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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Topological protection versus degree of entanglement of two-photon light

Konrad Tschernig, Kurt Busch, Armando Pérez-Leija

Published Jun 21, 2021• 0 citations
Publisher

Abstract

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.

DOI
10.1109/cleo/europe-eqec52157.2021.9541860

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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.
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.
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 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.
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.
We investigate spontaneous and pumped entanglement of two level systems in the vicinity of a photonic topological insulator interface, which supports a nonreciprocal (unidirectional), scattering-immune and topologically-protected surface plasmon polariton in the bandgap of the bulk material [1]. To this end, we derive a master equation for qubit interactions in a general three-dimensional, nonreciprocal, inhomogeneous and lossy environment. The environment is represented exactly, via the photonic Green function. The resulting entanglement is shown to be extremely robust to defects occurring in the material system, such that strong entanglement is maintained even if the interface exhibits electrically-large and geometrically sharp discontinuities. Alternatively, depending on the initial excitation state, using a non-reciprocal environment allows two qubits to remain unentangled even for very close spacing. The topological nature of the material is manifest in the insensitivity of the entanglement to variations in the material parameters that preserve the gap Chern number. Our formulation and results should be useful for both fundamental investigations of quantum dynamics in nonreciprocal environments, and technological applications related to entanglement in two-level systems.