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The combination of an in-plane honeycomb potential and of a photonic spin-orbit coupling (SOC) emulates a photonic/polaritonic analog of bilayer graphene. We show that modulating the SOC magnitude allows to change the overall lattice periodicity, emulating any type of moir\'e-arranged bilayer graphene with a unique all-optical access to the moir\'e band topology. We show that breaking the time-reversal symmetry by an effective exciton-polariton Zeeman splitting opens a large topological gap in the array of moir\'e flat bands. This gap contains one-way topological edge states whose constant group velocity makes an increasingly sharp contrast with the flattening moir\'e bands.

Bound states in the continuum (BIC) are of special interest in photonics due to their theoretically infinite radiative lifetime. Here, we design a structure composed of a GaN layer with guided exciton-polaritons and a TiO$_2$ 1D photonic crystal slab. The photonic BIC hosted by the photonic crystal slab couples with the excitons of GaN to form a polaritonic BIC with a negative mass. This allows condensation to be reached with a low threshold in a structure suitable for electrical injection, paving the way for room-temperature polariton microdevices. We study in detail how the repulsive interaction between exciton-polaritons affects the condensate distribution in reciprocal space and, consequently, the condensate's overlap with the BIC resonance and, therefore, the condensate lifetime. We study an intrinsic contribution related to the formation of a bright soliton and the extrinsic contribution related to the interaction with an excitonic reservoir induced by spatially focused non-resonant pumping. We then study the peculiar dynamics of the condensation process in a BIC state for interacting particles using Boltzmann equations and hybrid Boltzmann-Gross Pitaevskii equations. We find optimal conditions allowing one to benefit from the long lifetime of the BIC for polariton condensation in a real structure.

So far, exciton-polariton (polariton) lasers were mostly single mode lasers based on microcavities. Despite the large repulsive polariton-polariton interaction, pulsed mode-locked polariton laser was never reported. Here, we use a $60 \ \mu m-$long GaN-based waveguide surrounded by distributed Bragg reflectors forming a multi-mode horizontal cavity. We demonstrate experimentally and theoretically a polariton mode-locked micro-laser operating in the blue-UV, at room temperature, with a 300$\ GHz$ repetition rate and 100$\ fs$-long pulses. The mode locking is demonstrated by the compensation (linearization) of the mode dispersion by the self-phase modulation induced by the polariton-polariton interaction. It is also supported by the observation in experiment and theory of the typical envelope frequency profile of a bright soliton., Comment: 16 pages, 12 figures

Engineering of the orbital angular momentum (OAM) of light due to interaction with photonic lattices reveals rich physics and motivates potential applications. We report the experimental creation of regularly-distributed quantized vortex arrays in momentum space by probing the honeycomb and hexagonal photonic lattices with a single focused Gaussian beam. For the honeycomb lattice, the vortices are associated with Dirac points and mimic the Berry curvature sources. However, we show that the resulting spatial patterns of vortices are strongly defined by the symmetry of the wave packet evolving in the optical lattice but not by lattice topological properties. Our findings reveal the underlying physics by connecting the symmetry and OAM conversion, and provide a simple and efficient method to create regularly-distributed multiple vortices by unstructured light., Comment: 6 pages, 6 figures

We propose theoretically a scheme to get a room-temperature 2D topological exciton-polariton laser with propagating topological lasing modes. The structure uses guided modes in a photonic crystal slab. A ZnO layer provides strong excitonic resonances stable at room temperature. It is capped by a TiO$_2$ layer pierced by a triangular lattice. The exciton-polariton modes of the 3D structure are computed by solving numerically Maxwell's equations including the excitonic response. The designed triangular lattice shows a transverse electric gap. The triangular lattice is shown to be the limit of a staggered honeycomb lattice when one of the sub-lattices vanishes. Its topology can be characterized by symmetry indicators. The interface between two shifted triangular lattices supports two counter-propagating modes lying in the gap of the bulk modes. The interface states are analogous to quantum pseudospin Hall interface states. These modes show orthogonal polarizations. They can be selectively excited using polarized excitation and are well-protected from back-scattering. These modes can benefit from the exciton-polariton gain at room temperature because of their sufficiently large exciton fraction and favorable position in energy. The strong localization of these propagating modes makes them suitable to host topological lasing triggered by a non-resonant pump localized on the interface.

