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

被引:293
作者
Cardano, Filippo [1 ]
D'Errico, Alessio [1 ]
Dauphin, Alexandre [2 ]
Maffei, Maria [1 ,2 ]
Piccirillo, Bruno [1 ]
de Lisio, Corrado [1 ,3 ]
De Filippis, Giulio [1 ,3 ]
Cataudella, Vittorio [1 ,3 ]
Santamato, Enrico [1 ,3 ]
Marrucci, Lorenzo [1 ,4 ]
Lewenstein, Maciej [2 ,5 ]
Massignan, Pietro [2 ]
机构
[1] Univ Napoli Federico II, Dipartimento Fis, Complesso Univ Monte St Angelo,Via Cintia, I-80126 Naples, Italy
[2] Barcelona Inst Sci & Technol, ICFO Inst Ciencies Foton, Ave Carl Friedrich Gauss 3, Castelldefels 08860, Spain
[3] CNR SPIN, Complesso Univ Monte St Angelo,Via Cintia, I-80126 Naples, Italy
[4] Inst Appl Sci & Intelligent Syst, CNR ISASI, Via Campi Flegrei 34, I-80078 Pozzuoli, NA, Italy
[5] ICREA, Pg Lluis Co 23, E-08010 Barcelona, Spain
关键词
QUANTIZED HALL CONDUCTANCE; EDGE STATES; GEOMETRIC PHASE; INSULATORS; BANDS; SUPERCONDUCTORS; LATTICE; ATOMS; SOUND;
D O I
10.1038/ncomms15516
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
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.
引用
收藏
页数:7
相关论文
共 53 条
[41]   Topological insulators and superconductors [J].
Qi, Xiao-Liang ;
Zhang, Shou-Cheng .
REVIEWS OF MODERN PHYSICS, 2011, 83 (04)
[42]   Photonic Floquet topological insulators [J].
Rechtsman, Mikael C. ;
Zeuner, Julia M. ;
Plotnik, Yonatan ;
Lumer, Yaakov ;
Podolsky, Daniel ;
Dreisow, Felix ;
Nolte, Stefan ;
Segev, Mordechai ;
Szameit, Alexander .
NATURE, 2013, 496 (7444) :196-200
[43]   MACROSCOPIC POLARIZATION IN CRYSTALLINE DIELECTRICS - THE GEOMETRIC PHASE APPROACH [J].
RESTA, R .
REVIEWS OF MODERN PHYSICS, 1994, 66 (03) :899-915
[44]   Topological Transition in a Non-Hermitian Quantum Walk [J].
Rudner, M. S. ;
Levitov, L. S. .
PHYSICAL REVIEW LETTERS, 2009, 102 (06)
[45]   Anomalous Edge States and the Bulk-Edge Correspondence for Periodically Driven Two-Dimensional Systems [J].
Rudner, Mark S. ;
Lindner, Netanel H. ;
Berg, Erez ;
Levin, Michael .
PHYSICAL REVIEW X, 2013, 3 (03)
[46]   Visualizing edge states with an atomic Bose gas in the quantum Hall regime [J].
Stuhl, B. K. ;
Lu, H. -I. ;
Aycock, L. M. ;
Genkina, D. ;
Spielman, I. B. .
SCIENCE, 2015, 349 (6255) :1514-1517
[47]   QUANTIZED HALL CONDUCTANCE IN A TWO-DIMENSIONAL PERIODIC POTENTIAL [J].
THOULESS, DJ ;
KOHMOTO, M ;
NIGHTINGALE, MP ;
DENNIJS, M .
PHYSICAL REVIEW LETTERS, 1982, 49 (06) :405-408
[48]   THE QUANTIZED HALL-EFFECT [J].
VONKLITZING, K .
REVIEWS OF MODERN PHYSICS, 1986, 58 (03) :519-531
[49]   Berry phase effects on electronic properties [J].
Xiao, Di ;
Chang, Ming-Che ;
Niu, Qian .
REVIEWS OF MODERN PHYSICS, 2010, 82 (03) :1959-2007
[50]   Geometric phase and band inversion in periodic acoustic systems [J].
Xiao, Meng ;
Ma, Guancong ;
Yang, Zhiyu ;
Sheng, Ping ;
Zhang, Z. Q. ;
Chan, C. T. .
NATURE PHYSICS, 2015, 11 (03) :240-244