Topological Hong-Ou-Mandel interference.

The interplay of topology and optics provides a route to pursue robust photonic devices, with the application to photonic quantum computation in its infancy. However, the possibilities of harnessing topological structures to process quantum information with linear optics, through the quantum interference of photons, remain largely uncharted. Here, we present a Hong-Ou-Mandel interference effect of topological origin. We show that this interference of photon pairs-ranging from constructive to destructive-is solely determined by a synthetic magnetic flux, rendering it resilient to errors on a fundamental level. Our implementation establishes a quantized flux that facilitates exclusively destructive quantum interference. Our findings pave the way toward the development of next-generation photonic quantum circuitry and scalable quantum computing protected by virtue of topologically robust quantum gates.

Parity-time-symmetric photonic topological insulator.

Topological insulators are a concept that originally stems from condensed matter physics. As a corollary to their hallmark protected edge transport, the conventional understanding of such systems holds that they are intrinsically closed, that is, that they are assumed to be entirely isolated from the surrounding world. Here, by demonstrating a parity-time-symmetric topological insulator, we show that topological transport exists beyond these constraints. Implemented on a photonic platform, our non-Hermitian topological system harnesses the complex interplay between a discrete coupling protocol and judiciously placed losses and, as such, inherently constitutes an open system. Nevertheless, even though energy conservation is violated, our system exhibits an entirely real eigenvalue spectrum as well as chiral edge transport. Along these lines, this work enables the study of the dynamical properties of topological matter in open systems without the instability arising from complex spectra. Thus, it may inspire the development of compact active devices that harness topological features on-demand.

Remote Expert DVT Triaging of Novice-User Compression Sonography with AI-Guidance.

BACKGROUND: Compression ultrasonography of the leg is established for triaging proximal lower extremity deep vein thrombosis (DVT). AutoDVT, a machine-learning software, provides a tool for nonspecialists in acquiring compression sequences to be reviewed by an expert for patient triage. The purpose of this study was to test image acquisition and remote triaging in a clinical setting. METHODS: Patients with a suspected DVT were recruited at 2 centers in Germany and Greece. Enrolled patients underwent an artificial intelligence-guided two-point compression examination by a nonspecialist using a handheld ultrasound device prior to a standard scan. Images collected by the software were uploaded for blind review by 5 qualified physicians. All reviewers rated the quality of all sequences on the American College of Emergency Physicians (ACEP) image quality scale (score 1-5, ≥ 3 defined as adequate imaging quality) and for an ACEP score ≥3, chose "Compressible", "Incompressible", or "Other". Sensitivity and specificity were calculated for adequate quality scans with an assessment as "Compressible" or "Incompressible". We define this group as diagnostic quality. To simulate a triaging clinical algorithm, a post hoc analysis was performed merging the "incomplete", the "low quality", and the "Incompressible" into a high-risk group for proximal DVT. RESULTS: Seventy-three patients (average age 64.2 years, 44% females) were eligible for inclusion and scanned by 3 nonultrasound-qualified healthcare professionals. Three patients were excluded from further analysis due to incomplete scans. Sixty two of 70 (88.57%) of the completed scans were judged to be of adequate image quality with an average ACEP score of 3.35. Forty seven of 62 adequate AutoDVT scans were assessed as diagnostic quality, of which 8 were interpreted as positive for proximal DVT by the reviewers resulting in a sensitivity of 100% and specificity of 95.12%. When simulating a triaging algorithm, 34/73 (46.58%) of patients would be triaged as high risk and 8 would be confirmed as positive for proximal DVT (6 in the diagnostic and 2 in the low-quality cohort). Of 39/73 patients triaged as low risk, all were negative for proximal DVT in standard duplex; thus, this triaging algorithm could potentially save 53.42% of standard duplex scans. CONCLUSIONS: Machine learning software was able to aid nonexperts in acquiring valid ultrasound images of venous compressions and allowed remote triaging. This strategy allows faster diagnosis and treatment of high-risk patients and can spare the need for multiple unnecessary duplex scans, the vast majority being negative.

