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

TL;DR

This paper investigates the behavior of a three-state non-Hermitian system with two second order exceptional points, demonstrating a third order exceptional point through adiabatic encirclement and phase analysis, with potential applications in system control.

Contribution

It introduces a novel scheme to realize and analyze a third order exceptional point by encircling two second order EPs in a three-state system with topological parameter variation.

Findings

Successful realization of EP3 via encirclement of two EP2s

State exchange exhibits a phase shift of 6π for the common state

Potential for simplified control in non-Hermitian systems

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 2{\pi}. Such an exclusively reported scheme can be exploited in potential applications of exceptional points, manipulating fewer topological parameters in various non-Hermitian systems.