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Optical activity, also called circular birefringence, is known for two hundred years, but its applications for topological photonics remain unexplored. Unlike the Faraday effect, the optical activity provokes rotation of the linear polarization of light without magnetic effects, thus preserving the time-reversal symmetry. In this work, we report a direct measurement of the Berry curvature and quantum metric of the photonic modes of a planar cavity, containing a birefringent organic microcrystal (perylene) and exhibiting emergent optical activity. This experiment, performed at room temperature and at visible wavelength, establishes the potential of organic materials for implementing non-magnetic and low-cost topological photonic devices., Most work in topological photonics is performed in periodically structured systems. Here, the authors directly measure the nontrivial Berry curvature of the photonic modes of a birefringent continuous organic system exhibiting emergent optical activity.

The geometry of Hamiltonian's eigenstates is encoded in the quantum geometric tensor (QGT). It contains both the Berry curvature, central to the description of topological matter and the quantum metric. So far the full QGT has been measured only in Hermitian systems, where the role of the quantum metric is mostly shown to determine corrections to physical effects. On the contrary, in non-Hermitian systems, and in particular near exceptional points, the quantum metric is expected to diverge and to often play a dominant role, for example on the enhanced sensing and on wave packet dynamics. In this work, we report the first experimental measurement of the quantum metric in a non-Hermitian system. The specific platform under study is an organic microcavity with exciton-polariton eigenstates, which demonstrate exceptional points. We measure the quantum metric's divergence and we determine the scaling exponent $n=-1.01\pm0.08$, which is in agreement with theoretical predictions for the second-order exceptional points.

We study the formation of topological defects (quantum vortices) during the formation of a two-dimensional (2D) polariton condensate at the $\mathrm{\ensuremath{\Gamma}}$ point of a honeycomb lattice via the Kibble-Zurek mechanism. The lattice modifies the single-particle dispersion. The typical interaction energies at the quench time correspond to the linear part of the dispersion. The resulting scaling exponent for the density of topological defects is numerically found as $0.95\ifmmode\pm\else\textpm\fi{}0.05$. This value differs from the one expected for 2D massive particles (1/2), but is indeed compatible with the one expected for a linear dispersion. We moreover demonstrate that the vortices can be pinned to the lattice, which prevents their recombination and could facilitate their observation and counting in continuous wave experiments.

International audience; We derive semiclassical equations of motion for an accelerated wave packet in a two-band system. We show that these equations can be formulated in terms of the static band geometry described by the quantum metric. We consider the specific cases of the Rashba Hamiltonian with and without a Zeeman term. The semiclassical trajectories are in full agreement with the ones found by solving the Schrödinger equation. This formalism successfully describes the adiabatic limit and the anomalous Hall effect traditionally attributed to Berry curvature. It also describes the opposite limit of coherent band superposition, giving rise to a spatially oscillating Zitterbewegung motion, and all intermediate cases. At k=0, such a wave packet exhibits a circular trajectory in real space, with its radius given by the square root of the quantum metric. This quantity appears as a universal length scale, providing a geometrical origin of the Compton wavelength. The quantum metric semiclassical approach could be extended to an arbitrary number of bands.

International audience; Analog physics has successfully tackled the problems of gauge theories, event horizons, Big Bang and Universe expansion, and many others. Here, we suggest a photonic model system for a “time machine” based on the paraxial beam approximation. We demonstrate how the closed timelike curves and the well-known grandfather paradox can be studied experimentally in this system. We show how Novikov's self-consistency principle is realized in quantum mechanics owing to Heisenberg's uncertainty principle.

