Experimental Observation of the Topological Structure of Exceptional Points

C. Dembowski; H.-D. Gräf; H. L. Harney; A. Heine; W. D. Heiss; H. Rehfeld; A. Richter

doi:10.1103/PhysRevLett.86.787

Experimental Observation of the Topological Structure of Exceptional Points

C. Dembowski, H.-D. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter

Phys. Rev. Lett. 86, 787 – Published 29 January 2001

Abstract

We report on a microwave cavity experiment where exceptional points (EPs), which are square root singularities of the eigenvalues as function of a complex interaction parameter, are encircled in the laboratory. The real and imaginary parts of an eigenvalue are given by the frequency and width of a resonance and the eigenvectors by the field distributions. Repulsion of eigenvalues—always associated with EPs—implies frequency anticrossing (crossing) whenever width crossing (anticrossing) is present. The eigenvalues and eigenvectors are interchanged while encircling an EP, but one of the eigenvectors undergoes a sign change which can be discerned in the field patterns.

Received 26 April 2000

DOI:https://doi.org/10.1103/PhysRevLett.86.787

Authors & Affiliations

C. Dembowski¹, H.-D. Gräf¹, H. L. Harney², A. Heine¹, W. D. Heiss³, H. Rehfeld¹, and A. Richter¹

¹Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
²Max-Planck-Institut für Kernphysik, D-69029 Heidelberg, Germany
³Department of Physics, University of Witwatersrand, P.O. Wits 2050, Johannesburg, South Africa