Detecting topological invariants and revealing topological phase transition
Update: 2019-10-22 09:08:22      Author: yangjuan@csrc.ac.cn

Topological phases exhibit remarkable properties, and have stimulated extensive research interest in modern physics [1,2]. In contrast to conventional phases of matter which are characterized by symmetry properties and local order parameters, topological phases are typically parametrized by integer-valued topological invariants. While many experiments [3,4] are concerned with the detection and characterization of topological edge states, recent progress has led to the direct measurement of topological invariants in the bulk of synthetic topological systems. On the other hand, topological matter exhibits exotic properties yet phases characterized by large topological invariants are difficult to implement, despite rapid experimental progress. A promising route toward topological invariants (even large topological invariants) is via engineered Floquet systems, particularly in photonics, where flexible control holds the potential of extending the study of conventional topological matter to novel regimes.

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Fig. 1: Left: An experimental setup for three-step non-unitary quantum walk up to four time steps. Right: (a) Phase diagram for three-step non-unitary quantum walks characterized by the topological invariants as functions of the coin parameters. (b) Measured average displacements of three-step non-unitary quantum walk corresponding to U3 with different loss parameters.

 

A recent investigation [5] involving Xiaoping Wang, Lei Xiao, Kunkun Wang and Peng Xue from CSRC, Xingze Qiu and Wei Yi from University of Science and Technology of China, experimentally investigate topological phenomena in one-dimensional discrete-time photonic quantum walks using a combination of methods. They first detect winding numbers of the quantum walk by directly measuring the average chiral displacement, which oscillates around quantized winding numbers for finite-step quantum walks. Topological phase transitions can be identified as changes in the center of oscillation of the measured chiral displacement. The position of topological phase transition is then confirmed by measuring the moments of the walker probability distribution. Finally, they observe localized edge states at the boundary of regions with different winding numbers. They also confirm the robustness of edge states against chiral-symmetry-preserving disorder.

Topological matter exhibits exotic properties yet phases characterized by large topological invariants are difficult to implement, despite rapid experimental progress. A promising route toward higher topological invariants is via engineered Floquet systems, particularly in photonics, where flexible control holds the potential of extending the study of conventional topological matter to novel regimes. Here, Lei Xiao, Kunkun Wang, Zhihao Bian, Xiang Zhan and Peng Xue from CSRC, Xingze Qiu and Wei Yi from University of Science and Technology of China, Hideaki Obuse from Hokkaido University, and Barry C. Sanders from University of Calgary, implement a one-dimensional photonic quantum walk to explore large winding numbers [6]. By introducing partial measurements and hence loss into the system, they detect winding numbers of three and four in multistep non-unitary quantum walks, which agree well with theoretical predictions. Moreover, by probing statistical moments of the walker, they identify locations of topological phase transitions in the system and reveal the breaking of pseudo-unitary near topological phase boundaries. As the winding numbers are associated with non-unitary time evolution, their investigation enriches understanding of topological phenomena in non-unitary settings and create further opportunities in engineering unconventional topological phenomena using photonics.

References:

[1]      M. Z. Hasan and C. L. Kane, Colloquium: topological insulators, Rev. Mod. Phys. 82, 3045 (2010).

[2]      X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011).

[3]      L. Xiao, X. Zhan, Z. H. Bian, K. K.Wang, X. Zhang, X. P. Wang, J. Li, K. Mochizuki, D. Kim, N. Kawakami, W. Yi, H. Obuse, B. C. Sanders, and P. Xue, Observation of topological edge states in parity–time-symmetric quantum walks, Nature Physics 13, 1117–1123 (2017).

[4]      X. Zhan, L. Xiao, Z. H. Bian, K. K. Wang, X. Z. Qiu, B. C. Sanders, W. Yi, and P. Xue, Detecting topological invariants in nonunitary discrete-time quantum walks, Phys. Rev. Lett. 119, 130501 (2017).

[5]      X. P. Wang, L. Xiao, X. Qiu, K. K. Wang, W. Yi, and P. Xue, Detecting topological invariants and revealing topological phase transitions in discrete-time photonic quantum walks, Phys. Rev. A 98, 013835 (2018).

      [6]      L. Xiao, X. Qiu, K. K. Wang, Z. H. Bian, X. Zhan, H. Obuse, B. C. Sanders, W. Yi, and P. Xue, Higher winding number in a nonunitary photonic quantum walk, Phys. Rev. A 98, 063847 (2018).


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