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arXiv:2006.07963

Protecting Quantum Superposition and Entanglement with Photonic Higher-Order Topological Crystalline Insulator

Wang, Yao, Biye Xie, Yong‐Heng Lu, Chang, Yi-Jun, Hongfei Wang, Jun Gao, Zhi‐Qiang Jiao, Zhen Feng, Xiao-Yun Xu, Feng Mei, Suotang Jia, Ming‐Hui Lu, Xian‐Min Jin

Published Jun 14, 2020• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2006.07963

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Quantum entanglement, as the strictly non-classical phenomena, is the kernel of quantum computing and quantum simulation, and has been widely applied ranging from fundamental tests of quantum physics to quantum information processing. The decoherence of quantum states restricts the capability of building quantum simulators and quantum computers in a scalable fashion. Meanwhile, the topological phase is found inherently capable of protecting physical fields from unavoidable fabrication-induced disorder, which inspires the potential application of topological protection on quantum states. Here, we present the first experimental demonstration of topologically protected quantum polarization entangled states on a photonic chip. The process tomography shows that quantum entanglement can be well preserved by the boundary states even when the chip material substantially introduces relative polarization rotation in phase space. Our work links topology, material and quantum physics, opening the door to wide applications of topological enhancement in genuine quantum regime.
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Higher-order topological insulators have attracted significant interest in recent years. However, identifying a universal topological invariant capable of characterizing higher-order topology remains challenging. Here, we propose a entanglement topological invariant designed to characterize second-order topological systems. This entanglement topological invariant captures the entanglement of topological corner states under open boundary conditions by employing a bipartite entanglement entropy method. In several representative models, the entanglement topological invariant assumes a nonzero value exclusively in the presence of second-order topology, with its magnitude exactly matching the number of topologically protected corner states. Consequently, the proposed entanglement topological invariant not only provides a clear criterion for detecting higher-order topology, but also offers a quantitative measure for the related corner states. Our study establishes a universal and precise method for characterizing higher-order topological phases, opening avenues for their fundamental understanding and future investigations. Higher-order topological insulators have become a focus of research, but developing a universal way to characterize their unique higher-order topological properties remains a key challenge. The authors propose an entanglement topological invariant based on entanglement entropy, which not only reliably identifies second-order topological phases but also quantifies the number of topologically protected corner states.