Current theoretical research is showing that periodically‐driven systems generate much richer and more complex topological properties than their static counterparts. Therefore, the accurate detection of these topological properties is a key challenge.
In this talk, we derive and design a flexible and efficient theoretical method which allows to measure the Zak phases of one dimensional systems with chiral symmetry by direct imaging of single particle dynamics in their bulk. We then conﬁrm experimentally our theoretical ﬁndings by measuring the two independent Zak phases of a chiral quantum walk realized by twisted photons, i.e., in a photonic platform exploiting the spin and orbital angular momenta of light. Combining the two phase windings, they provide a complete and robust topological characterization of this periodically‐driven system .
Finally, this method does not require a filled band, nor the application of a force, but simply relies on the observation of real‐time dynamics. This may be extremely beneficial in systems where uniform band filling is not easy to achieve, such as the ones not affected by the Pauli principle (e.g., bosonic atoms, phonons, and photons).
 F. Cardano, A. D'Errico, A. Dauphin, M. Maffei, B. Piccirillo, C. de
Lisio, G. De Filippis, V. Cataudella, E. Santamato, L. Marrucci, M.
Lewenstein, P. Massignan, Nature Commun. 8, 15516 (2017).