Topologically protected defect states in open photonic systems with
  non-hermitian charge-conjugation and parity-time symmetry

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Abstract

We show that topologically protected defect states can exist in open (leaky or lossy) systems even when these systems are topologically trivial in the closed limit. The states appear from within the continuum, thus in absence of a band gap, and are generated via exceptional points (a spectral transition that occurs in open wave and quantum systems with a generalized time-reversal symmetry), or via a degeneracy induced by charge-conjugation-symmetry (which is related to the pole transition of Majorana zero modes). We demonstrate these findings for a leaking passive coupled-resonator optical waveguide with asymmmetric internal scattering, where the required symmetries (non-hermitian versions of time-reversal symmetry, chirality and charge-conjugation) emerge dynamically.

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Photonic Floquet Topological Insulators

Yonatan Plotnik, Mikael Rechtsman, Alexander Szameit … (2012)

The topological insulator is a fundamentally new phase of matter, with the striking property that the conduction of electrons occurs only on its surface, not within the bulk, and that conduction is topologically protected. Topological protection, the total lack of scattering of electron waves by disorder, is perhaps the most fascinating and technologically important aspect of this material: it provides robustness that is otherwise known only for superconductors. However, unlike superconductivity and the quantum Hall effect, which necessitate low temperatures or magnetic fields, the immunity to disorder of topological insulators occurs at room temperature and without any external magnetic field. For this reason, topological protection is predicted to have wide-ranging applications in fault-tolerant quantum computing and spintronics. Recently, a large theoretical effort has been directed towards bringing the concept into the domain of photonics: achieving topological protection of light at optical frequencies. Besides the interesting new physics involved, photonic topological insulators hold the promise for applications in optical isolation and robust photon transport. Here, we theoretically propose and experimentally demonstrate the first photonic topological insulator: a photonic lattice exhibiting topologically protected transport on the lattice edges, without the need for any external field. The system is composed of an array of helical waveguides, evanescently coupled to one another, and arranged in a graphene-like honeycomb lattice. The chirality of the waveguides results in scatter-free, one-way edge states that are topologically protected from scattering.

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Selective enhancement of topologically induced interface states

, , … (2014)

An attractive mechanism to induce robust spatially confined states utilizes interfaces between regions with topologically distinct gapped band structures. For electromagnetic waves, this mechanism can be realized in two dimensions by breaking symmetries in analogy to the quantum Hall effect or by employing analogies to the quantum spin Hall effect, while in one dimension it can be obtained by geometric lattice modulation. Induced by the presence of the interface, a topologically protected, exponentially confined state appears in the middle of the band gap. The intrinsic robustness of such states raises the question whether their properties can be controlled and modified independently of the other states in the system. Here, we draw on concepts from passive non-hermitian parity-time (PT)-symmetry to demonstrate the selective control and enhancement of a topologically induced state in a one-dimensional microwave set-up. In particular, we show that the state can be isolated from losses that affect all other modes in the system, which enhances its visibility in the temporal evolution of a pulse. The intrinsic robustness of the state to structural disorder persists in the presence of the losses. The combination of concepts from topology and non-hermitian symmetry is a promising addition to the set of design tools for optical structures with novel functionality.

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Analogs of quantum Hall effect edge states in photonic crystals

S Raghu, F D M Haldane (2006)

"Photonic crystals" built with time-reversal-symmetry-breaking Faraday-effect media can exhibit "chiral" edge modes that propagate unidirectionally along boundaries across which the Faraday axis reverses. These modes are precise analogs of the electronic edge states of quantum Hall effect (QHE) systems, and are also immune to backscattering and localization by disorder. The "Berry curvature" of the photonic bands plays a role analogous to that of the magnetic field in the QHE. Explicit calculations demonstrating the existence of such unidirectionally-propagating photonic edge states are presented.