A major topic of research in our experimental group is the study of quantum light in engineered microstructures. One important thread that guides our efforts along this line is the possibility of emulating interesting states of matter, notably topological phases, with photons. This represents an particularly advantageous approach for exploring condensed matter and topological physics beyond what is physically reachable in the solid-state. Indeed, not only can electromagnetic waves propagate in periodic structures similarly as electron Bloch waves in crystals, they can also inherit from their non-Hermitian, bosonic nature distinct properties that have no counterparts for electrons. Our jobs is thus to envision which photonic structures are the most interesting, fabricate and study them, and eventually use them to develop new architectures for photonic devices, from advanced lasers to quantum light sources.

**Topological photonic crystals**

Just like electrons form Bloch bands when they are confined in a periodic array of atoms, the electromagnetic spectrum can also exhibit a band structure when it is confined in a periodic potential. Photonic crystals are a canonical example of such *photonic materials*. They are typically formed by etching in a clean room a well-defined pattern of holes in a thin slab of dielectric material leading to a periodic variation of the index of refraction. Hence, the interference of photons give rise to dispersion relations analogous to band structures.

Our aim is to use these photonic crystals to emulate topological phases of matter for application in quantum photonics. Since one of the main hurdle preventing the scaling of quantum devices (photonics or not) is their extreme sensitivity to noise and other environmental perturbations, the unique robustness properties of topological systems offer an invaluable avenue to tackle this challenge. Our main motivation is thus guided by the prospect of developing more robust architectures, inspired by the complex symmetry present in topological matter.

To do this, we functionalize our crystals with optically active materials to generate, in a robust fashion, important quantum states of light. This functionalization can be realized in many different ways, but we have identified two particularly interesting ones on which we mainly focus: semiconductor monolayers (notably transition metal dichalcogenides) and dense ensemble of quantum emitters. This allows us to generate complex and interesting photonic states (e.g. single photons, entangled photons, superradiant states) within a topologically protected environment.

**Optical fiber loops network**

Another approach for emulating topological phases of matter with light consists in engineering a periodicity not in space but in frequency. This can be done by considering optical fiber loops where the periodicity consists now in the free spectral range of the cavity. Thus by modulating the fibers, it is possible to reproduce arbitrary band structures in the time domain.

This idea of *creating* such synthetic dimensions along which photons evolve is particularly well-suited for exploring higher-dimensional systems, i.e. larger than the usual 3 dimensions that we experience normally. In such complex spaces, intricate properties that have no counterparts in 3D materials can emerge, and eventually be harnessed to extend our capacity to control the dynamics of quantum light.

In our lab, we are mainly interested in studying the connection between topological physics, higher-dimensions, and thermodynamics. For example, in a recent work we have shown the ability to emulate atomic chain with arbitrary long range couplings, giving rise to larger topological invariants than what is typically observed in condensed matter.

**Collaborations**

Our group is focused on tackling very ambitious projects. And to do this, we need to work in close collaborations with many other leading groups, including **I. Carusotto** from **University of Trento, B**. **Coish **from** McGill University**, **S. Molesky **and **S. Kéna-Cohen **from** Polytechnique Montréal**, **P. Charrette **from** Université de Sherbrooke**, and I. **Sagnes **and **L. LeGratiet** from the **Center for Nanosciences and Nanotechnologies** in France.