The engineering of the energy dispersion of polaritons in microcavities through nanofabrication or through the exploitation of intrinsic material and cavity anisotropies has demonstrated many intriguing effects related to topology and emergent gauge fields such as the anomalous quantum Hall and Rashba effects. Here we show how we can obtain different Berry curvature distributions of polariton bands in a strongly coupled organic–inorganic two-dimensional perovskite single-crystal microcavity. The spatial anisotropy of the perovskite crystal combined with photonic spin–orbit coupling produce two Hamilton diabolical points in the dispersion. An external magnetic field breaks time-reversal symmetry owing to the exciton Zeeman splitting and lifts the degeneracy of the diabolical points. As a result, the bands possess non-zero integral Berry curvatures, which we directly measure by state tomography. In addition to the determination of the different Berry curvatures of the multimode microcavity dispersions, we can also modify the Berry curvature distribution, the so-called band geometry, within each band by tuning external parameters, such as temperature, magnetic field and sample thickness. Engineering the energy dispersion of polaritons in microcavities can yield intriguing effects such as the anomalous quantum Hall and Rashba effects. Now, different Berry curvature distributions of polariton bands are obtained in a strongly coupled organic–inorganic two-dimensional perovskite single-crystal microcavity and can be modified via temperature and magnetic field variation.

We report the realization of a synthetic magnetic field for photons and polaritons in a honeycomb lattice of coupled semiconductor micropillars. A strong synthetic field is induced in both the s and p orbital bands by engineering a uniaxial hopping gradient in the lattice, giving rise to the formation of Landau levels at the Dirac points. We provide direct evidence of the sublattice symmetry breaking of the lowest-order Landau level wavefunction, a distinctive feature of synthetic magnetic fields. Our realization implements helical edge states in the gap between n = 0 and n = ±1 Landau levels, experimentally demonstrating a novel way of engineering propagating edge states in photonic lattices. In light of recent advances in the enhancement of polariton–polariton nonlinearities, the Landau levels reported here are promising for the study of the interplay between pseudomagnetism and interactions in a photonic system., SCOPUS: ar.j, info:eu-repo/semantics/published

International audience; Collective excitations, such as vortex-antivortex and dark solitons, are among the most fascinating effects of macroscopic quantum states. However, two-dimensional (2D) dark solitons are unstable and collapse into vortices due to snake instabilities. Making use of the optical bistability in exciton-polariton microcavities, we demonstrate that a pair of dark solitons can be formed in the wake of an obstacle in a polariton flow resonantly supported by a homogeneous laser beam. Unlike the purely dissipative case where the solitons are gray and spatially separate, here the two solitons are fully dark, rapidly align at a specific separation distance, and propagate parallel as long as the flow is in the bistable regime. Remarkably, the use of this regime allows us to relax the phase fixing constraints imposed by the resonant pumping and to circumvent the polariton decay. Our work opens very wide possibilities for studying new classes of phase-density defects which can form in driven-dissipative quantum fluids of light.

Quantum simulations are one of the pillars of quantum technologies. These simulations provide insight in fields as varied as high energy physics, many-body physics, or cosmology to name only a few. Several platforms, ranging from ultracold-atoms to superconducting circuits through trapped ions have been proposed as quantum simulators. This article reviews recent developments in another well established platform for quantum simulations: polaritons in semiconductor microcavities. These quasiparticles obey a nonlinear Schr\"odigner equation (NLSE), and their propagation in the medium can be understood in terms of quantum hydrodynamics. As such, they are considered as "fluids of light". The challenge of quantum simulations is the engineering of configurations in which the potential energy and the nonlinear interactions in the NLSE can be controlled. Here, we revisit some landmark experiments with polaritons in microcavities, discuss how the various properties of these systems may be used in quantum simulations, and highlight the richness of polariton systems to explore non-equilibrium physics

International audience; Polariton lasers are mostly based on planar cavities. Here, we focus on an alternative configuration with slab waveguide modes strongly coupled to excitons confined in GaN/AlGaN quantum wells. We study experimentally and theoretically polariton relaxation at temperatures ranging from 4 to 200 K. We observe a good robustness of the lower polariton population peak energy position against temperature changes due to a balance between the shift of the exciton energy and the change in the normal mode splitting, a promising feature for future applications such as lasers and amplifiers where a small temperature drift in the emission wavelength is a desired asset. Finally, at T = 4 K we observe the signature of polariton nonlinearities occurring in the continuous wave regime that are assigned to an optical parametric oscillation process.

