Annihilation of exceptional points from different Dirac valleys in a 2D photonic system.

Topological physics relies on Hamiltonian's eigenstate singularities carrying topological charges, such as Dirac points, and - in non-Hermitian systems - exceptional points (EPs), lines or surfaces. So far, the reported non-Hermitian topological transitions were related to the creation of a pair of EPs connected by a Fermi arc out of a single Dirac point by increasing non-Hermiticity. Such EPs can annihilate by reducing non-Hermiticity. Here, we demonstrate experimentally that an increase of non-Hermiticity can lead to the annihilation of EPs issued from different Dirac points (valleys). The studied platform is a liquid crystal microcavity with voltage-controlled birefringence and TE-TM photonic spin-orbit-coupling. Non-Hermiticity is provided by polarization-dependent losses. By increasing the non-Hermiticity degree, we control the position of the EPs. After the intervalley annihilation, the system becomes free of any band singularity. Our results open the field of non-Hermitian valley-physics and illustrate connections between Hermitian topology and non-Hermitian phase transitions.

Domain-Wall Topology Induced by Spontaneous Symmetry Breaking in Polariton Graphene.

We present a numerical study of exciton-polariton (polariton) condensation in a staggered polariton graphene showing a gapped s band. The condensation occurs at the kinetically favorable negative mass extrema (K and K^{'} valleys) of the valence band. Considering attractive polariton-polariton interaction allows us to generate a spatially extended condensate. The symmetry breaking occurring during the condensate buildup leads to the formation of valley-polarized domains. This process can either be spontaneous, following the Kibble-Zurek scenario, or triggered, leading to a controlled spatial distribution of valley-polarized domains. The selection of a single valley breaks time-reversal symmetry, and the walls separating domains exhibit a reconfigurable topologically protected chiral current. This current emerges as a result of the interplay between the nontrivial valley topology and the condensation-induced symmetry breaking.

Measurement of the quantum geometric tensor and of the anomalous Hall drift.

Topological physics relies on the structure of the eigenstates of the Hamiltonians. The geometry of the eigenstates is encoded in the quantum geometric tensor1-comprising the Berry curvature2 (crucial for topological matter)3 and the quantum metric4, which defines the distance between the eigenstates. Knowledge of the quantum metric is essential for understanding many phenomena, such as superfluidity in flat bands5, orbital magnetic susceptibility6,7, the exciton Lamb shift8 and the non-adiabatic anomalous Hall effect6,9. However, the quantum geometry of energy bands has not been measured. Here we report the direct measurement of both the Berry curvature and the quantum metric in a two-dimensional continuous medium-a high-finesse planar microcavity10-together with the related anomalous Hall drift. The microcavity hosts strongly coupled exciton-photon modes (exciton polaritons) that are subject to photonic spin-orbit coupling11 from which Dirac cones emerge12, and to exciton Zeeman splitting, breaking time-reversal symmetry. The monopolar and half-skyrmion pseudospin textures are measured using polarization-resolved photoluminescence. The associated quantum geometry of the bands is extracted, enabling prediction of the anomalous Hall drift, which we measure independently using high-resolution spatially resolved epifluorescence. Our results unveil the intrinsic chirality of photonic modes, the cornerstone of topological photonics13-15. These results also experimentally validate the semiclassical description of wavepacket motion in geometrically non-trivial bands9,16. The use of exciton polaritons (interacting photons) opens up possibilities for future studies of quantum fluid physics in topological systems.

Stationary Quantum Vortex Street in a Driven-Dissipative Quantum Fluid of Light.

We investigate the formation of a new class of density-phase defects in a resonantly driven 2D quantum fluid of light. The system bistability allows the formation of low-density regions containing density-phase singularities confined between high-density regions. We show that, in 1D channels, an odd (1 or 3) or even (2 or 4) number of dark solitons form parallel to the channel axis in order to accommodate the phase constraint induced by the pumps in the barriers. These soliton molecules are typically unstable and evolve toward stationary symmetric or antisymmetric arrays of vortex streets straightforwardly observable in cw experiments. The flexibility of this photonic platform allows implementing more complicated potentials such as mazelike channels, with the vortex streets connecting the entrances and thus solving the maze.

Particlelike Behavior of Topological Defects in Linear Wave Packets in Photonic Graphene.

