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.

Statistical moments of quantum-walk dynamics reveal topological quantum transitions / Cardano, Filippo; Maffei, Maria; Massa, Francesco; Piccirillo, Bruno; DE LISIO, Corrado; DE FILIPPIS, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo. - In: NATURE COMMUNICATIONS. - ISSN 2041-1723. - 7:(2016), p. 11439. [10.1038/ncomms11439]

Statistical moments of quantum-walk dynamics reveal topological quantum transitions

CARDANO, FILIPPO;Maffei, Maria;PICCIRILLO, BRUNO;DE LISIO, CORRADO;DE FILIPPIS, GIULIO;CATAUDELLA, VITTORIO;SANTAMATO, ENRICO;MARRUCCI, LORENZO
2016

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.
2016
Statistical moments of quantum-walk dynamics reveal topological quantum transitions / Cardano, Filippo; Maffei, Maria; Massa, Francesco; Piccirillo, Bruno; DE LISIO, Corrado; DE FILIPPIS, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo. - In: NATURE COMMUNICATIONS. - ISSN 2041-1723. - 7:(2016), p. 11439. [10.1038/ncomms11439]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/636098
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 128
  • ???jsp.display-item.citation.isi??? 126
social impact