Unidirectional zero reflection as gauged parity-time symmetry

James Gear,Shiyi Xiao,Hong Chen,Liwen Zhang,Richard Fitzgerald,Stefan Rotter,Yong Sun,Jensen Li

doi:10.1088/1367-2630/aa9b56

James Gear, Shiyi Xiao + Show 6 more

Open Access

https://doi.org/10.1088/1367-2630/aa9b56

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Abstract

We introduce here the concept of establishing parity-time (PT)-symmetry through a gauge transformation involving a shift of the mirror plane for the parity operation. The corresponding unitary transformation on the system’s constitutive matrix allows us to generate and explore a family of equivalent PT-symmetric systems. We further derive that unidirectional zero reflection for a reciprocal two-port system can always be associated with a passively gauged PT-symmetry. We demonstrate this experimentally using a microstrip transmission-line with magnetoelectric coupling. This study allows us to use bianisotropy as a practical route to realise and explore exceptional point behaviour of PT-symmetric or generally non-Hermitian systems.

Highlights

IntroductionParity-time (PT) symmetric Hamiltonians have been proposed as a class of non-Hermitian Hamiltonians with real eigenvalues that could possibly generalize the conventional paradigm of quantum mechanics [1,2,3]
We provide a common framework for understanding unidirectional zero reflection (UZR) in all of these different contexts by showing that UZR can always be interpreted as a result of passive PT-symmetry through a gauged parity operation
To establish this connection between UZR and passive PT-symmetry experimentally, we use a microstrip transmission-line with bianisotropy to verify the validity of our theoretical predictions

Summary

Introduction

Parity-time (PT) symmetric Hamiltonians have been proposed as a class of non-Hermitian Hamiltonians with real eigenvalues that could possibly generalize the conventional paradigm of quantum mechanics [1,2,3]. A PT-symmetric Hamiltonian can be realized by optical components with a balanced gain/loss pair [5,6,7,9,10,11,12,13] This is understood as the ideal configuration of PT-symmetry. Further studies have shown that PT-symmetry breaking can occur in passive systems, which can be mapped back to the ideal PT symmetric Hamiltonian by biasing the system with the averaged level of loss [4]. Such a gain/loss unbalanced situation is called a passive PT symmetry [4,14]. To establish this connection between UZR and passive PT-symmetry experimentally, we use a microstrip transmission-line with bianisotropy to verify the validity of our theoretical predictions

Gauged PT-symmetry condition

Bianisotropic transmission line

Unidirectional zero reflection as passive PT-symmetry

Conclusion