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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.

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.

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.

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.

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.

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).