radiative coupling of leaky topological states. In addition, depending on the pump position in a large-size cavity, we generate selectively lasing from either edge or corner states within the topological bandgap. Our studies provide the direct observation of multipolar lasing and engineered collective resonances in active topological nanostructures.

127 citations


Journal ArticleDOI
TL;DR: In this paper, the authors review recent progress in the field of quantum-photonics applications of metasurfaces, focusing on innovative and promising approaches to create, manipulate, and detect nonclassical light.
Abstract: Rapid progress in the development of metasurfaces allowed to replace bulky optical assemblies with thin nanostructured films, often called metasurfaces, opening a broad range of novel and superior applications to the generation, manipulation, and detection of light in classical optics. Recently, these developments started making a headway in quantum photonics, where novel opportunities arose for the control of nonclassical nature of light, including photon statistics, quantum state superposition, quantum entanglement, and single-photon detection. In this Perspective, we review recent progress in the field of quantum-photonics applications of metasurfaces, focusing on innovative and promising approaches to create, manipulate, and detect nonclassical light.

113 citations


Journal ArticleDOI
02 Jun 2020-ACS Nano
TL;DR: It is demonstrated that monolithic dielectric nanoparticles made of CsPbBr3 halide perovskites can exhibit both efficient Mie-resonant lasing and structural coloring in visible and near-IR frequency ranges.
Abstract: Subwavelength particles supporting Mie resonances underpin a strategy in nanophotonics for efficient control and manipulation of light by employing both an electric and a magnetic optically induced multipolar resonant response. Here, we demonstrate that monolithic dielectric nanoparticles made of CsPbBr3 halide perovskites can exhibit both efficient Mie-resonant lasing and structural coloring in the visible and near-IR frequency ranges. We employ a simple chemical synthesis with nearly epitaxial quality for fabricating subwavelength cubes with high optical gain and demonstrate single-mode lasing governed by the Mie resonances from nanocubes as small as 310 nm by the side length. These active nanoantennas represent the most compact room-temperature nonplasmonic nanolasers demonstrated until now.

105 citations


Journal ArticleDOI
TL;DR: In this paper, bound states can dramatically reduce radiation from optical re-resonators, opening up new application prospects in nanophotonics, where bound states were identified nearly a century ago by early workers in quantum mechanics.
Abstract: Identified nearly a century ago by early workers in quantum mechanics, bound states can dramatically reduce radiation from optical resonators, opening up new application prospects in nanophotonics.

80 citations


Journal ArticleDOI
TL;DR: This work proposes and demonstrates experimentally active nanophotonic topological cavities incorporating III–V semiconductor quantum wells as a gain medium in the structure and shows room-temperature lasing with a narrow spectrum, high coherence, and threshold behaviour, a step towards topologically controlled ultrasmall light sources with nontrivial radiation characteristics.
Abstract: The study of topological phases of light underpins a promising paradigm for engineering disorder-immune compact photonic devices with unusual properties. Combined with an optical gain, topological photonic structures provide a novel platform for micro- and nanoscale lasers, which could benefit from nontrivial band topology and spatially localized gap states. Here, we propose and demonstrate experimentally active nanophotonic topological cavities incorporating III–V semiconductor quantum wells as a gain medium in the structure. We observe room-temperature lasing with a narrow spectrum, high coherence, and threshold behaviour. The emitted beam hosts a singularity encoded by a triade cavity mode that resides in the bandgap of two interfaced valley-Hall periodic photonic lattices with opposite parity breaking. Our findings make a step towards topologically controlled ultrasmall light sources with nontrivial radiation characteristics. Active topological cavities that can lase at room temperature could bring new opportunities for controlling light in integrated nanophotonic circuits. Smirnova et al. etched a special pattern of nanoscale holes into a 250 nm thick slab of the compound semiconductor InGaAsP to create a triangle-shaped cavity with optical behaviour governed by the band topology. The presence of quantum wells in the slab provides the cavity with optical gain allowing it to lase in the near-infrared when excited with nanosecond pump pulses at 980 nm. The laser emission is observed to be spectrally narrow with high coherence and hosts a donut-shaped singularity in Fourier space. The achievement opens the way to a new type of nanophotonic light source which exhibits unusual radiation characteristics and suits integration with metasurfaces.

