Origin of third order exceptional singularities and its signature in successive state conversion

Abstract

We report an open three-state perturbed system with quasi-statically varying Hamiltonian depending on the topological parameters. The effective system hosts two second order exceptional points (EP2s). Here a third order exceptional point (EP3) is explored with simultaneous encirclement of two EP2s by adiabatic variation of topological parameters. We study the robust successive state-exchange around the EP3. Applying adiabatic theorem, we estimate the evolution of total phase accumulated by each state during encirclement; where interestingly, the state-common to the pairs of coupled state picks up three times phase shift of 2π. Such an exclusively reported scheme can be exploited in potential applications of exceptional points, manipulating fewer topological parameters in various non-Hermitian systems.

11 pages 5 figures