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Observation of topological edge states in parity–time-symmetric quantum walks

Abstract

The study of non-Hermitian systems with parity–time (PT) symmetry is a rapidly developing frontier. Realized in recent experiments, PT-symmetric classical optical systems with balanced gain and loss hold great promise for future applications. Here we report the experimental realization of passive PT-symmetric quantum dynamics for single photons by temporally alternating photon losses in the quantum walk interferometers. The ability to impose PT symmetry allows us to realize and investigate Floquet topological phases driven by PT-symmetric quantum walks. We observe topological edge states between regions with different bulk topological properties and confirm the robustness of these edge states with respect to PT-symmetry-preserving perturbations and PT-symmetry-breaking static disorder. Our results contribute towards the realization of quantum mechanical PT-synthetic devices and suggest exciting possibilities for the exploration of the topological properties of non-Hermitian systems using discrete-time quantum walks.

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Figure 1: Phase diagram and experimental scheme for non-unitary QWs with alternating losses.
Figure 2: Experimental PT-symmetric homogeneous QWs with the walker starting from x = 0 and the initial coin state chosen to be |L |H〉 + i|V〉 via the delayed-choice setting.
Figure 3: Experimental observation of topological edge states in non-unitary QWs with the walker starting from x = 4 and the initial coin state chosen to be |H〉 via the delayed-choice setting.
Figure 4: Long-time survived edge states in the lossy system.
Figure 5: Edge states are robust against small perturbations.
Figure 6: Edge states are robust against static disorder to one of the rotations with angles θ1 + δθ where δθ is chosen uniformly from the intervals [−0.2,0.2].

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Acknowledgements

This work has been supported by the Natural Science Foundation of China (Grant Nos. 11474049, 11674056, 11374283 and 11522545) and the Natural Science Foundation of Jiangsu Province (Grant No. BK20160024). W.Y. acknowledges support from the National Key R&D Program (Grant No. 2016YFA0301700) and the ‘Strategic Priority Research Program(B)’ of the Chinese Academy of Sciences (Grant No. XDB01030200). N.K. and H.O. were supported by a Grant-in-Aid for Scientific Research on Innovative Areas ‘Topological Materials Science’ (Grant Nos JP15H05855, JP15K21717 and JP16H00975) and JSPS KAKENHI (Grant No. JP16K17760). B.C.S. acknowledges the 1000-Talent Plan and NSFC (Grant No. GG2340000241) for financial support.

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L.X., X.Z., Z.H.B. and K.K.W. performed the experiments. K.M., D.K., N.K. and H.O. performed the theoretical analysis. W.Y., H.O. and B.C.S. wrote part of the paper. P.X. designed the experiments, analysed the data and wrote most of the paper. All the authors participated in the discussions.

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Correspondence to P. Xue.

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Xiao, L., Zhan, X., Bian, Z. et al. Observation of topological edge states in parity–time-symmetric quantum walks. Nature Phys 13, 1117–1123 (2017). https://doi.org/10.1038/nphys4204

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