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arXiv:1212.6432 · New Journal of Physics

Topologically protected strongly correlated states of photons

Matouš Ringel, Mikhail Pletyukhov, Vladimir Gritsev

Published Nov 11, 2014• 26 citations
arXivHTMLPDF

Abstract

Hybrid photonic nanostructures allow the engineering of novel interesting states of light. One recent example is topological photonic crystals where a nontrivial Berry phase of the photonic band structure gives rise to topologically protected unidirectionally-propagating (chiral) edge states of photons. Here we demonstrate that by coupling an array of emitters to the chiral photonic edge state one can create strongly correlated states of photons in a highly controllable way. These are topologically protected and have a number of remarkable universal properties: the outcome of scattering does not depend on the positions of emitters and is given only by universal numbers, the zeroes of Laguerre polynomials; two-photon correlation functions manifest a well-pronounced even–odd effect with respect to the number of emitters; and the result of scattering is robust with respect to fluctuations in the emitters' transition frequencies.

DOI
10.1088/1367-2630/16/11/113030

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Hybrid photonic nanostructures allow the engineering of novel interesting states of light. One recent example is topological photonic crystals where a nontrivial Berry phase of the photonic band structure gives rise to topologically protected unidirectionally-propagating (chiral) edge states of photons. Here we demonstrate that by coupling an array of emitters to the chiral photonic edge state one can create strongly correlated states of photons in a highly controllable way. These are topologically protected and have a number of remarkable universal properties: the outcome of scattering does not depend on the positions of emitters and is given only by universal numbers, the zeroes of Laguerre polynomials; two-photon correlation functions manifest a well-pronounced even–odd effect with respect to the number of emitters; and the result of scattering is robust with respect to fluctuations in the emitters' transition frequencies.
The realization of robust strong coupling and entanglement between distant quantum emitters (QEs) is necessary for scalable quantum-information processes. However, it is hard to achieve it based on conventional systems. Here, we propose theoretically and demonstrate numerically a scheme to realize such strong coupling and entanglement. Our scheme is based on the photonic crystal platform with topologically protected edge state and zero-dimensional topological corner cavities. When the QEs are put into topological cavities, the strong coupling between them can be fulfilled with the assistance of the topologically protected interface state. Such a strong coupling can maintain a very long distance and be robust against various defects. In particular, we numerically prove that the topologically protected entanglement between two QEs can also be realized. Moreover, the duration of quantum beats for such entanglement can reach several orders longer than that for the entanglement in a conventional photonic cavity, making it beneficial for a scalable quantum-information process.
Topological insulators combine insulating properties in the bulk with scattering-free transport along edges, supporting dissipationless unidirectional energy and information flow even in the presence of defects and disorder. The feasibility of engineering quantum Hamiltonians with photonic tools, combined with the availability of entangled photons, raises the intriguing possibility of employing topologically protected entangled states in optical quantum computing and information processing. However, while two-photon states built as a product of two topologically protected single-photon states inherit full protection from their single-photon "parents", a high degree of non-separability may lead to rapid deterioration of the two-photon states after propagation through disorder. In this work, we identify physical mechanisms which contribute to the vulnerability of entangled states in topological photonic lattices. Further, we show that in order to maximize entanglement without sacrificing topological protection, the joint spectral correlation map of two-photon states must fit inside a well-defined topological window of protection.
Topological insulators combine insulating properties in the bulk with scattering-free transport along edges, supporting dissipationless unidirectional energy and information flow even in the presence of defects and disorder. The feasibility of engineering quantum Hamiltonians with photonic tools, combined with the availability of entangled photons, raises the intriguing possibility of employing topologically protected entangled states in optical quantum computing and information processing. However, while two-photon states built as a product of two topologically protected single-photon states inherit full protection from their single-photon "parents", high degree of non-separability may lead to rapid deterioration of the two-photon states after propagation through disorder. We identify physical mechanisms which contribute to the vulnerability of entangled states in topological photonic lattices and present clear guidelines for maximizing entanglement without sacrificing topological protection.
Cavity quantum electrodynamics studies light-matter interactions at single quanta level. Chiral photon-emitter coupling in photonic structures is characterized as unidirectional propagation locked by the local polarization of light. However, to realize the strong interaction of photon-emitter with direction-locked propagation, which will bring novel applications in nonreciprocal quantum devices, has not been reported yet. Here, we propose the coupled photonic crystal and metallic nanoparticle structure, where through strong local field with high helicity, the rate of circularly polarized photons emitting into photonic crystal waveguide is one order larger than that without the nanoparticle and the linewidth of Rabi splitting spectra is about one-tenth of that with only the nanoparticle, both with ∼\sim∼ 95%\%% photons propagating unidirectionally, which can be utilized in directional quantum light sources.
Topological insulators are materials that have a gapped bulk energy spectrum but contain protected in-gap states appearing at their surface. These states exhibit remarkable properties such as unidirectional propagation and robustness to noise that offer an opportunity to improve the performance and scalability of quantum technologies. For quantum applications, it is essential that the topological states are indistinguishable. We report high-visibility quantum interference of single-photon topological states in an integrated photonic circuit. Two topological boundary states, initially at opposite edges of a coupled waveguide array, are brought into proximity, where they interfere and undergo a beamsplitter operation. We observe Hong-Ou-Mandel interference with 93.1 ± 2.8% visibility, a hallmark nonclassical effect that is at the heart of linear optics-based quantum computation. Our work shows that it is feasible to generate and control highly indistinguishable single-photon topological states, opening pathways to enhanced photonic quantum technology with topological properties, and to study quantum effects in topological materials.
Up to now it remains challenging to couple photons from a circularly polarized emitter into a photonic structure to simultaneously realize strong photon-emitter interaction and unidirectional propagation locked by local helicity of the optical mode at the nanoscale. In this paper we propose a unique approach that combines a photonic crystal and metallic nanoparticle structure to create nanocavities with both strong local-field intensity and high helicity. In this system the rate of circularly polarized photons emitting into the photonic crystal waveguide reaches $148{\ensuremath{\gamma}}_{0}$, which is one order of magnitude larger than that without the nanoparticle, and in the ultranarrow band-edge mode the linewidth of Rabi splitting spectra is about one-tenth of that with the nanoparticle only, both with $\ensuremath{\approx}95%$ of photons propagating unidirectionally along the nanoscale waveguide. We suggest that our paper establishes a nanophotonic interface of chiral quantum electrodynamics for on-chip nonreciprocal quantum light sources, quantum circuits, and scalable quantum networks.