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Statistical moments of quantum-walk dynamics reveal topological quantum transitions

Author

Listed:
  • 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
    Present address: Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna 1090, Austria.)

  • 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
    CNR-SPIN, Complesso Universitario di Monte Sant'Angelo, Via Cintia)

  • Giulio De Filippis

    (Università di Napoli Federico II, Complesso Universitario di Monte Sant’Angelo
    CNR-SPIN, Complesso Universitario di Monte Sant'Angelo, Via Cintia)

  • Vittorio Cataudella

    (Università di Napoli Federico II, Complesso Universitario di Monte Sant’Angelo
    CNR-SPIN, Complesso Universitario di Monte Sant'Angelo, Via Cintia)

  • 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
    CNR-ISASI)

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.

Suggested Citation

  • Filippo Cardano & Maria Maffei & Francesco Massa & Bruno Piccirillo & Corrado de Lisio & Giulio De Filippis & Vittorio Cataudella & Enrico Santamato & Lorenzo Marrucci, 2016. "Statistical moments of quantum-walk dynamics reveal topological quantum transitions," Nature Communications, Nature, vol. 7(1), pages 1-8, September.
    • Handle: RePEc:nat:natcom:v:7:y:2016:i:1:d:10.1038_ncomms11439
    DOI: 10.1038/ncomms11439
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    Cited by:

    1. Mu Yang & Hao-Qing Zhang & Yu-Wei Liao & Zheng-Hao Liu & Zheng-Wei Zhou & Xing-Xiang Zhou & Jin-Shi Xu & Yong-Jian Han & Chuan-Feng Li & Guang-Can Guo, 2022. "Topological band structure via twisted photons in a degenerate cavity," Nature Communications, Nature, vol. 13(1), pages 1-7, December.

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