Observation of nonlinear fractal higher order topological insulator.

Higher-order topological insulators (HOTIs) are unique materials hosting topologically protected states, whose dimensionality is at least by 2 lower than that of the bulk. Topological states in such insulators may be strongly confined in their corners which leads to considerable enhancement of nonlinear processes involving such states. However, all nonlinear HOTIs demonstrated so far were built on periodic bulk lattice materials. Here, we demonstrate the first nonlinear photonic HOTI with the fractal origin. Despite their fractional effective dimensionality, the HOTIs constructed here on two different types of the Sierpinski gasket waveguide arrays, may support topological corner states for unexpectedly wide range of coupling strengths, even in parameter regions where conventional HOTIs become trivial. We demonstrate thresholdless spatial solitons bifurcating from corner states in nonlinear fractal HOTIs and show that their localization can be efficiently controlled by the input beam power. We observe sharp differences in nonlinear light localization on outer and multiple inner corners and edges representative for these fractal materials. Our findings not only represent a new paradigm for nonlinear topological insulators, but also open new avenues for potential applications of fractal materials to control the light flow.

Observation of π solitons in oscillating waveguide arrays.

Floquet systems with periodically varying in time parameters enable realization of unconventional topological phases that do not exist in static systems with constant parameters and that are frequently accompanied by appearance of novel types of the topological states. Among such Floquet systems are the Su-Schrieffer-Heeger lattices with periodically-modulated couplings that can support at their edges anomalous π modes of topological origin despite the fact that the lattice spends only half of the evolution period in topologically nontrivial phase, while during other half-period it is topologically trivial. Here, using Su-Schrieffer-Heeger arrays composed from periodically oscillating waveguides inscribed in transparent nonlinear optical medium, we report experimental observation of photonic anomalous π modes residing at the edge or in the corner of the one- or two-dimensional arrays, respectively, and demonstrate a new class of topological π solitons bifurcating from such modes in the topological gap of the Floquet spectrum at high powers. π solitons reported here are strongly oscillating nonlinear Floquet states exactly reproducing their profiles after each longitudinal period of the structure. They can be dynamically stable in both one- and two-dimensional oscillating waveguide arrays, the latter ones representing the first realization of the Floquet photonic higher-order topological insulator, while localization properties of such π solitons are determined by their power.

Observation of nonlinear disclination states.

Introduction of controllable deformations into periodic materials that lead to disclinations in their structure opens novel routes for construction of higher-order topological insulators hosting topological states at disclinations. Appearance of these topological states is consistent with the bulk-disclination correspondence principle, and is due to the filling anomaly that results in fractional charges to the boundary unit cells. So far, topological disclination states were observed only in the linear regime, while the interplay between nonlinearity and topology in the systems with disclinations has been never studied experimentally. We report here on the experimental observation of the nonlinear photonic disclination states in waveguide arrays with pentagonal or heptagonal disclination cores inscribed in transparent optical medium using the fs-laser writing technique. The transition between nontopological and topological phases in such structures is controlled by the Kekulé distortion coefficient r with topological phase hosting simultaneously disclination states at the inner disclination core and spatially separated from them corner-I, corner-II, and extended edge states at the outer edge of the structure. We show that the robust nonlinear disclination states bifurcate from their linear counterparts and that location of their propagation constants in the gap and, hence, their spatial localization can be controlled by their power. Nonlinear disclination states can be efficiently excited by Gaussian input beams, but only if they are focused into the waveguides belonging to the disclination core, where such topological states reside. Our results open new prospects for investigation of nonlinear effects in topological systems with disclinations and are relevant for different areas of science, including Bose-Einstein and polariton condensates, where potentials with the disclinations can be created.

Algorithm of quantum engineering of large-amplitude high-fidelity Schrödinger cat states.