Order-Invariant Two-Photon Quantum Correlations in PT-Symmetric Interferometers.

Multiphoton correlations in linear photonic quantum networks are governed by matrix permanents. Yet, surprisingly few systematic properties of these crucial algebraic objects are known. As such, predicting the overall multiphoton behavior of a network from its individual building blocks typically defies intuition. In this work, we identify sequences of concatenated two-mode linear optical transformations whose two-photon behavior is invariant under reversal of the order. We experimentally verify this systematic behavior in parity-time-symmetric complex interferometer arrangements of varying compositions. Our results underline new ways in which quantum correlations may be preserved in counterintuitive ways, even in small-scale non-Hermitian networks.

Photonic topological insulator induced by a dislocation in three dimensions.

The hallmark of topological insulators (TIs) is the scatter-free propagation of waves in topologically protected edge channels1. This transport is strictly chiral on the outer edge of the medium and therefore capable of bypassing sharp corners and imperfections, even in the presence of substantial disorder. In photonics, two-dimensional (2D) topological edge states have been demonstrated on several different platforms2-4 and are emerging as a promising tool for robust lasers5, quantum devices6-8 and other applications. More recently, 3D TIs were demonstrated in microwaves9 and  acoustic waves10-13, where the topological protection in the latter  is induced by dislocations. However, at optical frequencies, 3D photonic TIs have so far remained out of experimental reach. Here we demonstrate a photonic TI with protected topological surface states in three dimensions. The topological protection is enabled by a screw dislocation. For this purpose, we use the concept of synthetic dimensions14-17 in a 2D photonic waveguide array18 by introducing a further modal dimension to transform the system into a 3D topological system. The lattice dislocation endows the system with edge states propagating along 3D trajectories, with topological protection akin to strong photonic TIs19,20. Our work paves the way for utilizing 3D topology in photonic science and technology.

Observation of photonic constant-intensity waves and induced transparency in tailored non-Hermitian lattices.

Light propagation is strongly affected by scattering due to imperfections in the complex medium. It has been recently theoretically predicted that a scattering-free transport through an inhomogeneous medium is achievable by non-Hermitian tailoring of the complex refractive index. Here, we implement photonic constant-intensity waves in an inhomogeneous, linear, discrete mesh lattice. By extending the existing theoretical framework, we experimentally show that a driven non-Hermitian tailoring allows us to control the propagation and diffraction of light even in highly disordered systems. In this vein, we demonstrate the transmission of shape-preserving beams and the seemingly undistorted propagation of light excitations across a strongly inhomogeneous non-Hermitian photonic lattice that can be realized by coupled optical fiber loops. Our results lead to a deeper understanding of non-Hermitian wave control and further contribute to the development of non-Hermitian photonics.

Fractal photonic topological insulators.

Topological insulators constitute a newly characterized state of matter that contains scatter-free edge states surrounding an insulating bulk. Conventional wisdom regards the insulating bulk as essential, because the invariants that describe the topological properties of the system are defined therein. Here, we study fractal topological insulators based on exact fractals composed exclusively of edge sites. We present experimental proof that, despite the lack of bulk bands, photonic lattices of helical waveguides support topologically protected chiral edge states. We show that light transport in our topological fractal system features increased velocities compared with the corresponding honeycomb lattice. By going beyond the confines of the bulk-boundary correspondence, our findings pave the way toward an expanded perception of topological insulators and open a new chapter of topological fractals.

Bimorphic Floquet topological insulators.

Topological theories have established a unique set of rules that govern the transport properties in a wide variety of wave-mechanical settings. In a marked departure from the established approaches that induce Floquet topological phases by specifically tailored discrete coupling protocols or helical lattice motions, we introduce a class of bimorphic Floquet topological insulators that leverage connective chains with periodically modulated on-site potentials to reveal rich topological features in the system. In exploring a 'chain-driven' generalization of the archetypical Floquet honeycomb lattice, we identify a rich phase structure that can host multiple non-trivial topological phases associated simultaneously with both Chern-type and anomalous chiral states. Experiments carried out in photonic waveguide lattices reveal a strongly confined helical edge state that, owing to its origin in bulk flat bands, can be set into motion in a topologically protected fashion, or halted at will, without compromising its adherence to individual lattice sites.