The geometric phase is known to play a role both in the rotation of the Foucault pendulum and in the anomalous Hall effect (AHE) due to the Berry curvature. Here, we show that a 2D harmonic oscillator with AHE induced by Berry curvature behaves exactly like the Foucault pendulum: in both, the plane of the oscillations rotates with time. The rotating pendulum configuration enhances the AHE, simplifying its observation and allowing high-precision measurements of the Berry curvature. We also show how the non-adiabaticity and anharmonicity determine the maximal rotation angle and find the optimal conditions for the observations.

We study analytically an analog of the Andreev reflection at a normal-superfluid interface. The polariton gapped superfluid region is achieved by quasi-resonant optical pumping. The interacting polaritons are described with the driven-dissipative Gross-Pitaevskii equation. We find analytical formulas for the angles and amplitudes of the reflected and transmitted particles. There are limit angles and energies, above which Andreev reflection/transmission cannot be observed anymore and where the Andreev wave becomes a surface mode, exponentially localized on the interface. These properties are confirmed by solving numerically the Gross-Pitaevskii equation in simulations reproducing realistic experimental conditions.

We present a numerical study of exciton-polariton (polariton) condensation in a staggered polariton graphene showing a gapped s-band at the $K$ and $K'$ valleys. The condensation occurs at $K$ or $K'$, at the kinetically-favorable negative mass extrema of the valence band. Considering attractive polariton-polariton interaction allows to generate a spatially extended condensate. Spontaneous symmetry breaking occurring during the condensate build-up leads to the formation of valley-polarized domains following the Kibble-Zurek scenario. The selection of a single valley breaks time-reversal symmetry and the walls separating domains exhibit a topologically-protected chiral current. This current therefore emerges as a result of the interplay between the non-trivial valley topology and the condensation-induced symmetry breaking.

We experimentally demonstrate the difference between a ridge polariton laser, and a conventional edge-emitting ridge laser operating under electron-hole population inversion. The horizontal laser cavities are 20 -- 60 $\mu$m long GaN etched ridge structures with vertical Bragg reflectors. We investigate the laser threshold under optical pumping and assess quantitatively the effect of a varying optically-pumped length. The laser effect is achieved for an exciton reservoir length of just 15% of the cavity length, which would not be possible in a conventional ridge laser, with an inversion-less polaritonic gain about 10 times larger than in equivalent GaN lasers. The modelling of the cavity free spectral range demonstrates the polaritonic nature of the modes.

Topological physics relies on the existence of Hamiltonian's eigenstate singularities carrying a topological charge, such as quantum vortices, Dirac points, Weyl points and -- in non-Hermitian systems -- exceptional points (EPs), lines or surfaces. They appear only in pairs connected by a Fermi arc and are related to a Hermitian singularity, such as a Dirac point. The annihilation of 2D Dirac points carrying opposite charges has been experimentally reported. It remained elusive for Weyl points and second order EPs terminating different Fermi arcs. Here, we observe the annihilation of second order EPs issued from different Dirac points forming distinct valleys. We study a liquid crystal microcavity with voltage-controlled birefringence and TE-TM photonic spin-orbit-coupling. Two neighboring modes can be described by a two-band Hermitian Hamiltonian showing two topological phases with either two same-sign or four opposite-sign Dirac points (valleys). Non-Hermiticity is provided by polarization-dependent losses, which split Dirac points into pairs of EPs, connected by Fermi arcs. We measure their topological charges and control their displacement in reciprocal space by increasing the non-Hermiticity degree. EPs of opposite charges from different valleys meet and annihilate, connecting in a closed line the different Fermi arcs. This non-Hermitian topological transition occurs only when the Hermitian part of the Hamiltonian is topologically trivial (with four valleys), but is distinct from the Hermitian transition. Our results offer new perspectives of versatile manipulation of EPs, opening the new field of non-Hermitian valley-physics.

