Experimental measurement of the divergent quantum metric of an exceptional point

Abstract: The geometry of Hamiltonian's eigenstates is encoded in the quantum geometric tensor (QGT). It contains both the Berry curvature, central to the description of topological matter and the quantum metric. So far the full QGT has been measured only in Hermitian systems, where the role of the quantum metric is mostly shown to determine corrections to physical effects. On the contrary, in non-Hermitian systems, and in particular near exceptional points, the quantum metric is expected to diverge and to often play a dominant role, for example on the enhanced sensing and on wave packet dynamics. In this work, we report the first experimental measurement of the quantum metric in a non-Hermitian system. The specific platform under study is an organic microcavity with exciton-polariton eigenstates, which demonstrate exceptional points. We measure the quantum metric's divergence and we determine the scaling exponent $n=-1.01\pm0.08$, which is in agreement with theoretical predictions for the second-order exceptional points.