Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons

Filippo Cardano (), Alessio D’Errico, Alexandre Dauphin (), Maria Maffei, Bruno Piccirillo, Corrado de Lisio, Giulio De Filippis, Vittorio Cataudella, Enrico Santamato, Lorenzo Marrucci, Maciej Lewenstein and Pietro Massignan
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Filippo Cardano: Università di Napoli Federico II, Complesso Universitario di Monte Sant’Angelo
Alessio D’Errico: Università di Napoli Federico II, Complesso Universitario di Monte Sant’Angelo
Alexandre Dauphin: ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology
Maria Maffei: 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
Maciej Lewenstein: ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology
Pietro Massignan: ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology

Nature Communications, 2017, vol. 8, issue 1, 1-7

Abstract: Abstract Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, an observable that rapidly approaches a value proportional to the Zak phase during the free evolution of the system. Then we measure the Zak phase in a photonic quantum walk of twisted photons, by observing the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general and readily applicable to all present one-dimensional platforms simulating static or Floquet chiral systems.

Date: 2017
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DOI: 10.1038/ncomms15516

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