Realization of Third Order Exceptional Singularities in a Three level non-Hermitian System: Towards Cascaded State Conversion

TL;DR

This paper demonstrates the realization of third order exceptional points in a three-level non-Hermitian system, revealing complex eigenvalue dynamics and phase exchange phenomena during cascaded state conversions.

Contribution

It introduces a three-level non-Hermitian Hamiltonian hosting multiple second order EPs and explores the dynamics around third order EPs through parameter variation.

Findings

Identification of third order EP signatures in eigenvalue dynamics

Observation of phase exchange during cascaded state conversions

Analysis of phase accumulation around EPs

Abstract

The appearance of topological singularities, namely exceptional points (EPs) is an intriguing feature of parameter-dependent open quantum or wave systems. EPs are the special type of nonHermitian degeneracies where two (or more) eigenstates of the underlying system coalesce. In this paper, we present a three level non-Hermitian Hamiltonian which hosts three interacting eigenstates. The matrix elements are optimized in such a way that the intermediate eigenstate interacts with both the other states and the underlying system hosts at least two different second order EPs. The impact of quasi-static parameter variation along a cyclic contour around the embedded EPs on the dynamics of interacting eigenvalues is well investigated in the context of cascaded state conversion. Such dynamics of the eigenvalues shows a clear signature of the third order EP with a combined effect of both the second order EPs. Moreover, we examine the accumulation of phases around the identified EPs and study the hallmark of phase exchange during cascaded state conversions accompanied by the parametric encirclement of the third order EP.