Experimental observation of the topological structure of exceptional points

We report on a microwave cavity experiment where exceptional points (EPs), which are square root singularities of the eigenvalues as function of a com plex interaction parameter, are encircled in the laboratory. The real and i maginary parts of an eigenvalue are given by the frequency and width of a r esonance and the eigenvectors by the field distributions. Repulsion of eige nvalues-always associated with EPs-implies frequency anticrossing (crossing ) whenever width crossing (anticrossing) is present. The eigenvalues and ei genvectors are interchanged while encircling an EP, but one of the eigenvec tors undergoes a sign change which can be discerned in the field patterns.