Topological defects, such as quantum vortices, determine the properties of quantum fluids. Their study has been at the center of activity in solid state and BEC communities. In parallel, the nontrivial behavior of linear wave packets with complex phase patterns was investigated by singular optics. Here, we study the formation, evolution, and interaction of optical vortices in wave packets at the Dirac point in photonic graphene. We show that while their exact behavior goes beyond the Dirac equation and requires a full account of the lattice properties, it can be still approximately described by an effective theory considering the phase singularities as "particles". These particles are capable of mutual interaction, with their trajectory obeying the laws of dynamics.

Edge-emitting polariton laser and amplifier based on a ZnO waveguide.

We demonstrate edge-emitting exciton-polariton (polariton) laser operation from 5 to 300 K and polariton amplifiers based on polariton modes within ZnO waveguides. The guided mode dispersion below and above the lasing threshold is directly measured using gratings placed on top of the sample, fully demonstrating the polaritonic nature of the lasing modes. The threshold is found to be smaller than that expected for radiative polaritons in planar ZnO microcavities below 150 K and comparable above. These results open up broad perspectives for guided polaritonics by enabling easier and more straightforward implementation of polariton integrated circuits that exploit fast propagating polaritons, and, possibly, topological protection.

Valley coherent exciton-polaritons in a monolayer semiconductor.

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.

Robust quantum valley Hall effect for vortices in an interacting bosonic quantum fluid.

Topologically protected pseudospin transport, analogous to the quantum spin Hall effect, cannot be strictly implemented for photons and in general bosons because of the lack of symmetry-protected pseudospins. Here we show that the required protection can be provided by the real-space topological excitation of an interacting quantum fluid: a quantum vortex. We consider a Bose-Einstein condensate at the Γ point of the Brillouin zone of a quantum valley Hall system based on two staggered honeycomb lattices. We demonstrate the existence of a coupling between the vortex winding and the valley of the bulk Bloch band. This leads to chiral vortex propagation on each side of the zigzag interface between two regions of inverted staggering. The topological protection provided by the vortex winding prevents valley pseudospin mixing and resonant backscattering, allowing a truly topologically protected valley pseudospin transport.

Effective Theory of Nonadiabatic Quantum Evolution Based on the Quantum Geometric Tensor.

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.

Chirality of Topological Gap Solitons in Bosonic Dimer Chains.

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.

Kibble-Zurek Mechanism in Topologically Nontrivial Zigzag Chains of Polariton Micropillars.

We consider a zigzag chain of coupled micropillar cavities, taking into account the polarization of polariton states. We show that the TE-TM splitting of photonic cavity modes yields topologically protected polariton edge states. During the strongly nonadiabatic process of polariton condensation, the Kibble-Zurek mechanism leads to a random choice of polarization, equivalent to the dimerization of polymer chains. We show that dark-bright solitons appear as domain walls between polarization domains, analogous to the Su-Schrieffer-Heeger solitons in polymers. The soliton density scales as a power law with respect to the quenching parameter.

Exciton-polaritons in van der Waals heterostructures embedded in tunable microcavities.

Layered materials can be assembled vertically to fabricate a new class of van der Waals heterostructures a few atomic layers thick, compatible with a wide range of substrates and optoelectronic device geometries, enabling new strategies for control of light-matter coupling. Here, we incorporate molybdenum diselenide/hexagonal boron nitride (MoSe2/hBN) quantum wells in a tunable optical microcavity. Part-light-part-matter polariton eigenstates are observed as a result of the strong coupling between MoSe2 excitons and cavity photons, evidenced from a clear anticrossing between the neutral exciton and the cavity modes with a splitting of 20 meV for a single MoSe2 monolayer, enhanced to 29 meV in MoSe2/hBN/MoSe2 double-quantum wells. The splitting at resonance provides an estimate of the exciton radiative lifetime of 0.4 ps. Our results pave the way for room-temperature polaritonic devices based on multiple-quantum-well van der Waals heterostructures, where polariton condensation and electrical polariton injection through the incorporation of graphene contacts may be realized.

Polariton Z topological insulator.

