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Nature Communications

Topological protection versus degree of entanglement of two-photon light in photonic topological insulators

Konrad Tschernig, Álvaro Jiménez-Galán, Demetrios N. Christodoulides, Misha Ivanov, Kurt Busch, Miguel A. Bandres, Armando Pérez-Leija

Published Mar 30, 2021• 38 citations
Publisher

Abstract

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.

DOI
10.1038/s41467-021-22264-3

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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.
The possibility of implementing quantum Hamiltonians using linear optical systems and entangled photons has opened the door to employing topologically protected entangled states in optical quantum information processing. In two-dimmensional photonic topologial insulators, single photon edge-states inhabit in the gap between the energy bands supporting the bulk states. Breaking the topological protection requires disorder with sufficient strength to close such a bandgap. For states comprising two indistinguishable photons, the same bandgap does not exists. The reason is because when a linear optical system is excited by two indistinguishable photons, all possible two-photon eigenstates are given by the symmetric combinations of the single-photon eigenstates. Consequently, the corresponding two-photon eigenvalues are given by the combinations of the single-photon eigenvaues λ (2) = λ m + λ n . This fundamental additive property of the single photon eigenenergies removes the bandgap and leads to massive degeneracies of the edge-edge, edge-bulk, and bulk-bulk two-photon states.
Abstract We study theoretically the evolution of entangled non-Gaussian two-photon states in disordered topological lattices. Specifically, we consider spatially entangled two-photon states, modulated by Laguerre polynomials up to the 3rd order, which feature ring-shaped spatial and spectral correlation patterns. Such states are discrete analogs of photon-subtracted squeezed states, which are ubiquitous in optical quantum information processing or sensing applications. We find that, in general, a higher degree of entanglement coincides with a loss of topological protection against disorder, this is in line with previous results for Gaussian two-photon states. However, we identify a particular regime in the parameter space of the considered non-Gaussian states, where the situation is reversed and an increase of entanglement can be beneficial for the transport of two-photon quantum states through disordered regions.
Higher-order topological insulator, as a newly found non-trivial material and structure, possesses a topological phase beyond the bulk-boundary correspondence. Here, we present an experimental observation of photonic higher-order topological crystalline insulator and its topological protection to quantum superposition and entanglement in a two-dimensional lattice. By freely writing the insulator structure with femtosecond laser and directly measuring evolution dynamics with single-photon imaging techniques, we are able to observe the distinct features of the topological corner states in C_4 and C_2 photonic lattice symmetry. Especially, we propose and experimentally identify the topological corner states by exciting the photonic lattice with single-photon superposition state, and we examine the protection impact of topology on quantum entanglement for entangled photon states. The single-photon dynamics and the protected entanglement reveal an intrinsic topological protection mechanism isolating multi-partite quantum states from diffusion-induced decoherence. The higher-order topological crystalline insulator, built-in superposition state generation, heralded single-photon imaging and quantum entanglement demonstrated here link topology, material, and quantum physics, opening the door to wide investigations of higher-order topology and applications of topological enhancement in genuine quantum regime.
Abstract Entangled multiphoton states lie at the heart of quantum information, computing, and communications. In recent years, topology has risen as a new avenue to robustly transport quantum states in the presence of fabrication defects, disorder, and other noise sources. Whereas topological protection of single photons and correlated photons has been recently demonstrated experimentally, the observation of topologically protected entangled states has thus far remained elusive. Here, we experimentally demonstrate the topological protection of spatially entangled biphoton states. We observe robustness in crucial features of the topological biphoton correlation map in the presence of deliberately introduced disorder in the silicon nanophotonic structure, in contrast with the lack of robustness in non‐topological structures. The topological protection is shown to ensure the coherent propagation of the entangled topological modes, which may lead to robust propagation of quantum information in disordered systems.