Abstract

Topology is a branch of mathematics, which enables classifying geometrical objects according to global properties labels by an integer (genus number). Interestingly topology has appeared as a power tool in physics, providing profound new insights into physical phenomena such as the quantum Hall effect or the valley Hall effect. The geometrical objects to which these mathematical concepts apply in the context of condensed matter physics are the energy bands, and topological invariants called Chern numbers can be deduced from the eigenstates. Non-zero Chern numbers are responsible for anomalous velocity, or for the appearance of robust edge states at the border of a finite size system.

With the development of synthetic platforms, concepts of topology have been pushed far beyond what exists in actual material. The exploration of topology in presence of non-linearity, non hermiticity, higher dimension an emerging field of research with flourishing theoretical proposals to be emulated experimentally.

In the present talk, I will present some of our recent experiments performed using lattice of driven dissipative non-linear resonator. We use semiconductor microcavities operating in the strong exciton-photon regime, platform of choice for investigating topological physics. Indeed, due to their part-light part-matter character, exciton polaritons, the eigenstates of the system, can undergo i) spin-orbit coupling (photon part), while simultaneously experiencing ii) non-linearities and time-reversal symmetry breaking as a consequence of their susceptibility to magnetic fields (exciton part).

I will show how we can realize a full tomography of Bloch eigensates and experimentally retrieve Berry curvature and Chern numbers. Using the driven dissipative nature of the sytem, exotic non-linear steady states can be stabilized with novel emerging topological properties. We will discuss the physics of topological solitons and propose an interaction induced topological pump will.