A decision support tool to place drinking water sources in rural communities.

Installing more drinking water sources is a promising way to achieve the 6th sustainable development goal "Clean water and sanitation" in rural communities. A key parameter for the installation of new water pumps is geographical position, because the number of people who could gain access to drinking water depends on the location of the pump. To improve the choice of the most appropriate location, we propose a decision support tool to place a new drinking water source in a rural community. This tool relies on four complementary maps, which are obtained from GPS data, survey data, and a water source choice model. The first map shows the spatial distribution of the households and of the existing water sources in the village. The three remaining maps present the following quantities as a function of the position of a new drinking water source in the village: the number of users of the new drinking water source, the improvement of drinking water access, and the daily water demand per capita at the new drinking water source. The decision support tool is applied to a village in Burkina Faso. Results indicate that using the proposed method could allow eight times more people to gain access to drinking water in comparison to a random positioning of the new drinking water source. The original contribution of this work is, first, the consideration of existing water sources in the village, as well as seasonality. Second, we base our analysis on a water source choice model, which accounts for water quality in addition to the distance to the water source. Third, we consider the variability of the water volume collected by the households throughout the village. The developed tool is generic, transferable to other villages and useful for various decision-making entities (e.g. local authorities and non-governmental organizations).

Exploring complex graphs using three-dimensional quantum walks of correlated photons.

Graph representations are a powerful concept for solving complex problems across natural science, as patterns of connectivity can give rise to a multitude of emergent phenomena. Graph-based approaches have proven particularly fruitful in quantum communication and quantum search algorithms in highly branched quantum networks. Here, we introduce a previously unidentified paradigm for the direct experimental realization of excitation dynamics associated with three-dimensional networks by exploiting the hybrid action of spatial and polarization degrees of freedom of photon pairs in complex waveguide circuits with tailored birefringence. This testbed for the experimental exploration of multiparticle quantum walks on complex, highly connected graphs paves the way toward exploiting the applicative potential of fermionic dynamics in integrated quantum photonics.

Nonlinearity-induced photonic topological insulator.

A hallmark feature of topological insulators is robust edge transport that is impervious to scattering at defects and lattice disorder. We demonstrate a topological system, using a photonic platform, in which the existence of the topological phase is brought about by optical nonlinearity. The lattice structure remains topologically trivial in the linear regime, but as the optical power is increased above a certain power threshold, the system is driven into the topologically nontrivial regime. This transition is marked by the transient emergence of a protected unidirectional transport channel along the edge of the structure. Our work studies topological properties of matter in the nonlinear regime, providing a possible route for the development of compact devices that harness topological features in an on-demand fashion.

Symmetry-controlled edge states in the type-II phase of Dirac photonic lattices.

The exceptional properties exhibited by two-dimensional materials, such as graphene, are rooted in the underlying physics of the relativistic Dirac equation that describes the low energy excitations of such molecular systems. In this study, we explore a periodic lattice that provides access to the full solution spectrum of the extended Dirac Hamiltonian. Employing its photonic implementation of evanescently coupled waveguides, we indicate its ability to independently perturb the symmetries of the discrete model (breaking, also, the barrier towards the type-II phase) and arbitrarily define the location, anisotropy, and tilt of Dirac cones in the bulk. This unique aspect of topological control gives rise to highly versatile edge states, including an unusual class that emerges from the type-II degeneracies residing in the complex space of k. By probing these states, we investigate the topological nature of tilt and shed light on novel transport dynamics supported by Dirac configurations in two dimensions.

Publisher Correction: A square-root topological insulator with non-quantized indices realized with photonic Aharonov-Bohm cages.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Fermionic time-reversal symmetry in a photonic topological insulator.

