Open dissipative systems described by non-Hermitian Hamiltonians have attracted a lot of interest because they exhibit a wide range of counterintuitive physical effects aided by the balance of gain and loss. An accessible platform for studying non-Hermitian effects is a hybrid light-matter system of microcavity exciton polaritons, which arises from the strong coupling of semiconductor excitons and cavity photon modes.

In this Midterm Seminar, I present my theoretical works in investigating the consequences of non-Hermiticity for the dynamics, topology, and quantum geometry of exciton polaritons. I show that non-Hermiticity naturally leads to an effective self-acceleration of exciton-polariton wave packets [1]. The wave packet dynamics also leads to the emergence of pseudospin topological defects (half skyrmions). I also discuss how to induce the non-Hermitian skin effect in momentum space, where all eigenstates of the system localise on its edge. Furthermore, I present the non-Hermitian generalisation of the quantum geometric tensor, whose real part is a metric that defines the distance between quantum states, while its imaginary part is the Berry curvature. I propose an experimental protocol [2] for measuring different versions of the quantum geometric tensor using the polarisation of light emitted by exciton polaritons. Finally, I present further directions for exploring non-Hermitian topology using exciton polaritons.