Journal ArticleDOI
TL;DR: The classical lens theory is revisited and a generalized Gaussian lens equation for nonlinear imaging is suggested, verified both experimentally and analytically.
Abstract: Nonlinear metasurfaces incorporate many of the functionalities of their linear counterparts such as wavefront shaping, but simultaneously they perform nonlinear optical transformations. This dual functionality leads to a rather unintuitive physical behavior which is still widely unexplored for many photonic applications. The nonlinear processes render some basic principles governing the functionality of linear metasurfaces. Exemplarily, the superposition principle and the geometric optics approximation become not directly applicable to nonlinear metasurfaces. On the other hand, nonlinear metasurfaces facilitate new phenomena that are not possible in the linear regime. Here, we study the imaging of objects through a dielectric nonlinear metalens. We illuminate objects by infrared light and record their generated images at the visible third-harmonic wavelengths. We revisit the classical lens theory and suggest a generalized Gaussian lens equation for nonlinear imaging, verified both experimentally and analytically. We also demonstrate experimentally higher-order spatial correlations facilitated by the nonlinear metalens, resulting in additional image features.

Journal ArticleDOI
TL;DR: The field of nonlinear optical metamaterials is a well-established discipline that relies on macroscopic media and employs propagation distances longer than a wavelength of light.
Abstract: The field of nonlinear optics is a well-established discipline that relies on macroscopic media and employs propagation distances longer than a wavelength of light. Recent progress with electromagnetic metamaterials has allowed for the expansion of this field into new directions of new phenomena and novel functionalities. In particular, nonlinear effects in thin, artificially structured materials such as metasurfaces do not rely on phase-matching conditions and symmetry-related selection rules of natural materials; they may be substantially enhanced by strong local and collective resonances of fields inside the metasurface nanostructures. Consequently, nonlinear processes may extend beyond simple harmonic generation and spectral broadening due to electronic nonlinearities. This article provides a brief review of basic concepts and recent results in the field of nonlinear optical metasurfaces.

Journal ArticleDOI
TL;DR: The work in this article was supported by the Australian Research Council (Grant number FT160100153) and the Strategic Fund of the Australian National University (SfU) and was conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility.
Abstract: The work was supported by the Australian Research Council (Grant number FT160100153) and the Strategic Fund of the Australian National University. A portion of this research was conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility. The authors also acknowledge support from the Singapore Ministry of Education AcRF Tier 1 (Grant RG191/17). K.K. acknowledges a support from the Russian Science Foundation (grant 18-72-10140).

Journal ArticleDOI
TL;DR: In this paper, the authors acknowledge support by the Ministry of Education and Science of the Russian Federation (3.1500.2017/4.6) and the Australian Research Council (ARCC).
Abstract: S.H., P.P., Y.K.S., and R.S. acknowledge Singapore Ministry of Education (MOE), Grants MOE2016-T3-1-006, MOE2017-T2-1-110, and RG191/17. M.V.R. and Y.S.K. acknowledge support by the Ministry of Education and Science of the Russian Federation (3.1500.2017/4.6) and the Australian Research Council.

Journal ArticleDOI
TL;DR: It is predicted the existence of a novel interaction-induced spatial localization in a periodic array of qubits coupled to a waveguide, which can be described as a quantum analogue of a self-induced optical lattice between two indistinguishable photons.
Abstract: We predict the existence of a novel interaction-induced spatial localization in a periodic array of qubits coupled to a waveguide. This localization can be described as a quantum analogue of a self-induced optical lattice between two indistinguishable photons, where one photon creates a standing wave that traps the other photon. The localization is caused by the interplay between on-site repulsion due to the photon blockade and the waveguide-mediated long-range coupling between the qubits.

