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Conference on Lasers and Electro-Optics

Topological protection versus degree of entanglement of two-photon edge states

Konrad Tschernig, Kurt Busch, Armando Pérez-Leija

Published Jan 1, 2021• 0 citations
Publisher

Abstract

We investigate theoretically the physical mechanisms that contribute to the vulnerability of highly entangled two-photon edge states propagating in topological insulator photonic lattices. We present clear guidelines for maximizing entanglement without sacrificing topological protection.
DOI
10.1364/cleo_at.2021.jw1a.10

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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.
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.