Much of the recent attention directed towards topological insulators is motivated by their hallmark feature of protected chiral edge states. In electronic (or fermionic) topological insulators, these states originate from time-reversal symmetry and allow carriers with opposite spin-polarization to propagate in opposite directions at the edge of an insulating bulk. By contrast, photonic (or bosonic) systems are generally assumed to be precluded from supporting edge states that are intrinsically protected by time-reversal symmetry. Here, we experimentally demonstrate counter-propagating chiral states at the edge of a time-reversal-symmetric photonic waveguide structure. The pivotal step in our approach is the design of a Floquet driving protocol that incorporates effective fermionic time-reversal symmetry, enabling the realization of the photonic version of an electronic topological insulator. Our findings allow for fermionic properties to be harnessed in bosonic systems, thereby offering alternative opportunities for photonics as well as acoustics, mechanical waves and cold atoms.

A square-root topological insulator with non-quantized indices realized with photonic Aharonov-Bohm cages.

Topological Insulators are a novel state of matter where spectral bands are characterized by quantized topological invariants. This unique quantized nonlocal property commonly manifests through exotic bulk phenomena and corresponding robust boundary effects. In our work we study a system where the spectral bands are associated with non-quantized indices, but nevertheless possess robust boundary states. We present a theoretical analysis, where we show that the square of the Hamiltonian exhibits quantized indices. The findings are experimentally demonstrated by using photonic Aharonov-Bohm cages.

Experimental Realization of PT-Symmetric Flat Bands.

The capability to temporarily arrest the propagation of optical signals is one of the main challenges hampering the ever more widespread use of light in rapid long-distance transmission as well as all-optical on-chip signal processing or computations. To this end, flat-band structures are of particular interest, since their hallmark compact eigenstates not only allow for the localization of wave packets, but importantly, also protect their transverse profile from deterioration without the need for additional diffraction management. In this work, we experimentally demonstrate that, far from being a nuisance to be compensated, judiciously tailored loss distributions can, in fact, be the key ingredient in synthesizing such flat bands in non-Hermitian environments. We probe their emergence in the vicinity of an exceptional point and directly observe the associated compact localized modes that can be excited at arbitrary positions of the periodic lattice.

Association of Estradiol and Visceral Fat With Structural Brain Networks and Memory Performance in Adults.

Importance: Changes in estradiol during aging are associated with increased dementia risk. It remains unclear how estradiol supports cognitive health and whether risk factors, such as midlife obesity, are exacerbated by estrogen loss. Objectives: To assess whether visceral adipose tissue (VAT) moderates the association between age and brain network structure and to investigate whether estradiol moderates the association between VAT and brain network structure. Design, Setting, and Participants: Cross-sectional study of data from 974 cognitively healthy adults in Germany who participated in the Health Study of the Leipzig Research Centre for Civilization Diseases, a previously described population-based cohort study. Two moderation analyses were performed, including VAT as the moderator variable between age and brain network structure and estradiol as the moderator variable between VAT and brain network structure. The study was conducted from August 1, 2011, to November 23, 2014. Analyses were conducted from August 2017 to September 2018. Exposures: Serum estradiol levels from fasting blood and visceral adipose tissue volume from T1-weighted magnetic resonance imaging (MRI). Main Outcomes and Measures: Brain network covariance (individual loading on structural network derived from T1-weighted MRI) and memory performance (composite score from the Consortium to Establish a Registry for Alzheimer Disease [CERAD] verbal episodic memory test on learning [score range, 0-30], recall [score range, 0-10], and recognition [score range, 0-20]). Results: Final analyses included data from 473 women (mean [SD] age, 50.10 [15.63] years) and 501 men (mean [SD] age, 51.24 [15.67] years). Visceral adipose tissue was associated with an exacerbation of the negative association of aging with network covariance for women (interaction term ß = -0.02; 95% bias-corrected bootstrap CI, -0.03 to -0.01; P = .001) and men (interaction term ß = -0.02; 95% bias-corrected bootstrap CI, -0.03 to -0.01; P < .001). Estradiol level was associated with a reduction in the negative association of VAT with network covariance in women (interaction term ß = 0.63; 95% bias-corrected bootstrap CI, 0.14-1.12; P = .01), with no significant association in men. In the female midlife subgroup (age range, 35-55 years, when menopause transition occurs), low estradiol levels were associated with lower memory network covariance (Cohen d = 0.61; t80 = 2.76; P = .007) and worse memory performance (Cohen d = 0.63; t76 = 2.76; P = .007). Conclusions and Relevance: This study reports a novel association between VAT, estradiol, and structural brain networks as a potential mechanism underlying cognitive decline in women. These findings appear to highlight the need for sex-specific strategies, including VAT and hormonal screening during midlife, to support healthy cognitive aging.