Journal ArticleDOI
TL;DR: A review of the recent results on the generation and observation of polarization singularities in metaphotonics can be found in this article, where a discussion of various photonic-crystal structures, for which both near and far-field patterns manifest diverse polarization singularity characterized by the integer Poincare or more general half-integer Hopf indices (topological charges).
Abstract: Polarization singularities of vectorial electromagnetic fields locate at the positions (such as points, lines, or surfaces) where properties of polarization ellipses are not defined. They are manifested as circular and linear polarization, for which respectively the semi-major axes and normal vectors of polarization ellipses become indefinite. First observed in conical diffraction in the 1830s, the field of polarization singularities has been systematically reshaped and deepened by many pioneers of wave optics. Together with other exotic phenomena such as non-Hermiticity and topology, polarization singularities have been introduced into the vibrant field of nanophotonics, rendering unprecedented flexibilities for manipulations of light-matter interactions at the nanoscale. Here we review the recent results on the generation and observation of polarization singularities in metaphotonics. We start with the discussion of polarization singularities in the Mie theory, where both electric and magnetic multipoles are explored from perspectives of local and global polarization properties. We then proceed with the discussion of various photonic-crystal structures, for which both near- and far-field patterns manifest diverse polarization singularities characterized by the integer Poincare or more general half-integer Hopf indices (topological charges). Next, we review the most recent studies of conversions from polarization to phase singularities in scalar wave optics, demonstrating how bound states in the continuum can be exploited to generate directly optical vortices of various charges. Throughout our paper, we discuss and highlight several fundamental concepts and demonstrate their close connections and special links to metaphotonics. We believe polarization singularities can provide novel perspectives for light-matter manipulation for both fundamental studies and their practical applications.

Journal ArticleDOI
01 May 2020
TL;DR: In this article, a topology optimization approach for inversely designing the higher-order photonic topological insulators with edge and corner states at various frequencies is proposed, which allows for topological routing via the edge and corners states.
Abstract: This paper proposes a topology optimization approach for inversely designing the higher-order photonic topological insulators with edge and corner states at various frequencies. Programming newly-created structures allows for topological routing via the edge and corner states.

Journal ArticleDOI
TL;DR: In this paper, the authors demonstrate the lasing action of corner states in a nanophotonic topological cavity and identify four multipole corner modes with distinct emission profiles via hyperspectral imaging and discern signatures of non-Hermitian radiative coupling of leaky topological states.
Abstract: Topological photonics provides a fundamental framework for robust manipulation of light, including directional transport and localization with built-in immunity to disorder. Combined with an optical gain, active topological cavities hold special promise for a design of light-emitting devices. Most studies to date have focused on lasing at topological edges of finite systems or domain walls. Recently discovered higher-order topological phases enable strong high-quality confinement of light at the corners. Here we demonstrate lasing action of corner states in a nanophotonic topological cavity. We identify four multipole corner modes with distinct emission profiles via hyperspectral imaging and discern signatures of non-Hermitian radiative coupling of leaky topological states. In addition, depending on the pump position in a large-size cavity, we selectively generate lasing from either edge or corner states within the topological bandgap. Our findings introduce pathways to engineer collective resonances and tailor generation of light in active topological circuits.

Posted Content
TL;DR: The concept of optical bound states in the continuum (BICs) underpins the existence of strongly localized waves embedded into the radiation spectrum that can enhance the electromagnetic fields in subwavelength photonic structures.
Abstract: The concept of optical bound states in the continuum (BICs) underpins the existence of strongly localized waves embedded into the radiation spectrum that can enhance the electromagnetic fields in subwavelength photonic structures. Early studies of optical BICs in waveguides and photonic crystals uncovered their topological properties, and the concept of quasi-BIC metasurfaces facilitated applications of strong light-matter interactions to biosensing, lasing, and low-order nonlinear processes. Here we employ BIC-empowered dielectric metasurfaces to generate efficiently high optical harmonics up to the 11th order. We optimize a BIC mode for the first few harmonics and observe a transition between perturbative and nonperturbative nonlinear regimes. We also suggest a general strategy for designing subwavelength structures with strong resonances and nonperturbative nonlinearities. Our work bridges the fields of perturbative and nonperturbative nonlinear optics on the subwavelength scale.


