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Measuring the winding number in a large-scale chiral quantum walk
- Publication Year :
- 2018
- Publisher :
- arXiv, 2018.
-
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 birefringent crystal collinearly cut based on 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 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$\pm$0.007. Particularly, we can reconstruct the complete wave-function of the walker that starts the walk in a single lattice site through local tomography of each site. Through a Fourier transform, the wave-function in quasi-momentum space can be obtained. With this ability, we propose and report a method to reconstruct the eigenvectors of the system Hamiltonian in quasi-momentum space and directly read out the winding numbers in different topological phases (trivial and non-trivial) in the presence of chiral symmetry. By introducing nonequivalent time-frames, we show that the whole topological phases in periodically driven system can also be characterized by two different winding numbers. Our method can also be extended to the high winding number situation.<br />Comment: 26 pages, 8 figures
- Subjects :
- Physics
Quantum Physics
Photon
Winding number
General Physics and Astronomy
FOS: Physical sciences
02 engineering and technology
021001 nanoscience & nanotechnology
Topology
01 natural sciences
symbols.namesake
Fourier transform
Hadamard transform
0103 physical sciences
symbols
Quantum walk
010306 general physics
0210 nano-technology
Hamiltonian (quantum mechanics)
Wave function
Quantum Physics (quant-ph)
Eigenvalues and eigenvectors
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....bba0d84f6c9677af9e9aceb877fd85f6
- Full Text :
- https://doi.org/10.48550/arxiv.1808.09278