Dynamically encircling an exceptional point in anti-parity-time symmetric systems: asymmetric mode switching for symmetry-broken modes

Xu-Lin Zhang,C T Chan,Tianshu Jiang

doi:10.1038/s41377-019-0200-8

Abstract

Dynamically encircling an exceptional point (EP) in parity-time (PT) symmetric waveguide systems exhibits interesting chiral dynamics that can be applied to asymmetric mode switching for symmetric and anti-symmetric modes. The counterpart symmetry-broken modes (i.e., each eigenmode is localized in one waveguide only), which are more useful for applications such as on-chip optical signal processing, exhibit only non-chiral dynamics and therefore cannot be used for asymmetric mode switching. Here, we solve this problem by resorting to anti-parity-time (anti-PT) symmetric systems and utilizing their unique topological structure, which is very different from that of PT-symmetric systems. We find that the dynamical encircling of an EP in anti-PT-symmetric systems with the starting point in the PT-broken phase results in chiral dynamics. As a result, symmetry-broken modes can be used for asymmetric mode switching, which is a phenomenon and application unique to anti-PT-symmetric systems. We perform experiments to demonstrate the new wave-manipulation scheme, which may pave the way towards designing on-chip optical systems with novel functionalities.

Highlights

Introduction NonHermitian systems obeying parity-time (PT) symmetry, i.e., [PT,H] = 0, with H being the non-Hermitian Hamiltonian, have attracted considerable attention in recent years[1,2,3,4]
Most of the interesting properties of nonHermitian systems are found at the exceptional point (EP)[5,6], which has led to many novel phenomena and plausible applications[7,8,9,10,11,12,13,14,15,16,17]
The topological structure of the energy Riemann surface around the EP is of great interest, and it is known that adiabatically encircling an EP can result in an intriguing “flipping of the eigenstate” phenomenon, in which an eigenstate does not come back to itself after going around a loop in parameter space[18]

Summary

Introduction

The starting/end point of the loop lies in the PT-symmetric phase, where the eigenmodes are symmetric and anti-symmetric modes[30]. It is demonstrated that when the starting point of the loop lies in the PT-broken phase where the eigenmodes are symmetry-broken modes, dynamically encircling the EP results in a non-chiral transmission behaviour[34]. We discover a chiral transmission behaviour when the starting/end point of the loop lies in the PT-broken phase, where the eigenmodes are symmetry-broken modes.

Results

Conclusion