Strong coupling between light and the fundamental excitations of a two-dimensional electron gas (2DEG) are of foundational importance both to pure physics and to the understanding and development of future photonic nanotechnologies. Here we study the relationship between spin polarization of a 2DEG in a monolayer semiconductor, MoSe$_2$, and light-matter interactions modified by a zero-dimensional optical microcavity. We find robust spin-susceptibility of the 2DEG to simultaneously enhance and suppress trion-polariton formation in opposite photon helicities. This leads to observation of a giant effective valley Zeeman splitting for trion-polaritons (g-factor >20), exceeding the purely trionic splitting by over five times. Going further, we observe robust effective optical non-linearity arising from the highly non-linear behaviour of the valley-specific strong light-matter coupling regime, and allowing all-optical tuning of the polaritonic Zeeman splitting from 4 to >10 meV. Our experiments lay the groundwork for engineering quantum-Hall-like phases with true unidirectionality in monolayer semiconductors, accompanied by giant effective photonic non-linearities rooted in many-body exciton-electron correlations.

We derive semiclassical equations of motion for an accelerated wavepacket 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 Schr\"odinger 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. At $k=0$, such wavepacket 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.

We study the formation of topological defects (quantum vortices) during the formation of a 2D polariton condensate at the $\Gamma$ 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 $0.95\pm0.05$. 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.

Nonlinear topological photonics is an emerging field aiming at extending the fascinating properties of topological states to the realm where interactions between the system constituents cannot be neglected. Interactions can indeed trigger topological phase transitions, induce symmetry protection and robustness properties for the many-body system. Moreover when coupling to the environment via drive and dissipation is also considered, novel collective phenomena are expected to emerge. Here, we report the nonlinear response of a polariton lattice implementing a non-Hermitian version of the Su-Schrieffer-Heeger model. We trigger the formation of solitons in the topological gap of the band structure, and show that these solitons demonstrate robust nonlinear properties with respect to defects, because of the underlying sub-lattice symmetry. Leveraging on the system non-Hermiticity, we engineer the drive phase pattern and unveil bulk solitons that have no counterpart in conservative systems. They are localized on a single sub-lattice with a spatial profile alike a topological edge state. Our results demonstrate a tool to stabilize the nonlinear response of driven dissipative topological systems, which may constitute a powerful resource for nonlinear topological photonics.

We demonstrate the formation of a high angular momentum turbulent state in an exciton-polariton quantum fluid with TE-TM Spin-Orbit Coupling (SOC). The transfer of particles from quasi-resonantly cw pumped \spl component to \sm component is accompanied with the generation of a turbulent gas of quantum vortices by inhomogeneities. We show that this system is unstable with respect to the formation of bogolons at a finite wave vector, controlled by the laser detuning. In a finite-size cavity, the domains with this wave vector form a ring-like structure along the border of a cavity, with a gas of mostly same-sign vortices in the center. The total angular momentum is imposed by the sign of TE-TM SOC, the wave vector of instability, and the cavity size. This effect can be detected experimentally via local dispersion measurements or by interference. The proposed configuration thus allows simultaneous experimental studies of quantum turbulence and high-angular momentum states in continuously-pumped exciton-polariton condensates., Comment: 9 pages, 5 figures

Analogue physics has successfully tackled the problems of chromodynamics, 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 time-like curves and the well-known grandfather paradox can be studied experimentally in this system. We show how the Novikov's self-consistency principle is realized in quantum mechanics thanks to the Heisenberg's uncertainty principle.

The usual concepts of topological physics, such as the Berry curvature, cannot be applied directly to 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 wavepacket trajectories. The quantum metric behaviour is responsible for a constant acceleration with a fixed direction, and for a non-vanishing constant velocity with a controllable direction. Both contributions are independent of the wavepacket size.

We generate experimentally a honeycomb refractive index pattern in an atomic vapor cell using electromagnetically-induced transparency. We study experimentally and theoretically the propagation of polarized light beams in such "photonic graphene". 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 plays an important role in many configurations where it has been previously neglected.

Artificial gauge fields, simulating real phenomenologies that unfold in a vast variety of systems, offer extraordinary possibilities to study extreme physical effects in many different environments, from high energy physics to quantum mechanics and cosmology. They are also at the heart of topological physics. Here, exploiting a strongly anisotropic material under strong coupling regime, we experimentally synthesize a Yang-Mills non-Abelian gauge field acting on an exciton-polariton quantum flow like a magnetic field. We observe experimentally the corresponding curved trajectories and spin precession. This motion follows chromodynamics equations which normally describe the quarks strong interactions and their color. Our work therefore opens exciting perspectives of simulating quark-gluon dynamics using highly flexible photonic simulators. It makes of sub-atomic physics a potential new playground to apply topological physics concepts.