Compression dramatically changes the transport and localization properties of graphene. This is intimately related to the change of symmetry of the Dirac cone when the particle hopping is different along different directions of the lattice. In particular, for a critical compression, a semi-Dirac cone is formed with massless and massive dispersions along perpendicular directions. Here we show direct evidence of the highly anisotropic transport of polaritons in a honeycomb lattice of coupled micropillars implementing a semi-Dirac cone. If we optically induce a vacancy-like defect in the lattice, we observe an anisotropically localized polariton distribution in a single sublattice, a consequence of the semi-Dirac dispersion. Our work opens up new horizons for the study of transport and localization in lattices with chiral symmetry and exotic Dirac dispersions., Comment: 6 pages, 3 figures

Topological Physics relies on the specific structure of the eigenstates of Hamiltonians. Their geometry is encoded in the quantum geometric tensor containing both the celebrated Berry curvature, crucial for topological matter, and the quantum metric. The latter is at the heart of a growing number of physical phenomena such as superfluidity in flat bands, orbital magnetic susceptibility, exciton Lamb shift, and non-adiabatic corrections to the anomalous Hall effect. Here, we report the first direct measurement of both Berry curvature and quantum metric in a two-dimensional continuous medium. The studied platform is a planar microcavity of extremely high finesse, in the strong coupling regime. It hosts mixed exciton-photon modes (exciton-polaritons) subject to photonic spin-orbit-coupling which makes emerge Dirac cones and exciton Zeeman splitting breaking time-reversal symmetry. The monopolar and half-skyrmion pseudospin textures are measured by polarisation-resolved photoluminescence. The associated quantum geometry of the bands is straightforwardly extracted from these measurements. Our results unveil the intrinsic chirality of photonic modes which is at the basis of topological photonics. This technique can be extended to measure Bloch band geometries in artificial lattices. The use of exciton-polaritons (interacting photons) opens wide perspectives for future studies of quantum fluid physics in topological systems.

International audience; The usual concepts of topological physics, such as the Berry curvature, are not always relevant for non-Hermitian systems. We show that another object, the quantum metric, which often plays a secondary role in Hermitian systems, becomes a crucial quantity near exceptional points in non-Hermitian systems, where it diverges in a way that fully controls the description of wave-packet trajectories. The quantum metric behavior is responsible for a constant acceleration with a fixed direction, and for a nonvanishing constant velocity with a controllable direction. Both contributions are independent of the wave-packet size.

Conduction through materials crucially depends on how ordered they are. Periodically ordered systems exhibit extended Bloch waves that generate metallic bands, whereas disorder is known to limit conduction and localize the motion of particles in a medium. In this context, quasiperiodic systems, which are neither periodic nor disordered, reveal exotic conduction properties, self-similar wavefunctions, and critical phenomena. Here, we explore the localization properties of waves in a novel family of quasiperiodic chains obtained when continuously interpolating between two paradigmatic limits: the Aubry-Andr\'e model, famous for its metal-to-insulator transition, and the Fibonacci chain, known for its critical nature. Using both theoretical analysis and experiments on cavity-polariton devices, we discover that the Aubry-Andr\'e model evolves into criticality through a cascade of band-selective localization/delocalization transitions that iteratively shape the self-similar critical wavefunctions of the Fibonacci chain. Our findings offer (i) a unique new insight into understanding the criticality of quasiperiodic chains, (ii) a controllable knob by which to engineer band-selective pass filters, and (iii) a versatile experimental platform with which to further study the interplay of many-body interactions and dissipation in a wide range of quasiperiodic models., Comment: 7 pages, 4 figures + supplementary material (9 pages, 6 figures, 2 videos), comments are welcome

