Direct Measurement of a Non-Hermitian Topological Invariant in a Hybrid\n Light-Matter System

Abstract

Topology is central to understanding and engineering materials that display\nrobust physical phenomena immune to imperfections. Different topological phases\nof matter are characterised by topological invariants. In energy-conserving\n(Hermitian) systems, these invariants are determined by the winding of\neigenstates in momentum space. In non-Hermitian systems, a novel topological\ninvariant is predicted to emerge from the winding of the complex eigenenergies.\nHere, we directly measure the non-Hermitian topological invariant arising from\nexceptional points in the momentum-resolved spectrum of exciton polaritons.\nThese are hybrid light-matter quasiparticles formed by photons strongly coupled\nto electron-hole pairs (excitons) in a halide perovskite semiconductor at room\ntemperature. We experimentally map out both the real (energy) and imaginary\n(linewidth) parts of the spectrum near the exceptional points and extract the\nnovel topological invariant - fractional spectral winding. Our work represents\nan essential step towards realisation of non-Hermitian topological phases in a\ncondensed matter system.\n