Integrated circuits of photonic components are the goal of applied polaritonics. Here, we propose a compact clock generator based on an exciton-polariton micropillar, providing optical signal with modulation frequency up to 100 GHz. This generator can be used for driving polariton devices. The clock frequency can be controlled by the driving laser frequency. The device also features low power consumption (1 pJ/pulse).

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 (1-3) or even (2-4) 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 anti-symmetric arrays of vortex streets straightforwardly observable in \emph{cw} experiments. The flexibility of this photonic platform allows implementing more complicated potentials such as maze-like channels, with the vortex streets connecting the entrances and thus solving the maze.

The coexistence of the energy and enstrophy cascades in 2D quantum turbulence is one of the important open questions in the studies of quantum fluids. Here, we show that polariton condensates are particularly suitable for the possible observation of scaling on sufficiently large scales. The shape of raw energy spectra depends on the procedure of condensate excitation (stirring), but the energy spectra of clustered vortices always exhibit the -5/3 power law. In the optimal case, the cascade can be observed over almost 2 decades., Comment: 13 pages, 14 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.

Planar microcavities filled with active materials containing excitonic resonances host radiative exciton-polariton (polariton) modes with in-plane wave vectors within the light cone. They also host at least one mode guided in the cavity plane by total internal reflection and which is not radiatively coupled to the vacuum modes except through defects or sample edges. We show that polariton lasing mediated by polariton stimulated scattering can occur concomitantly in both types of modes in a microcavity. By adjusting the detuning between the exciton and the radiative photon mode one can favor polariton lasing either in the radiative or in the guided modes. Our results suggest that the competition between these two types of polariton lasing modes may have played a role in many previous observations of polariton lasing and polariton Bose Einstein condensation.

Analog physics allows simulating inaccessible objects, such as black holes, in the lab. We propose to implement an acoustic Kerr black hole with quantized angular momentum in a polariton Bose-Einstein condensate. We show that the metric of the condensate is equivalent to the Kerr's one, exhibiting a horizon and an ergosphere. Using topological defects as test particles, we demonstrate an analog Penrose effect, extracting the rotation energy of the black hole. The particle trajectories are well described by the time-like geodesics of the Kerr metric, confirming the potential of analog gravity.

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)

Two-dimensional transition metal dichalcogenide (TMD) semiconductors provide a unique possibility to access the electronic valley degree of freedom using polarized light, opening the way to valley information transfer between distant systems. Excitons with a well-defined valley index (or valley pseudospin) as well as superpositions of the exciton valley states can be created with light having circular and linear polarization, respectively. However, the generated excitons have short lifetimes (ps) and are also subject to the electron-hole exchange interaction leading to fast relaxation of the valley pseudospin and coherence. Here we show that control of these processes can be gained by embedding a monolayer of WSe$_2$ in an optical microcavity, where part-light-part-matter exciton-polaritons are formed in the strong light-matter coupling regime. We demonstrate the optical initialization of the valley coherent polariton populations, exhibiting luminescence with a linear polarization degree up to 3 times higher than that of the excitons. We further control the evolution of the polariton valley coherence using a Faraday magnetic field to rotate the valley pseudospin by an angle defined by the exciton-cavity-mode detuning, which exceeds the rotation angle in the bare exciton. 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.

We first consider a generic two-band model which can be mapped to a pseudospin on a Bloch sphere. We establish the link between the pseudospin orientation and the components of the quantum geometric tensor (QGT): the metric tensor and the Berry curvature. We show how the k-dependent pseudospin orientation can be measured in photonic systems with radiative modes. We consider the specific example: a 2D planar cavity with two polarization eigenmodes, where the pseudospin measurement can be performed via polarization-resolved photoluminescence. We also consider the s-band of a staggered honeycomb lattice for polarization-degenerate modes (scalar photons). The sublattice pseudospin can be measured by performing spatially resolved interferometric measurements. In the second part, we consider a more complicated four-band model, which can be mapped to two entangled pseudospins. We show how the QGT components can be obtained by measuring six angles. The specific four-band system we considered is the s-band of a honeycomb lattice for polarized (spinor) photons. We show that all six angles can indeed be measured in this system. We simulate realistic experimental situations in all cases. We find the photon eigenstates by solving Schrodinger equation including pumping and finite lifetime, and then simulate the measurement of the relevant angles to finally extract realistic mappings of the k-dependent QGT components.

