Measuring the winding number in a large-scale chiral quantum walk

TL;DR

This paper demonstrates an experimental method to measure the winding number in a large-scale chiral quantum walk using a compact, lossless setup with high-fidelity single-photon implementation, enabling topological phase characterization.

Contribution

It introduces a novel protocol for directly reconstructing eigenvectors and measuring winding numbers in topological quantum walks with high fidelity and scalability.

Findings

Successfully performed a 50-step quantum walk with high fidelity.

Reconstructed the complete wave-function and eigenvectors in quasi-momentum space.

Measured winding numbers to identify trivial and non-trivial topological phases.

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.