Parity-Time Symmetry Breaking beyond One Dimension: The Role of Degeneracy

We consider the role of degeneracy in parity-time (PT ) symmetry breaking for non-Hermitian wave equations beyond one dimension. We show that if the spectrum is degenerate in the absence of T breaking, and T is broken in a generic manner (without preserving other discrete symmetries), then the stand...

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Bibliographic Details
Published in:Physical review. X Vol. 4; no. 3; p. 031011
Main Authors: Ge, Li, Stone, A. Douglas
Format: Journal Article
Language:English
Published: College Park American Physical Society 01.07.2014
Subjects:
Absorptivity
Amplification
Atomic physics
Broken symmetry
Decoupling
Eigenvalues
Hamiltonian functions
Light amplifiers
Luminous intensity
Optical components
Parity
Perturbation
Symmetry
Wave attenuation
Wave equations
ISSN:2160-3308, 2160-3308
Online Access:Get full text
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Summary:We consider the role of degeneracy in parity-time (PT ) symmetry breaking for non-Hermitian wave equations beyond one dimension. We show that if the spectrum is degenerate in the absence of T breaking, and T is broken in a generic manner (without preserving other discrete symmetries), then the standard PT symmetry-breaking transition does not occur, meaning that the spectrum is complex even for infinitesimal strength of gain and loss. However, the realness of the entire spectrum can be preserved over a finite interval if additional discrete symmetries χ are imposed when T is broken, if χ decouples all degenerate modes. When the decoupling holds only for a subset of the degenerate spectrum, there can be a partial PT transition in which this subset remains real over a finite interval of T breaking. If the spectrum has odd degeneracy, a fraction of the degenerate spectrum can remain in the symmetric phase even without imposing additional discrete symmetries, and they are analogous to dark states in atomic physics. These results are illustrated by the example of different T -breaking perturbations of a uniform dielectric disk and sphere, and a group-theoretical analysis is given in the disk case. Finally, we show that multimode coupling is capable of restoring the PT -symmetric phase at finite T breaking. We also analyze these questions when the parity operator is replaced by another spatial symmetry operator and find that the behavior can be qualitatively different.
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ISSN:2160-3308
2160-3308
DOI:10.1103/PhysRevX.4.031011