Phase frustration in periodic lattices is responsible for the formation of dispersionless flat bands. The absence of any kinetic energy scale makes flat band physics critically sensitive to perturbations and interactions. We report here on the experimental investigation of the nonlinear dynamics of cavity polaritons in the gapped flat band of a one-dimensional Lieb lattice. We observe the formation of gap solitons with quantized size and very abrupt edges, signature of the frozen propagation of switching fronts. This type of gap solitons belongs to the class of truncated Bloch waves, and had only been observed in closed systems up to now. Here the driven-dissipative character of the system gives rise to a complex multistability of the nonlinear domains generated in the flat band. These results open up interesting perspective regarding more complex 2D lattices and the generation of correlated photon phases., 6 pages, 4 figures + supplemental material (6 pages, 6 figures)

International audience; The extraordinary electronic properties of Dirac materials, the two-dimensional partners of Weyl semimetals, arise from the linear crossings in their band structure. When the dispersion around the Dirac points is tilted, one can predict the emergence of intricate transport phenomena such as modified Klein tunneling, intrinsic anomalous Hall effects, and ferrimagnetism. However, Dirac materials are rare, particularly with tilted Dirac cones. Recently, artificial materials whose building blocks present orbital degrees of freedom have appeared as promising candidates for the engineering of exotic Dirac dispersions. Here we take advantage of the orbital structure of photonic resonators arranged in a honeycomb lattice to implement photonic lattices with semi-Dirac, tilted, and, most interestingly, type-III Dirac cones that combine flat and linear dispersions. Type-III Dirac cones emerge from the touching of a flat and a parabolic band when synthetic photonic strain is introduced in the lattice, and they possess a nontrivial topological charge. This photonic realization provides a recipe for the synthesis of orbital Dirac matter with unconventional transport properties and, in combination with polariton nonlinearities, opens the way to study Dirac superfluids in topological landscapes.

We demonstrate how to tailor the losses of nonlinear cavities in order to suppress their reflection and enhance their non-reciprocal transmission. We derive analytical expressions predicting the existence of zero-reflection channels in single and coupled nonlinear cavities, depending on the driving frequency and loss rates. While suppressing the reflection from a single cavity imposes a stringent condition on the input-output leakage rates, we demonstrate that this condition can be significantly relaxed in systems of coupled cavities. In particular, zero-reflection and non-reciprocity can be achieved across a range of driving frequencies in coupled cavities by tuning the output leakage rate alone. Numerical calculations based on the driven-dissipative Gross-Pitaevksii equation, usually employed to describe microcavity polaritons, reveal the spatial phenomenology associated with zero-reflection states and provide design guidelines for the construction of nonlinear optical isolators., 12 pages, 7 figures

International audience; Analogue physics became very popular in recent decades. It allows simulating inaccessible physical phenomena, such as black holes, in the laboratory. The first success of analogue physics is in fact much older being due to Maxwell, who derived his equations for the electromagnetic field by analogy with fluid dynamics in presence of vortices. Here we propose to use vortices for analogue gravity. We implement an acoustic Kerr black hole with quantized angular momentum in a Bose-Einstein condensate. We show that the condensate's metric is equivalent to the Kerr's one, exhibiting a horizon and an ergosphere. We confirm that this metric is obeyed not only by weak density waves, but also by quantum vortices which behave as massive test particles. We use these topological defects to demonstrate a quantum Penrose effect, extracting the rotation energy of the black hole by quanta of angular momentum. The particle trajectories are well described by the timelike geodesics of the Kerr metric, confirming the potential of analogue quantum gravity.

