Higher order topological degeneracies and towards unique successive state-switching in a four-level open system

TL;DR

This paper explores the physical properties and dynamics of fourth-order exceptional points (EP4s) in a four-level non-Hermitian system, revealing new state-switching phenomena and robustness of EP4s under parameter variations.

Contribution

It introduces an analytical and numerical study of EP4s in a four-level system, demonstrating multiple EP4s, state-switching, and chiral behavior, advancing understanding of high-order topological degeneracies.

Findings

Realization of EP4 through four coupled states.

Observation of successive state-switching near EP4.

Robustness of EP4 phenomena despite different EP orders.

Abstract

The physics of topological singularities, namely exceptional points (EPs), has been a key to wide range of intriguing and unique physical effects in non-Hermitian systems. In this context, the mutual interactions among four coupled states around fourth-order EPs (EP4s) are yet to be explored. Here we report a four-level parameter-dependent perturbed non-Hermitian Hamiltonian, mimicking quantum or wave-based systems, to explore the physical aspects of an EP4 analytically as well as numerically. The proposed Hamiltonian exhibit different orders of interaction schemes with the simultaneous presence of different higher-order EPs. Here an EP4 has been realized by mutual interaction between four coupled states with proper parameter manipulation. We comprehensively investigate the dynamics of corresponding coupled eigenvalues with stroboscopic parametric variation in the vicinity of the embedded EP4 to establish a new successive state-switching phenomenon among them; which proves to be robust even in the presence of different order of EPs. Implementing the relation of the perturbation parameters with the coupling control parameters, we exclusively report a region to host multiple EP4 in a specific system. The chiral behaviour of successive state-exchange has also been established near EP4. Proposed scheme enriched with physical aspects of EP4s should provide a new light manipulation tool in any anisotropic multi-state integrated system.