Statistical moments of quantum-walk dynamics reveal topological quantum transitions

Filippo Cardano, Maria Maffei, Francesco Massa, Bruno Piccirillo, Corrado de Lisio, Giulio De Filippis, Vittorio Cataudella, Enrico Santamato and Lorenzo Marrucci ()
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Filippo Cardano: Università di Napoli Federico II, Complesso Universitario di Monte Sant’Angelo
Maria Maffei: Università di Napoli Federico II, Complesso Universitario di Monte Sant’Angelo
Francesco Massa: Università di Napoli Federico II, Complesso Universitario di Monte Sant’Angelo
Bruno Piccirillo: Università di Napoli Federico II, Complesso Universitario di Monte Sant’Angelo
Corrado de Lisio: Università di Napoli Federico II, Complesso Universitario di Monte Sant’Angelo
Giulio De Filippis: Università di Napoli Federico II, Complesso Universitario di Monte Sant’Angelo
Vittorio Cataudella: Università di Napoli Federico II, Complesso Universitario di Monte Sant’Angelo
Enrico Santamato: Università di Napoli Federico II, Complesso Universitario di Monte Sant’Angelo
Lorenzo Marrucci: Università di Napoli Federico II, Complesso Universitario di Monte Sant’Angelo

Nature Communications, 2016, vol. 7, issue 1, 1-8

Abstract: Abstract Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems.

Date: 2016
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DOI: 10.1038/ncomms11439

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