Symmetry recovery of exceptional points and their dynamical encircling in a two-state system

Abstract

Exceptional points are degeneracies in non-Hermitian systems. A two-state system with parity-time (PT) symmetry usually has only one exceptional point beyond which the eigenmodes are PT-symmetry broken. The so-called symmetry recovery, i.e., eigenmodes become PT-symmetric again, typically occurs in multi-state systems. Here we show that a two-state ferromagnetic waveguide system can have an exceptional point and a subsequent symmetry recovery due to the presence of accidental degeneracy points when the system is lossless. By introducing a parameter space where both exceptional points reside, we designed a system in which the trajectory in the parameter space can be controlled in situ using an adiabatically tunable external field, allowing us to explore the topological and chiral character of the system by encircling zero, one or two exceptional points. We performed microwave experiments to demonstrate the presence of the exceptional point, symmetry recovery, and the effects arising from their dynamical encircling.

43 pages, 23 figures

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• Hybrid exceptional point created from type III Dirac point
• Evolution and global charge conservation for polarization singularities emerging from nonhermitian degeneracies
• Exceptional points make an astroid in non-Hermitian Lieb lattice: evolution and topological protection
• Exceptional points and their coalescence of PT-symmetric interface states in photonic crystals
• Robust mode conversion in NV centers using exceptional points
• Excitation of absorbing exceptional points in the time domain
• Non-Hermitian physics and engineering in silicon photonics
• Non-adiabatic transitions in parabolic and super-parabolic $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian systems
• Comment on 'Winding around non-Hermitian singularities' by Zhong et al., Nat. Commun. 9, 4808 (2018)
• Spectral branch points of the Bloch-Torrey operator
• Unidirectional weak visibility in band gap and singular scattering in conduction band of one-dimensional parity-time symmetric photonic crystal
• Equations of motion governing the dynamics of the exceptional points of parameterically dependent nonhermitian Hamiltonians