We demonstrate that honeycomb arrays of microcavity pillars behave as an optical-frequency two-dimensional photonic topological insulator. We show that the interplay between the photonic spin-orbit coupling natively present in this system and the Zeeman splitting of exciton polaritons in external magnetic fields leads to the opening of a nontrivial gap characterized by a C=±2 set of band Chern numbers and to the formation of topologically protected one-way edge states.

Vortex chain in a resonantly pumped polariton superfluid.

Exciton-polaritons are light-matter mixed states interacting via their exciton fraction. They can be excited, manipulated, and detected using all the versatile techniques of modern optics. An exciton-polariton gas is therefore a unique platform to study out-of-equilibrium interacting quantum fluids. In this work, we report the formation of a ring-shaped array of same sign vortices after injection of angular momentum in a polariton superfluid. The angular momentum is injected by a ℓ = 8 Laguerre-Gauss beam. In the linear regime, a spiral interference pattern containing phase defects is visible. In the nonlinear (superfluid) regime, the interference disappears and eight vortices appear, minimizing the energy while conserving the quantized angular momentum. The radial position of the vortices evolves in the region between the two pumps as a function of the density. Hydrodynamic instabilities resulting in the spontaneous nucleation of vortex-antivortex pairs when the system size is sufficiently large confirm that the vortices are not constrained by interference when nonlinearities dominate the system.

Spin-orbit coupling and the optical spin Hall effect in photonic graphene.

We study the spin-orbit coupling induced by the splitting between TE and TM optical modes in a photonic honeycomb lattice. Using a tight-binding approach, we calculate analytically the band structure. Close to the Dirac point, we derive an effective Hamiltonian. We find that the local reduced symmetry (D_{3h}) transforms the TE-TM effective magnetic field into an emergent field with a Dresselhaus symmetry. As a result, particles become massive, but no gap opens. The emergent field symmetry is revealed by the optical spin Hall effect.

High-speed DC transport of emergent monopoles in spinor photonic fluids.

We investigate the spin dynamics of half-solitons in quantum fluids of interacting photons (exciton polaritons). Half-solitons, which behave as emergent monopoles, can be accelerated by the presence of effective magnetic fields. We study the generation of dc magnetic currents in a gas of half-solitons. At low densities, the current is suppressed due to the dipolar oscillations. At moderate densities, a magnetic current is recovered as a consequence of the collisions between the carriers. We show a deviation from Ohm's law due to the competition between dipoles and monopoles.

Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons.

Two-dimensional lattices of coupled micropillars etched in a planar semiconductor microcavity offer a workbench to engineer the band structure of polaritons. We report experimental studies of honeycomb lattices where the polariton low-energy dispersion is analogous to that of electrons in graphene. Using energy-resolved photoluminescence, we directly observe Dirac cones, around which the dynamics of polaritons is described by the Dirac equation for massless particles. At higher energies, we observe p orbital bands, one of them with the nondispersive character of a flatband. The realization of this structure which holds massless, massive, and infinitely massive particles opens the route towards studies of the interplay of dispersion, interactions, and frustration in a novel and controlled environment.

Non-Abelian gauge fields in photonic cavities and photonic superfluids.

We show that the TE-TM modes splitting and the structure anisotropy of a semiconductor microcavity combine into a non-Abelian gauge field for exciton-polaritons or cavity photons. The field texture can be tuned simply by rotating the sample and ranges continuously from a Rashba to a monopolar field. In the noninteracting regime, the latter leads to remarkable focusing and conical diffraction effects. In the interacting regime, the spin-orbit coupling induces a breakdown of superfluidity. The spatially homogeneous flows become unstable and dynamically evolve into spin textured states, such as stripes or domain walls.

All-optical phase modulation in a cavity-polariton Mach-Zehnder interferometer.

Quantum fluids based on light is a highly developing research field, since they provide a nonlinear platform for developing optical functionalities and quantum simulators. An important issue in this context is the ability to coherently control the properties of the fluid. Here we propose an all-optical approach for controlling the phase of a flow of cavity-polaritons, making use of their strong interactions with localized excitons. Here we illustrate the potential of this method by implementing a compact exciton-polariton interferometer, which output intensity and polarization can be optically controlled. This interferometer is cascadable with already reported polariton devices and is promising for future polaritonic quantum optic experiments. Complex phase patterns could be also engineered using this optical method, providing a key tool to build photonic artificial gauge fields.