There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.

Topological Photonics

This article reviews recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonlinear optical systems. In the presence of effective photon-photon interactions induced by the optical nonlinearity of the medium, a many-photon system can behave collectively as a quantum fluid with a number of novel features stemming from its intrinsically nonequilibrium nature. A rich variety of recently observed photon hydrodynamical effects is presented, from the superfluid flow around a defect at low speeds, to the appearance of a Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles. While the review is mostly focused on a specific class of semiconductor systems that have been extensively studied in recent years (planar semiconductor microcavities in the strong light-matter coupling regime having cavity polaritons as elementary excitations), the very concept of quantum fluids of light applies to a broad spectrum of systems, ranging from bulk nonlinear crystals, to atomic clouds embedded in optical fibers and cavities, to photonic crystal cavities, to superconducting quantum circuits based on Josephson junctions. The conclusive part of the article is devoted to a review of the future perspectives in the direction of strongly correlated photon gases and of artificial gauge fields for photons. In particular, several mechanisms to obtain efficient photon blockade are presented, together with their application to the generation of novel quantum phases.

Quantum fluids of light

One of the most exciting tools that have entered the material science toolbox in recent years is machine learning. This collection of statistical methods has already proved to be capable of considerably speeding up both fundamental and applied research. At present, we are witnessing an explosion of works that develop and apply machine learning to solid-state systems. We provide a comprehensive overview and analysis of the most recent research in this topic. As a starting point, we introduce machine learning principles, algorithms, descriptors, and databases in materials science. We continue with the description of different machine learning approaches for the discovery of stable materials and the prediction of their crystal structure. Then we discuss research in numerous quantitative structure–property relationships and various approaches for the replacement of first-principle methods by machine learning. We review how active learning and surrogate-based optimization can be applied to improve the rational design process and related examples of applications. Two major questions are always the interpretability of and the physical understanding gained from machine learning models. We consider therefore the different facets of interpretability and their importance in materials science. Finally, we propose solutions and future research paths for various challenges in computational materials science.

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Recent advances and applications of machine learning in solid-state materials science

Optical Waveguide Theory

The performances of point-to-point quantum protocols is strongly dependent on the nature of the quantum channel and it rapidly deteriorates with distance. Well-known fundamental and practical limitations prevent to achieve simultaneously high rates, long distances and unconditional security. In this scenario, the rate of quantum communications between users placed at arbitrary points of a quantum communication network will strongly depend on the structure of the network, on its extension and on the nature of the communication channels. Purpose of the present work is to develop a theoretical framework to understand how the properties of the underlying network influence the rate and security of quantum communications and illustrate a potential strategy of network optimization.This work is part of the activities of the PON project “Development of quantum systems and technologies for IT security in communication networks” (QUANCOM) which aims to the realization of a metropolitan quantum communication network through the collaboration between universities, research centers and companies operating in the communication market area.

Paths in quantum communication networks

We propose a straightforward and effective approach to design, by strain-engineering, photonic topological insulators supporting high quality factors edge states. Chiral strain-engineering creates opposite synthetic gauge fields in two domains resulting in Landau levels with the same energy spacing but different topological numbers. The boundary of the two topological domains hosts robust time-reversal and spin-momentum-locked edge states, exhibiting high quality factors due to continuous strain modulation. By shaping the synthetic gauge field, we obtain a remarkable field confinement and tunability, with the strain strongly affecting the degree of localization of the edge states. Notably the two-domain design stabilizes the strain-induced topological edge state. The large potential bandwidth of the strain-engineering and the opportunity to induce the mechanical stress at the fabrication stage enables large scalability for many potential applications in photonics, such as tunable microcavities, new lasers and information processing devices, including the quantum regime.

Strain-tunable synthetic gauge fields in topological photonic graphene

Three-dimensional printing technologies are attracting more attentions to develop devices for effective control and manipulation of electromagnetic waves. Due to the limitation of resolution of apparatus, 3D printing technologies were originally applied to the radio-frequency. Thanks to the continuous innovation of hardware, materials and processes in the 3D printing, structures with smaller minimum features can be fabricated, opening up the possibilities of creating 3D-printed components for the THz ranges [1] .

Terahertz waves transmission in 3D printed photonic crystals

The theory of the optical response of a Wannier exciton confined in a 2D quantum well embodied in a 3/2 λ planar cavity is briefly reviewed in the semiclassical self-consistent framework and in the effective mass approximation. The enhancement of the Rabi splitting energy due to the guided mode with high component of parallel wave vector, induced by a 1D dielectric grating located at one of the antinodes of the electric field in the cavity, is computed, and compared with the case of a dielectric grating engraved at the surface of the sample. The effect of light polarization in the optical response is also discussed. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Guided waves in semiconductor patterned microcavities

Bound states in the continuum (BIC) in metamaterials have recently attracted attention for their promising applications in photonics. Here, we investigate the transition from Fano resonances to BIC, at terahertz (THz) frequencies, of a one-dimensional photonic crystal slab made of rectangular dielectric rods. Simulations performed by an analytical exact solution of the Maxwell equations showed that symmetry-protected, high-quality factor (Q), BIC emerge at normal incidence. For non-normal incidence, BIC couple with the freely propagating waves and appear in the scattering field as a Fano resonance. Simulations were verified by realizing the photonic crystal slab by 3D-printing technique. THz time-domain spectroscopy measurements as a function of the incidence angle matched the simulation to good accuracy and confirmed the evolution of Fano resonances to high-Q resonances typical of BIC. These results point out the design of highly sensitive and low-cost THz devices for sensing for a wide range of applications.

Laura Pilozzi

Papers

Paths in quantum communication networks

Strain-tunable synthetic gauge fields in topological photonic graphene

Terahertz waves transmission in 3D printed photonic crystals

Guided waves in semiconductor patterned microcavities

Observation of terahertz transition from Fano resonances to bound states in the continuum.