Topological photonics has emerged as a novel route to engineer the flow of light. Topologically-protected photonic edge modes, which are supported at the perimeters of topologically-nontrivial insulating bulk structures, have been of particular interest as they may enable low-loss optical waveguides immune to structural disorder. Very recently, there is a sharp rise of interest in introducing gain materials into such topological photonic structures, primarily aiming at revolu-tionizing semiconductor lasers with the aid of physical mechanisms existing in topological physics. Examples of re-markable realizations are topological lasers with unidirectional light output under time-reversal symmetry breaking and topologically-protected polariton and micro/nano-cavity lasers. Moreover, the introduction of gain and loss provides a fascinating playground to explore novel topological phases, which are in close relevance to non-Hermitian and parity-time symmetric quantum physics and are in general difficult to access using fermionic condensed matter systems. Here, we review the cutting-edge research on active topological photonics, in which optical gain plays a pivotal role. We discuss recent realizations of topological lasers of various kinds, together with the underlying physics explaining the emergence of topological edge modes. In such demonstrations, the optical modes of the topological lasers are deter-mined by the dielectric structures and support lasing oscillation with the help of optical gain. We also address recent researches on topological photonic systems in which gain and loss themselves essentially influence on topological prop-erties of the bulk systems. We believe that active topological photonics provides powerful means to advance mi-cro/nanophotonics systems for diverse applications and topological physics itself as well., Comment: 23 pages, 11 figures, review paper to appear in Nanophotonics

In resonantly pumped polariton superfluids we recently explored a new regime based on the bistability of the polariton system to enhance the propagation of polariton fluids up to macroscopic distances. This technique together with an all-optical imprinting method allowed the generation and control of various topological excitations such as quantized vortices and dark solitons. The flexibility and scalability of the new experimental scheme opens the way to the systematic study of quantum turbulence in driven dissipative quantum fluids of light. In this article we review the basic working principles of the bistability enhanced propagation and of the imprinting technique and we discuss the main achieved results as well as the most promising future research directions., Review, 12 pages, 16 figures

Spin–orbit coupling of electromagnetic waves is one of the most important effects in topological photonics, but so far it has not been studied in photonic graphene implementations based on paraxial configuration, in particular, in atomic vapor cells. We generate experimentally a honeycomb refractive index pattern in such a cell using electromagnetically induced transparency. We demonstrate that an effective spin–orbit coupling appears as a correction to the paraxial beam equations because of the strong spatial gradients of the permittivity. It leads to the coupling of spin and angular momentum at the Dirac points of the graphene lattice. Our results suggest that the polarization degree of freedom plays an important role in many configurations where it has been previously neglected.

In crystalline nanoparticles, the Raman peak is downshifted with respect to the bulk material and has asymmetric broadening. These effects are straightly related to the finite size of nanoparticles, giving the perspective to use Raman spectroscopy as the size probe. By combining the dynamical matrix method (DMM) and the bond polarization model (BPM), we develop a new (DMM–BPM) approach for the description of Raman spectra of nanoparticle powders. The numerical variant of this approach is suitable for the description of small particles, whereas its analytical version is simpler to implement and allows one to obtain the Raman spectra of arbitrary-sized particles. Focusing on nanodiamond powders, the DMM–BPM theory is shown to fit the most recent experimental data much better than the commonly used phonon confinement model.

We report polariton lasing in localised gap states in a honeycomb lattice of coupled micropillars. Localisation of the modes is induced by the optical potential created by the excitation beam, requiring no additional engineering of the otherwise homogeneous polariton lattice. The spatial shape of the gap states arises from the interplay of the orbital angular momentum eigenmodes of the cylindrical potential created by the excitation beam and the hexagonal symmetry of the underlying lattice. Our results provide insights into the engineering of defect states in two-dimensional lattices., Comment: 18 pages, 8 figures, submitted to SciPost (rev)

We study the role of the quantum geometric tensor (QGT) in the evolution of two-band quantum systems. We show that all its components play an important role on the extra phase acquired by a spinor and on the trajectory of an accelerated wave packet in any realistic finite-duration experiment. While the adiabatic phase is determined by the Berry curvature (the imaginary part of the tensor), the nonadiabaticity is determined by the quantum metric (the real part of the tensor). We derive, for geodesic trajectories (corresponding to acceleration from zero initial velocity), the semiclassical equations of motion with nonadiabatic corrections. The particular case of a planar microcavity in the strong coupling regime allows us to extract the QGT components by direct light polarization measurements and to check their effects on the quantum evolution.

