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Measuring the Winding Number in a Large-Scale Chiral Quantum Walk
Xiao-Ye Xu1,2, Qin-Qin Wang1,2, Wei-Wei Pan1,2
1CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China.
Physical Review Letters
|July 14, 2018
Summary
We experimentally measured the winding number in quantum walks, a key topological invariant. This method uses single photons and high-fidelity quantum walks to characterize topological phases.
Area of Science:
- Quantum Physics
- Topological Matter
- Quantum Information Science
Background:
- Quantum walks are a quantum analogue of classical random walks.
- Topological phases of matter are characterized by topological invariants, such as the winding number.
- Chiral symmetry is a crucial property in topological phases.
Purpose of the Study:
- To experimentally measure the winding number in a unitary chiral quantum walk.
- To develop a method for reconstructing Hamiltonian eigenvectors and topological invariants.
- To characterize topological phases in periodically driven systems.
Main Methods:
- Implementing spin-orbit coupling in discrete-time quantum walks using a birefringent crystal and time-multiplexing.
- Utilizing heralded single photons as walkers and high time-resolution single-photon detection.
- Performing local tomography to reconstruct the walker's wave function and applying Fourier transform to obtain quasimomentum space representation.
Main Results:
- Achieved high-fidelity (0.948±0.007) 50-step Hadamard discrete-time quantum walks.
- Successfully reconstructed Hamiltonian eigenvectors in quasimomentum space.
- Directly measured winding numbers in trivial and nontrivial topological phases with chiral symmetry.
Conclusions:
- The developed method allows direct readout of winding numbers, characterizing topological phases.
- Periodically driven systems can be characterized by winding numbers using nonequivalent time frames.
- The experimental protocol is scalable for large-scale quantum walks and adaptable for higher winding numbers.
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