Journal ArticleDOI
TL;DR: In this article, the generalized Kerker conditions were employed to overlap electric and magnetic Mie resonances in each meta-atom of MAPbBr3 perovskite metasurface and demonstrate broadband suppression of reflection down to 4%.
Abstract: Meta-optics based on optically-resonant dielectric nanostructures is a rapidly developing research field with many potential applications. Halide perovskite metasurfaces emerged recently as a novel platform for meta-optics, and they offer unique opportunities for control of light in optoelectronic devices. Here we employ the generalized Kerker conditions to overlap electric and magnetic Mie resonances in each meta-atom of MAPbBr3 perovskite metasurface and demonstrate broadband suppression of reflection down to 4%. We reveal also that metasurface nanostructuring is also beneficial for the enhancement of photoluminescence. Our results may be useful for applications of nanostructured halide perovskites in photovoltaics and semi-transparent multifunctional metadevices where reflection reduction is important for their high efficiency.

Journal ArticleDOI
TL;DR: This work study experimentally stimulated Raman scattering (SRS) in isolated silicon (c-Si) nanoparticles and observes a transition from spontaneous to stimulated scattering manifested in a nonlinear growth of the signal intensity above a certain pump threshold.
Abstract: Resonant dielectric structures have emerged recently as a new platform for subwavelength nonplasmonic photonics. It was suggested and demonstrated that magnetic and electric Mie resonances can enhance substantially many effects at the nanoscale including spontaneous Raman scattering. Here, we demonstrate stimulated Raman scattering (SRS) for isolated crystalline silicon (c-Si) nanoparticles and observe experimentally a transition from spontaneous to stimulated scattering manifested in a nonlinear growth of the signal intensity above a certain pump threshold. At the Mie resonance, the light gets confined into a low volume of the resonant mode with enhanced electromagnetic fields inside the c-Si nanoparticle due to its high refractive index, which leads to an overall strong SRS signal at low pump intensities. Our finding paves the way for the development of efficient Raman nanolasers for multifunctional photonic metadevices.

Posted Content
TL;DR: In this article, the generalized Kerker conditions were employed to overlap electric and magnetic Mie resonances in each meta-atom of MAPbBr3 perovskite metasurface and demonstrate broadband suppression of reflection down to 4%.
Abstract: Meta-optics based on optically-resonant dielectric nanostructures is a rapidly developing research field with many potential applications. Halide perovskite metasurfaces emerged recently as a novel platform for meta-optics, and they offer unique opportunities for control of light in optoelectronic devices. Here we employ the generalized Kerker conditions to overlap electric and magnetic Mie resonances in each meta-atom of MAPbBr3 perovskite metasurface and demonstrate broadband suppression of reflection down to 4%. We reveal also that metasurface nanostructuring is also beneficial for the enhancement of photoluminescence. Our results may be useful for applications of nanostructured halide perovskites in photovoltaics and semi-transparent multifunctional metadevices where reflection reduction is important for their high efficiency.

Journal ArticleDOI
27 Jul 2020
TL;DR: In this paper, a scheme for quantized pumping without a uniform band occupation in a time-modulated and tilted lattice was proposed using Bloch oscillations to sample the momentum space uniformly.
Abstract: This paper provides a scheme for quantized pumping without a uniform band occupation in a time-modulated and tilted lattice. The authors propose using Bloch oscillations to sample the momentum space uniformly.