Two-dimensional transition metal dichalcogenides (TMDs) provide a unique possibility to generate and read-out excitonic valley coherence using linearly polarized light, opening the way to valley information transfer between distant systems. However, these excitons have short lifetimes (ps) and efficiently lose their valley coherence via the electron-hole exchange interaction. Here, we show that control of these processes can be gained by embedding a monolayer of WSe2 in an optical microcavity, forming part-light-part-matter exciton-polaritons. We demonstrate optical initialization of valley coherent polariton populations, exhibiting luminescence with a linear polarization degree up to 3 times higher than displayed by bare excitons. We utilize an external magnetic field alongside selective exciton-cavity-mode detuning to control the polariton valley pseudospin vector rotation, which reaches 45° at B = 8 T. This work provides unique insight into the decoherence mechanisms in TMDs and demonstrates the potential for engineering the valley pseudospin dynamics in monolayer semiconductors embedded in photonic structures., The short exciton life time in atomically thin transition metal dichalcogenides poses limitations to efficient control of the valley pseudospin and coherence. Here, the authors manipulate the exciton coherence in a WSe2 monolayer embedded in an optical microcavity in the strong light-matter coupling regime.

Modulational instabilities play a key role in a wide range of nonlinear optical phenomena, leading e.g. to the formation of spatial and temporal solitons, rogue waves and chaotic dynamics. Here we experimentally demonstrate the existence of a modulational instability in condensates of cavity polaritons, arising from the strong coupling of cavity photons with quantum well excitons. For this purpose we investigate the spatiotemporal coherence properties of polariton condensates in GaAs-based microcavities under continuous-wave pumping. The chaotic behavior of the instability results in a strongly reduced spatial and temporal coherence and a significantly inhomogeneous density. Additionally we show how the instability can be tamed by introducing a periodic potential so that condensation occurs into negative mass states, leading to largely improved coherence and homogeneity. These results pave the way to the exploration of long-range order in dissipative quantum fluids of light within a controlled platform., 7 pages, 5 figures

We propose a scheme of a topological optical isolator based on the quantum anomalous Hall effect with strongly coupled exciton-polaritons in a patterned GaAs cavity. We study the practical properties of such a device and optimize its parameters. We obtain an isolation ratio of 49 dB at a wavelength of 783 nm for a device of 40 μm with a maximal signal modulation frequency of 300 GHz, operating at temperatures up to 50 K.

We calculate the dispersion of spinor exciton-polaritons in a planar microcavity with its active region containing a single Transitional Metal Dichalcogenide (TMD) monolayer, taking into account excitonic and photonic spin-orbit coupling. We consider the radial propagation of polaritons in presence of disorder. We show that the reduction of the disorder scattering induced by the formation of polariton states allows to observe an optical Valley Hall effect, namely the coherent precession of the locked valley and polarization pseudospins leading to the formation of spatial valley-polarized domains.

International audience; Semiconductor microcavities in the strong-coupling regime exhibit an energy scale in the terahertz (THz) frequency range, which is fixed by the Rabi splitting between the upper and lower exciton-polariton states. While this range can be tuned by several orders of magnitude using different excitonic media, the transition between both polaritonic states is dipole forbidden. In this work, we show that, in cadmium telluride microcavities, the Rabi-oscillation-driven THz radiation is actually active without the need for any change in the microcavity design. This feature results from the unique resonance condition which is achieved between the Rabi splitting and the phonon-polariton states and leads to a giant enhancement of the second-order nonlinearity.

