Statistical moments of quantum-walk dynamics reveal topological quantum transitions

被引：155

作者：

Cardano, Filippo ^{[1
]}

Maffei, Maria ^{[1
]}

Massa, Francesco ^{[1
,4
]}

Piccirillo, Bruno ^{[1
]}

de Lisio, Corrado ^{[1
,2
]}

De Filippis, Giulio ^{[1
,2
]}

Cataudella, Vittorio ^{[1
,2
]}

Santamato, Enrico ^{[1
]}

Marrucci, Lorenzo ^{[1
,3
]}

机构：

[1] Univ Naples Federico II, Dipartimento Fis, Complesso Univ Monte St Angelo,Via Cintia, I-80126 Naples, Italy

[2] CNR SPIN, Complesso Univ Monte St Angelo,Via Cintia, I-80126 Naples, Italy

[3] CNR ISASI, Via Campi Flegrei 34, I-80078 Pozzuoli, NA, Italy

[4] Univ Vienna, Fac Phys, Boltzmanngasse 5, A-1090 Vienna, Austria

来源：

NATURE COMMUNICATIONS | 2016年 / 7卷

基金：

欧盟第七框架计划;

关键词：

INVARIANTS; FERMIONS; STATES; PHASE;

D O I：

10.1038/ncomms11439

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页数：8

共 29 条

[1] Symmetries, topological phases, and bound states in the one-dimensional quantum walk [J].