High winding number of topological phase in periodic quantum walks

Xiao-Ye Xu, Qinqin Wang, Wei-Wei Pan +8 more

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.

János K. Asbóth, Arindam Mallick

Lin Zhang, Long Zhang, Sen Niu +1 more

S. Panahiyan, S. Fritzsche

Quantum walks are versatile simulators of topological phases and phase transitions as observed in condensed-matter physics. Here, we utilize a step-dependent coin in quantum walks and investigate what topological phases we can simulate with it, their topological invariants, bound states, and possibility of phase transitions. These quantum walks simulate nontrivial phases characterized by topological invariants (winding number) $\ifmmode\pm\else\textpm\fi{}1$, which are similar to the ones observed in topological insulators and polyacetylene. We confirm that the number of phases and their corresponding bound states increase step dependently. In contrast, the size of topological phase and distance between two bound states are decreasing functions of steps resulting into formation of multiple phases as quantum walks proceed (multiphase configuration). We show that, in the bound states, the winding number and group velocity are ill defined and the second moment of the probability density distribution in position space undergoes an abrupt change. Therefore, there are phase transitions taking place over the bound states and between two topological phases with different winding numbers.

Lei Xiao, Xingze Qiu, Kunkun Wang +6 more

Topological matter exhibits exotic properties yet phases characterized by large topological invariants are difficult to implement, despite rapid experimental progress. A promising route toward higher topological invariants is via engineered Floquet systems, particularly in photonics, where flexible control holds the potential of extending the study of conventional topological matter to novel regimes. Here we implement a one-dimensional photonic quantum walk to explore large winding numbers. By introducing partial measurements and hence loss into the system, we detect winding numbers of three and four in multistep nonunitary quantum walks, which agree well with theoretical predictions. Moreover, by probing statistical moments of the walker, we identify locations of topological phase transitions in the system and reveal the breaking of pseudounitary near topological phase boundaries. As the winding numbers are associated with nonunitary time evolution, our investigation enriches understanding of topological phenomena in nonunitary settings.

健 望月