Periodic Reporting for period 1 - ToPol (Topological Polaritonics) Reporting period: 2018-04-01 to 2020-03-31 Summary of the context and overall objectives of the project The study of topological phases of matter in artificial platforms, notably photonic crystals, has attracted much attention over the last years as it allows exploring topological physics often beyond what is physically reachable in the solid-state. Indeed, this exploration has led to the development of new technological functionalities with robust properties, like protected lasers immune to disorder or fabrication defects. However, so far the field of topological photonics (i.e. emulating topological phases of matter in photonic systems) has remained mainly limited to the single-particle regimes, i.e. in systems where the nonlinearity remains very weak. The aim of this action is specifically to address this issue, and to explore and study the interplay between topological physics and nonlinear optics.This is highly relevant both at the fundamental and technological levels. At the more technological level, this could allow engineering new photonic active devices (e.g. switches, diodes, sources...) that are immune to the presence of local defects and environmental fulctuations. At the more fundamental point of view, it will pave the way to the exploration of new physical objects that are inherently nonlinear, like topological solitons or vortices. The implementation of such novel objects is crucial to better understand topological phases of matter in the presence of inter-particle interactions.The objective of this action is precisely to study this question using exciton-polaritons confined in arrays of semiconductor microresonators. Thanks to their excitonic part, these hybrid light-matter quasiparticles exhibit strong Kerr-like nonlinearities. More specifically the objectives of this project are divided in three parts: 1- implementing topological phases of matter that break time-reversal symmetry in polaritonic arrays, 2- implementing nonlinear effects in simpler polaritonic lattices that do not break time-reversal symmetry, and 3- combined both to explore nonlinear topological physics in systems that break time-reversal. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far (For the final period please include an overview of the results and their exploitation and dissemination)Since the beginning of the project, the work realized can be classified in the following classes:1- Demonstrating the onset of a lasing action in a benzene-like polaritonic molecule. This has allowed generating a coherent emission from a state that carries a well-defined topological charge. Furthermore, by using a circularly-polarized laser pump, it was possible to optically break time-reversal symmetry in a well-defined manner and control the chirality of the emission field, see image 1 attached. This is in line with the first objectvie described above, and has led to the following publication: Nat. Photonics 13, 283–288 (2019).2- Using the device fabricated in the previous point, we were able to explore the nonlinear regime by working at high driving power. Thanks to gain saturation, we were able to observe a bistable regime between two modes carrying a distinct topological charge. This was the first observation of such a nonlinear effect with chiral light, and it is in line with the second objective described above. It has led to the following publication: Opt. Letters 44, 18, 4531-4534 (2019) 3- Recently, I have collaborated with a PhD student to observe nonlinear effects in topological arrays of higher dimensionality. Namely, we have demonstrated the onset of symmetry-protected solitons in a 1D topological lattice. This is also an important result in relation with the second objective. A manuscript is right now finalized, and should be submitted shortly to a high-impact journal.4- In order to push the exploration of this physics in 2-dimension lattices, I have realized an important work where we have measured topological invariants in a honeycomb lattice that emulates the physics graphene, see image 2 attached. This is very relevant, as a similar lattice will be used to demonstrate (under a magnetic field) 2-dimensional topological lattices that break time-reversal symmetry. A manuscript has been updated on arXiv (2002.09528) and is currently under revision in a high-impact journal. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) The results described above have clearly shifted the state of the art, as they represent some of the only results available so far in the litterature that explore this interplay between topological physics and nonlinear optics. Until the end of the project, we are expecting new results that will push the state of the art even further, by implementing nonlinear effects in 2-dimensional lattices with broken time-reversal symmetry. The sample to realize these high impact experiments is currently under fabrication, and should be finished by the end of the summer; the experiments just be finished by fall considering that we have already gathered very interesting and promising preliminary results. This fabrication process was delayed by the moving of the laboratory and the pandemic, but is now in process. This is expected to lead to a very high-impact in the community, as it will represents the first nonlinear experiments in a photonic systems that emulate the quantum Hall effect.