$\mathbb{Z}_2$ topological insulators for photons and in general bosons cannot be strictly implemented because of the lack of symmetry-protected pseudospins. We show that the required protection can be provided by the real-space topological excitation of an interacting quantum fluid: quantum vortex. We consider a Bose-Einstein Condensate at the $\Gamma$ 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 winding number of a vortex and the valley of the bulk Bloch band. This leads to chiral vortex propagation at the zigzag interface between two regions of inverted staggering, where the winding-valley coupling provides true topological protection against backscattering, contrary to the interface states of the non-interacting Hamiltonian. This configuration is an analog of a $\mathbb{Z}_2$ topological insulator for quantum vortices.

We demonstrate edge-emitting exciton-polariton (polariton) lasing from 5 to 300 K and amplification of non-radiative guided polariton modes within ZnO waveguides. The mode dispersion below and above the lasing threshold is directly measured using gratings present on top of the sample, fully demonstrating the polaritonic nature of the lasing modes. The threshold is found to be similar to that of radiative polarions in planar ZnO microcavities. These results open broad perspectives for guided polaritonics by allowing an easier and more straightforward implementation of polariton integrated circuits exploiting fast propagating polaritons.

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., Comment: arXiv admin note: text overlap with arXiv:1606.07410

While conventional semiconductor technology relies on the manipulation of electrical charge for the implementation of computational logic, additional degrees of freedom such as spin and valley offer alternative avenues for the encoding of information. In transition metal dichalcogenide (TMD) monolayers, where spin-valley locking is present, strong retention of valley chirality has been reported for MoS$_2$, WSe$_2$ and WS$_2$ while MoSe$_2$ shows anomalously low valley polarisation retention. In this work, chiral selectivity of MoSe$_2$ cavity polaritons under helical excitation is reported with a polarisation degree that can be controlled by the exciton-cavity detuning. In contrast to the very low circular polarisation degrees seen in MoSe$_2$ exciton and trion resonances, we observe a significant enhancement of up to 7 times when in the polaritonic regime. Here, polaritons introduce a fast decay mechanism which inhibits full valley pseudospin relaxation and thus allows for increased retention of injected polarisation in the emitted light. A dynamical model applicable to cavity-polaritons in any TMD semiconductor, reproduces the detuning dependence through the incorporation of the cavity-modified exciton relaxation, allowing an estimate of the spin relaxation time in MoSe$_2$ which is an order of magnitude faster than those reported in other TMDs. The valley addressable exciton-polaritons reported here offer robust valley polarised states demonstrating the prospect of valleytronic devices based upon TMDs embedded in photonic structures, with significant potential for valley-dependent nonlinear polariton-polariton interactions.

We study the role of the quantum geometric tensor (QGT) in the evolution of 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 wavepacket in any realistic finite-duration experiment. While the adiabatic phase is determined by the Berry curvature (the imaginary part of the tensor), the non-adiabaticity is determined by the quantum metric (the real part of the tensor) and allows to determine corrections in the regimes where Landau-Zener approach is inapplicable. The particular case of a planar microcavity in the strong coupling regime allows to extract the QGT components by direct light polarization measurements and to check their effects on the quantum evolution.

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.

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 non-trivial texture of the sublattice pseudospin. We reveal their chiral nature by demonstrating the anisotropy of their behavior in presence of a localized energy potential.

Exciton-polariton lattices allow to implement topologically protected photonic edge states at optical frequencies. Taking advantage of the interacting character of polaritons, we show that several topological phases, belonging to the Quantum Anomalous Hall family, can occur in polariton graphene with the TE-TM spin-orbit coupling and an effective Zeeman field. This Zeeman field can be entirely controlled by the non-linearity of the macro-occupied mode created by circularly polarized resonant pumping. The topological phases found are distinct from the ones of normal graphene in presence of a combination of Rashba and Zeeman field.

The optical modes of photonic structures are the so-called TE and TM modes which bring intrinsic spin-orbit coupling and chirality to these systems. This, combined with the unique flexibility of design of the photonic potential, and the possibility to mix photon states with excitonic resonances, sensitive to magnetic field and interactions, allows to achieve many phenomena, often analogous to other solid state systems. In this contribution, we review in a qualitative and comprehensive way several of these realizations, namely the optical spin Hall effect, the creation of spin currents protected by a non-trivial geometry, Berry curvature for photons, and the photonic/polaritonic topological insulator.

