Measuring the Winding Number in a Large-Scale Chiral Quantum Walk

Xiao-Ye Xu, Qin-Qin Wang, Wei-Wei Pan, Kai Sun, Jin-Shi Xu, Geng Chen, Jian-Shun Tang, Ming Gong, Yong-Jian Han, Chuan-Feng Li, and Guang-Can Guo
Phys. Rev. Lett. 120, 260501 – Published 26 June 2018
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Abstract

We report the experimental measurement of the winding number in an unitary chiral quantum walk. Fundamentally, the spin-orbit coupling in discrete time quantum walks is implemented via a birefringent crystal collinearly cut based on a time-multiplexing scheme. Our protocol is compact and avoids extra loss, making it suitable for realizing genuine single-photon quantum walks at a large scale. By adopting a heralded single photon as the walker and with a high time resolution technology in single-photon detection, we carry out a 50-step Hadamard discrete-time quantum walk with high fidelity up to 0.948±0.007. Particularly, we can reconstruct the complete wave function of the walker that starts the walk in a single lattice site through the local tomography of each site. Through a Fourier transform, the wave function in quasimomentum space can be obtained. With this ability, we propose and report a method to reconstruct the eigenvectors of the system Hamiltonian in quasimomentum space and directly read out the winding numbers in different topological phases (trivial and nontrivial) in the presence of chiral symmetry. By introducing nonequivalent time frames, we show that whole topological phases in a periodically driven system can also be characterized by two different winding numbers. Our method can also be extended to the high winding number situation.

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  • Received 27 October 2017
  • Revised 25 April 2018

DOI:https://doi.org/10.1103/PhysRevLett.120.260501

© 2018 American Physical Society

Physics Subject Headings (PhySH)

General PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Xiao-Ye Xu1,2, Qin-Qin Wang1,2, Wei-Wei Pan1,2, Kai Sun1,2, Jin-Shi Xu1,2, Geng Chen1,2, Jian-Shun Tang1,2, Ming Gong1,2, Yong-Jian Han1,2,*, Chuan-Feng Li1,2,†, and Guang-Can Guo1,2

  • 1CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People’s Republic of China
  • 2Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People’s Republic of China

  • *smhan@ustc.edu.cn
  • cfli@ustc.edu.cn

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Issue

Vol. 120, Iss. 26 — 29 June 2018

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