We present an algorithm of quantum engineering of large-amplitude [Formula: see text] high-fidelity [Formula: see text] even/odd Schrödinger cat states (SCSs) using a single mode squeezed vacuum (SMSV) state as resource. Set of [Formula: see text] beam splitters (BSs) with arbitrary transmittance and reflectance coefficients sequentially following each other acts as a hub that redirects a multiphoton state into the measuring modes simultaneously measured by photon number resolving (PNR) detectors. We show that the multiphoton state splitting guarantees significant increase of the success probability of the SCSs generator compared to its implementation in a single PNR detector version and imposes less requirements on ideal PNR detectors. We prove that the fidelity of the output SCSs and its success probability are in conflict with each other (which can be quantified) in a scheme with ineffective PNR detectors, especially when subtracting large (say, [Formula: see text]) number of photons, i.e., increasing the fidelity to perfect values leads to a sharp decrease in the success probability. In general, the strategy of subtracting up to [Formula: see text] photons from initial SMSV in setup with two BSs is acceptable for achieving sufficiently high values of the fidelity and success probability at the output of the generator of the SCSs of amplitude [Formula: see text] with two inefficient PNR detectors.

Time-domain Hong-Ou-Mandel interference of quasi-thermal fields and its application in linear optical circuit characterization.

We study temporal correlations of interfering quasi-thermal fields, obtained by scattering laser radiation on a rotating ground glass disk. We show that the Doppler effect causes oscillations in the temporal cross correlation function. Furthermore, we propose how to use Hong-Ou-Mandel interference of quasi-thermal fields in the time domain to characterize linear optical circuits.

Architecture agnostic algorithm for reconfigurable optical interferometer programming.

We develop the learning algorithm to build an architecture agnostic model of a reconfigurable optical interferometer. A procedure of programming a unitary transformation of optical modes of an interferometer either follows an analytical expression yielding a unitary matrix given a set of phase shifts or requires an optimization routine if an analytic decomposition does not exist. Our algorithm adopts a supervised learning strategy which matches a model of an interferometer to a training set populated by samples produced by a device under study. A simple optimization routine uses the trained model to output phase shifts corresponding to a desired unitary transformation of the interferometer with a given architecture. Our result provides the recipe for efficient tuning of interferometers even without rigorous analytical description which opens opportunity to explore new architectures of the interferometric circuits.

The Nutrition and Health Status of Residents of the Northern Regions of Russia: Outlook of Vertical Agricultural Farms.

This paper is dedicated to studying the nutrition, health status and food provision of the people living the northern regions of Russia. The authors developed a concept of comprehensive interdisciplinary research of traditional and innovative behavioral practices of actors in the northern regions of Russia in the field of food production and consumption in order to study the structure of nutrition of the population, its health status and the technologies that are used to provide the people with food products. The interdisciplinary comprehensive research applied the following methods: (a) statistical method; (b) sociological method of mass survey; (c) sociological method of expert interviews; (d) method of feasibility study; (e) method of mathematical modeling. According to the results of the analysis, the nutrition of the people living in the norther regions is characterized by insufficient consumption of fresh vegetables, meat and processed meat, fish and seafood, milk and dairy products, some vitamins and bio-elements (such as selenium, calcium) and excessive consumption of saturated fats and flour products. The following problems related to providing the population of the northern regions of Russia with food products were identified: the agriculture in almost all northern regions of Russia has negative profitability; imported food products and food ingredients are mostly used; there are drawbacks of logistics, transportation and storage of food products; the natural and climate conditions are unfavorable for traditional agriculture. The paper substantiates the economic, environmental, social, and political advantages of highly automated agro-industrial complex of vertical farming as an alternative method for providing food security of the inhabitants of the northern regions of Russia.

Femtosecond Laser Written Depressed-Cladding Waveguide 2 × 2, 1 × 2 and 3 × 3 Directional Couplers in Tm3+:YAG Crystal.

Ion-doped crystal-based compact devices capable of beam splitting and coupling are enthralling for a broad range of classical and quantum integrated photonics applications. In this work, we report on the fabrication of depressed-cladding waveguide 2D 2 × 2, 1 × 2 and 3D 3 × 3 directional couplers in Tm 3 + :YAG crystal by femtosecond laser writing. The performances of the couplers are characterized at 810 nm, showing single-mode guidance, polarization independence, finely matched splitting ratios. These results open up new opportunities in the beneficial fabrication of 3D circuits and devices in crystals.

Identifying entanglement using quantum ghost interference and imaging.

We report a quantum interference and imaging experiment which allows identifying the entanglement in momentum and position variables of a two-photon system. The measurements show indeed that the uncertainties in the sum of momenta and in the difference of positions of the entangled two-photon satisfy both EPR inequalities Delta(k(1)+k(2))