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Phys Rev Lett. 2018 Jun 29;120(26):260501. doi: 10.1103/PhysRevLett.120.260501.

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

Xu XY1,2, Wang QQ1,2, Pan WW1,2, Sun K1,2, Xu JS1,2, Chen G1,2, Tang JS1,2, Gong M1,2, Han YJ1,2, Li CF1,2, Guo GC1,2.

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CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China.
Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China.


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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