Journal ArticleDOI
TL;DR: In this article, disorder-robust topological arrays of Mie-resonant nanoparticles are used for polarisation control of photoluminescence of nanocrystals.
Abstract: Rare-earth doped nanocrystals are emerging light sources used for many applications in nanotechnology enabled by human ability to control their various optical properties with chemistry and material science. However, one important optical problem -- polarisation of photoluminescence -- remains largely out of control by chemistry methods. Control over photoluminescence polarisation can be gained via coupling of emitters to resonant nanostructures such as optical antennas and metasurfaces. However, the resulting polarization is typically sensitive to position disorder of emitters, which is difficult to mitigate. Recently, new classes of disorder-immune optical systems have been explored within the framework of topological photonics. Here we explore disorder-robust topological arrays of Mie-resonant nanoparticles for polarisation control of photoluminescence of nanocrystals. We demonstrate polarized emission from rare-earth-doped nanocrystals governed by photonic topological edge states supported by zigzag arrays of dielectric resonators. We verify the topological origin of polarised photoluminescence by comparing emission from nanoparticles coupled to topologically trivial and nontrivial arrays of nanoresonators.

Journal ArticleDOI
TL;DR: The coupling of light from free space to optical fibers is essential for many applications, while commonly used step-index optical fibers provide insufficient coupling efficiencies especially at large scales as discussed by the authors.
Abstract: Coupling of light from free space to optical fibers is essential for many applications, while commonly used step-index optical fibers provide insufficient coupling efficiencies especially at large ...

Book ChapterDOI
01 Jan 2020
TL;DR: In this paper, the authors describe the scattering properties of planar metasurfaces composed of arrays of dielectric resonators supporting both electric and magnetic Mie resonances, and present the effect of perfect reflection, perfect transmission, and perfect absorption of light at the normal or oblique incidence.
Abstract: We describe the scattering properties of planar metasurfaces composed of arrays of dielectric resonators supporting both electric and magnetic Mie resonances. We focus on the study of metasurfaces with such functionalities as perfect reflection, perfect transmission, and perfect absorption of light at the normal or oblique incidence. Each effect is presented in its simplest form for the cases of electric and magnetic dipole resonances. Generalizations to higher orders and higher numbers of multipoles are discussed as well.

Posted Content
TL;DR: In this paper, the quantum Hall phase with topological edge states, spectral Landau levels and Hofstadter butterfly can emerge in a simple quantum system, where topological order arises solely from interactions without any fine-tuning.
Abstract: Topological quantum phases underpin many concepts of modern physics. While the existence of disorder-immune topological edge states of electrons usually requires magnetic fields, direct effects of magnetic field on light are very weak. As a result, demonstrations of topological states of photons employ synthetic fields engineered in special complex structures or external time-dependent modulations. Here, we reveal that the quantum Hall phase with topological edge states, spectral Landau levels and Hofstadter butterfly can emerge in a simple quantum system, where topological order arises solely from interactions without any fine-tuning. Such systems, arrays of two-level atoms (qubits) coupled to light being described by the classical Dicke model, have recently been realized in experiments with cold atoms and superconducting qubits. We believe that our finding will open new horizons in several disciplines including quantum physics, many-body physics, and nonlinear topological photonics, and it will set an important reference point for experiments on qubit arrays and quantum simulators.

Journal ArticleDOI
TL;DR: In this article, the magnetic dipole orders of the lattices of meta-atoms can appear in low-symmetry Mie-resonant metasurfaces where each asymmetric dielectric (nonmagnetic) meta-atom supports a localized trapped mode.
Abstract: Artificial magnetism at optical frequencies can be realized in metamaterials composed of periodic arrays of subwavelength elements, also called ``meta-atoms.'' Optically induced magnetic moments can be arranged in both unstaggered structures, naturally associated with ferromagnetic (FM) order, or staggered structures, linked correspondingly to antiferromagnetic (AFM) order. Here we demonstrate that such magnetic dipole orders of the lattices of meta-atoms can appear in low-symmetry Mie-resonant metasurfaces where each asymmetric dielectric (nonmagnetic) meta-atom supports a localized trapped mode. We reveal that these all-dielectric resonant metasurfaces possess not only strong optical magnetic response but also they demonstrate a significant polarization rotation of the propagating electromagnetic waves at both FM and AFM resonances. We confirm these findings experimentally by measuring directly the spectral characteristics of different modes excited in all-dielectric metasurfaces, and mapping near-field patterns of the electromagnetic fields at the microwave frequencies.