GaN and ZnO microcavities have been grown on patterned silicon substrate. Thanks to a common platform these microcavities share similar photonic properties with large quality factors and low photonic disorder which gives the possibility to determine the optimal spot diameter and to realize a complete comparative phase diagram study. Both systems have been investigated under the same experimental condition. Experimental results are well reproduced by simulation using Boltzmann equations. Lower polariton lasing threshold has been measured at low temperature in the ZnO microcavity as expected due to a larger Rabi splitting. However the threshold is strongly impacted by LO phonons through phonon-assisted polariton relaxation. We observe and discuss this effect as a function of temperature and detuning. Finally the polariton lasing threshold at room temperature is quite similar in both microcavities. This study highlights polariton relaxation mechanism and their importance for threshold optimization.

We study Bogoliubov excitations of a spinor Bose Einstein condensate in a honeycomb periodic potential, in the presence of a Zeeman field and of a spin-orbit coupling specific for photonic systems, which is due to the energy splitting between TE and TM polarized eigenstates. We also consider spin-anisotropic interactions typical for cavity polaritons. We show that the non-trivial topology of the single particle case is also present for the interacting system. At low condensate density, the topology of the single-particle bands is transferred to the bogolon dispersion. At a critical value, the self-induced Zeeman field at the Dirac points of the dispersion becomes equal to the real Zeeman field and then exceeds it. The gap is thus closed and then re-opened with inverted Chern numbers. This change of topology is accompanied by a change of the propagation directions of the one-way edge modes. This result demonstrates that the chirality of a topological insulator can be reversed by collective effects in a Bose-Einstein condensate.

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 non-adiabatic process of polariton condensation, the Kibble-Zurek mechanism leads to a random choice of polarization, equivalent to 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.

Layered materials can be assembled vertically to fabricate a new class of van der Waals (VDW) 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/boron nitride (MoSe$_2$/hBN) quantum wells (QWs) in a tunable optical microcavity. Part-light-part-matter polariton eigenstates are observed as a result of the strong coupling between MoSe$_2$ 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 MoSe$_2$ monolayer QW, enhanced to 29 meV in MoSe$_2$/hBN/MoSe$_2$ double-QWs. 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-QW VDW heterostructures, where polariton condensation and electrical polariton injection through the incorporation of graphene contacts may be realised.

We observe condensation of exciton polaritons in quantum states composed of concentric rings when exciting cylindrical pillar GaAs/AlGaAs microcavities non-resonantly by a focused laser beam normally incident at the center of the pillar. The number of rings depends on the pumping intensity and the pillar size, and may achieve 5 in the pillar of 40 mkm diameter. Breaking the axial symmetry when moving the excitation spot away from the pillar center leads to transformation of the rings into a number of bright lobes corresponding to quantum states with nonzero angular momenta. The number of lobes, their shape and location are dependent on the spot position. We describe the out-of-equilibrium condensation of polaritons in the states with different principal quantum numbers and angular momenta with a formalism based on Boltzmann-Gross-Pitaevskii equations accounting for repulsion of polaritons from the exciton reservoir formed at the excitation spot and their spatial confinement by the pillar boundary., Comment: 9 figures, Submitted to the Physical Review B

We propose an implementation of a CNOT quantum gate for quantum computing based on a patterned microcavity polariton system, which can be manufactured using the modern technological facilities. The qubits are encoded in the spin of polaritons. The structure consists of two wire cavities oriented at 45 degrees with a micropillar between them. The polariton spin rotates due to the Longitudinal-Transverse splitting between polarisation eigenstates in the wires. In the pillar, the optically generated circularly polarised polariton macrooccupied state plays the role of the control qubit. Because of the spin-anisotropic polariton interaction, it induces an effective magnetic field along the Z-direction with a sign depending on the qubit value.