We consider theoretically staggered honeycomb lattices for photons which can be viewed as photonic analogs of transitional metal dichalcogenides (TMD) monolayers. We propose a simple realization of a photonic Quantum Valley Hall effect (QVHE) at the interface between two TMD analogs with opposite staggering on each side. This results in the formation of valley-polarized propagating modes whose existence relies on the difference between the valley Chern numbers, which is a $\mathbb{Z}_2$ topological invariant. We show that the magnitude of the photonic spin-orbit coupling based on the energy splitting between TE and TM photonic modes allows to control the number and propagation direction of these interface modes. Finally, we consider the interface between a staggered and a regular honeycomb lattice subject to a non-zero Zeeman field, therefore showing Quantum Anomalous Hall Effect (QAHE). In such a case, the topologically protected one-way modes of the QAHE become valley-polarized and the system behaves as a perfect valley filter.

We derive the diagram of the topological phases accessible within a generic Hamiltonian describing quantum anomalous Hall effect for photons and electrons in honeycomb lattices in presence of a Zeeman field and Spin-Orbit Coupling (SOC). The two cases differ crucially by the winding number of their SOC, which is 1 for the Rashba SOC of electrons, and 2 for the photon SOC induced by the energy splitting between the TE and TM modes. As a consequence, the two models exhibit opposite Chern numbers $\pm 2$ at low field. Moreover, the photonic system shows a topological transition absent in the electronic case. If the photonic states are mixed with excitonic resonances to form interacting exciton-polaritons, the effective Zeeman field can be induced and controlled by a circularly polarized pump. This new feature allows an all-optical control of the topological phase transitions., arXiv admin note: text overlap with arXiv:1606.07410

We study gap solitons which appear in the topological gap of 1D bosonic dimer chains within the mean-field approximation. We find that such solitons have a nontrivial texture of the sublattice pseudospin. We reveal their chiral nature by demonstrating the anisotropy of their behavior in the presence of a localized energy potential.

Suppl. Mat. added; improved data/error analysis; International audience; Topological materials rely on engineering global properties of their bulk energy bands called topological invariants. These invariants, usually defined over the entire Brillouin zone, are related to the existence of protected edge states. However, for an important class of Hamiltonians corresponding to 2D lattices with time-reversal and chiral symmetry (e.g., graphene), the existence of edge states is linked to invariants that are not defined over the full 2D Brillouin zone, but on reduced 1D subspaces. Here, we demonstrate a novel scheme based on a combined real- and momentum-space measurement to directly access these 1D topological invariants in lattices of semiconductor microcavities confining exciton polaritons. We extract these invariants in arrays emulating the physics of regular and critically compressed graphene where Dirac cones have merged. Our scheme provides a direct evidence of the bulk-edge correspondence in these systems and opens the door to the exploration of more complex topological effects, e.g., involving disorder and interactions.

We report the observation of a parametric instability in the out-of-equilibrium steady state of two coupled Kerr microresonators coherently driven by a laser. Using a resonant excitation, we drive the system into an unstable regime, where we observe the appearance of intense and well resolved sideband modes in the emission spectrum. This feature is a characteristic signature of self-sustained oscillations of the intracavity field. We comprehensively model our findings using semiclassical Langevin equations for the cavity field dynamics combined with a linear stability analysis. The inherent scalability of our semiconductor platform, enriched with a strong Kerr nonlinearity, is promising for the realization of integrated optical parametric oscillator networks operating in a few-photon regime., 6 pages, 3 figures

The application of topology, the mathematics of conserved properties under continuous deformations, is creating a range of new opportunities throughout photonics. This field was inspired by the discovery of topological insulators, in which interfacial electrons transport without dissipation, even in the presence of impurities. Similarly, the use of carefully designed wavevector-space topologies allows the creation of interfaces that support new states of light with useful and interesting properties. In particular, this suggests unidirectional waveguides that allow light to flow around large imperfections without back-reflection. This Review explains the underlying principles and highlights how topological effects can be realized in photonic crystals, coupled resonators, metamaterials and quasicrystals., United States. Army Research Office (Contract W911NF-07-D-0004), National Science Foundation (U.S.). Materials Research Science and Engineering Centers (Program) (Award DMR-0819762), United States. Dept. of Energy. Office of Science (Solid-State Solar-Thermal Energy Conversion Center Grant DE-SC0001299)