Berlin 2018 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 76: Topology: Other Topics

TT 76.4: Vortrag

Mittwoch, 14. März 2018, 17:45–18:00, A 053

Non-Hermitian Hamiltonian for exceptional points of cavity modes — •Heinrich-Gregor Zirnstein and Bernd Rosenow — Institut für Theoretische Physik, Universität Leipzig, Germany

Recently, the existence of exceptional points in uniaxial optical cavities has been predicted [S. Richter et al., Phys. Rev. A 95, 023836 (2017)]. In order to pave the way for a topological characterization of these exceptional points, it is desirable to derive an effective non-Hermitian Hamiltonian that describes the corresponding cavity modes. Since open cavities are characterized by their transmission and reflection coefficients, i.e. their S-matrix, we use the Mahaux-Weidenmüller formula together with a partial fraction expansion to connect the S-matrix to a non-Hermitian Hamiltonian. In an exactly solvable toy model with two coalescing resonances, i.e. an exceptional point, we find that the Hamiltonian and the S-matrix describe the exceptional point with excellent agreement. Using a more realistic model for an optical cavity, we demonstrate that two exceptional points with opposite chirality merge into a Dirac point in the hypothetical limit of a decoupled cavity.