Dipolariton is a voltage controlled mixture of direct and indirect excitons in asymmetric double quantum wells coupled by resonant carrier tunneling, and a microcavity photon. We calculate the voltage dependence of the spin-singlet and spin-triplet interaction parameters $\alpha_{1}$ and $\alpha_{2}$. Both parameters can reach values one order of magnitude larger than that of exciton-polaritons thanks to the strong interaction between indirect excitons. We show that the variation of the indirect exciton fraction of the dipolaritons induces a changes of sign of $\alpha_{2}$ increasing voltage: the interaction passes from attractive to repulsive. For large enough voltage $\alpha_{2}$ becomes larger than $\alpha_{1}$ which in principle can lead to the formation of a circularly polarised dipolariton condensate. We propose an application of the $\alpha_{2}$ dependence to a voltage-controlled dipolaritonic optical parametric oscillator. The change of sign of $\alpha_{2}$ allows an on-site control of the linear polarization degree of the optical signal and its on-demand inversion.

We propose a scheme of an optical amplifier based on GaN and ZnO waveguides operating in the regime of strong coupling between photonic modes and excitonic resonances. Amplification of the guided exciton-polaritons is obtained by stimulated scattering from the excitonic reservoir, which is found to be fast enough compared with the large velocity of the guided polariton modes. We analyze the device parameters at different temperatures. We find that an 80 $\mu$m-long amplifier can provide a gain of 10dB at room temperature, being supplied by 5 mA current in the $cw$ regime.

Recent search for optical analogues of topological phenomena mainly focuses on mimicking the key feature of quantum Hall and quantum spin Hall effects (QHE and QSHE): edge currents protected from disorder. QHE relies on time-reversal symmetry breaking, which can be realised in photonic gyromagnetic crystals. In the optical range, the weak magneto-optical activity may be replaced with helical design of coupled waveguides, converting light propagation into a time-dependent perturbation. Finally, optical QHE due to artificial gauge fields was predicted in microcavity lattices. Here, we consider honeycomb arrays of microcavity pillars as an alternative optical-frequency 2D 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 non-trivial gap characterised by $C=\pm 2$ set of band Chern numbers and to the formation of topologically protected one-way edge states.

We investigate exciton-polariton condensation under magnetic field in a single high-quality semiconductor micropillar cavity. We observe successive polariton condensation of each spin component for two distinct threshold powers. Pronounced and non-monotonous variations of both the Zeeman splitting and the circular polarization of the emission are measured across these two condensation thresholds. This unexpected behavior deeply deviates from the so-called spin Meissner effect predicted for a fully thermalized system. Our measurements can be understood in a kinetic approach taking into account spin-anisotropic interactions within the entire system: the polariton condensate and the cloud of uncondensed excitons.

One of the most fundamental properties of electromagnetism and special relativity is the coupling between the spin of an electron and its orbital motion. This is at the origin of the fine structure in atoms, the spin Hall effect in semiconductors, and underlies many intriguing properties of topological insulators, in particular their chiral edge states. Configurations where neutral particles experience an effective spin-orbit coupling have been recently proposed and realized using ultracold atoms and photons. Here we use coupled micropillars etched out of a semiconductor microcavity to engineer a spin-orbit Hamiltonian for photons and polaritons in a microstructure. The coupling between the spin and orbital momentum arises from the polarisation dependent confinement and tunnelling of photons between micropillars arranged in the form of a hexagonal photonic molecule. Dramatic consequences of the spin-orbit coupling are experimentally observed in these structures in the wavefunction of polariton condensates, whose helical shape is directly visible in the spatially resolved polarisation patterns of the emitted light. The strong optical nonlinearity of polariton systems suggests exciting perspectives for using quantum fluids of polaritons11 for quantum simulation of the interplay between interactions and spin-orbit coupling., Comment: main text: pages 1-11 (4 figures); supplementary material: pages 12-28 (9 figures)

We present an experimental study on the ignition and decay of a polariton optical parametric oscillator (OPO) in a semiconductor microcavity pillar. The combination of a continuous wave laser pump, under quasi-phase matching conditions, and a non-resonant, 2 ps-long pulse probe allows us to obtain the full dynamics of the system. The arrival of the probe induces a blue-shift in the polariton emission, bringing the OPO process into resonance with the pump, which triggers the OPO-process. We time-resolve the polariton OPO signal emission for more than 1 nanosecond in both real and momentum-space. We fully characterize the emission of the OPO signal with spectral tomography techniques. Our interpretations are backed up by theoretical simulations based on the 2D coupled Gross-Pitaevskii equation for excitons and photons., Comment: 8 pages, 8 figures