Exploring topological phases in quantum walks of twisted light

Filippo Cardano

doi:10.1117/12.2251367

27 February 2017 Exploring topological phases in quantum walks of twisted light

Filippo Cardano

Proceedings Volume 10120, Complex Light and Optical Forces XI; 101200V (2017) https://doi.org/10.1117/12.2251367
Event: SPIE OPTO, 2017, San Francisco, California, United States

Abstract

Emerged as the quantum counterpart of classical random walks, quantum walks are established precious resources in a variety of quantum sciences. Recent studies have shown that quantum walks may be characterized by topological invariants, in close analogy to condensed matter systems exhibiting topological order. Exploiting these features, quantum walks are currently used to simulate topological systems and to probe their exotic features. Here we present the implementation of a one-dimensional quantum walk protocol based on the orbital angular momentum of light, manifesting the topological phases that characterize time-periodic systems (Floquet topological insulators) showing chiral symmetry. By considering the orbital angular momentum spectrum of a light beam undergoing this quantum evolution, we show that the associated statistical moments have marked differences in distinct phases and contain information on the system topology. While varying a control parameter determining the value of the invariants, these moments in the large step-number limit exhibit a sharp variation at the phase changes. We show that these phenomena arise from the singular behavior of the dispersion relation at the transition points. The extension of our results to systems featuring different symmetries, or characterized by higher spatial dimensions, may unveil novel intriguing features associated with these complex systems.

Citation Download Citation

Filippo Cardano "Exploring topological phases in quantum walks of twisted light", Proc. SPIE 10120, Complex Light and Optical Forces XI, 101200V (27 February 2017); https://doi.org/10.1117/12.2251367

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