Neuroanatomical correlates of food addiction symptoms and body mass index in the general population.

The food addiction model suggests neurobiological similarities between substance-related and addictive disorders and obesity. While structural brain differences have been consistently reported in these conditions, little is known about the neuroanatomical correlates of food addiction. We therefore aimed to determine whether symptoms of food addiction related to body mass index (BMI), personality, and brain structure in a large population-based sample. Participants of the LIFE-Adult study (n = 625; 20-59 years old, 45% women) answered the Yale Food Addiction Scale (YFAS) and further personality measures, underwent anthropometric assessments and high-resolution 3T-neuroimaging. A higher YFAS symptom score correlated with higher BMI, eating behavior traits, neuroticism, and stress. Higher BMI predicted significantly lower thickness of (pre)frontal, temporal and occipital cortex and increased volume of left nucleus accumbens. In a whole-brain analysis, YFAS symptom score was not associated with significant differences in cortical thickness or subcortical gray matter volumes. A hypothesis-driven Bayes factor analysis suggested a small, additional contribution of YFAS symptom score to lower right lateral orbitofrontal cortex thickness over the effect of BMI. Our study indicates that symptoms of food addiction do not account for the major part of the structural brain differences associated with BMI in the general population. Yet, symptoms of food addiction might explain additional variance in orbitofrontal cortex, a hub area of the reward network. Longitudinal studies implementing both anatomical and functional MRI could further disentangle the neural mechanisms of addictive eating behaviors.

Demonstration of a two-dimensional [Formula: see text]-symmetric crystal.

With the discovery of [Formula: see text]-symmetric quantum mechanics, it was shown that even non-Hermitian systems may exhibit entirely real eigenvalue spectra. This finding did not only change the perception of quantum mechanics itself, it also significantly influenced the field of photonics. By appropriately designing one-dimensional distributions of gain and loss, it was possible to experimentally verify some of the hallmark features of [Formula: see text]-symmetry using electromagnetic waves. Nevertheless, an experimental platform to study the impact of [Formula: see text] -symmetry in two spatial dimensions has so far remained elusive. We break new grounds by devising a two-dimensional [Formula: see text]-symmetric system based on photonic waveguide lattices with judiciously designed refractive index landscape and alternating loss. With this system at hand, we demonstrate a non-Hermitian two-dimensional topological phase transition that is closely linked to the emergence of topological mid-gap edge states.

Scattering detection of a solenoidal Poynting vector field.

The Poynting vector S plays a central role in electrodynamics as it is directly related to the power and the momentum carried by an electromagnetic wave. In the presence of multiple electromagnetic waves with different polarizations and propagation directions, the Poynting vector may exhibit solenoidal components which are not associated to any power flow. Here, we demonstrate theoretically and experimentally that the presence of such solenoidal components has physical consequences, and it is not a mere artifact of the gauge invariance of S. In particular, we identify a simple field configuration displaying solenoidal components of S and theoretically show that a judiciously designed scatterer can act as a "Poynting vector detector" which when immersed in such field distribution would experience a transverse optical force orthogonal to the incidence plane. We experimentally validate our theoretical predictions by observing a pronounced asymmetry in the scattering pattern of a spherical nanoparticle.