Measuring a dynamical topological order parameter in quantum walks

Xu Xiao-Ye; Wang Qin-Qin; Heyl Markus; Budich Jan Carl; Pan Wei-Wei; Chen Zhe; Jan Munsif; Sun Kai; Xu Jin-Shi; Han Yong-Jian; Li Chuan-Feng; Guo Guang-Can

doi:10.1038/s41377-019-0237-8

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Measuring a dynamical topological order parameter in quantum walks

Article

- Measuring a dynamical topological order parameter in quantum walks
- Measuring a dynamical topological order parameter in quantum walks
- LSA 2020年9卷第1期页码：60-70
- Affiliations：
  
  1.CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
  2.CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
  3.Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straẞe 38, D-01187 Dresden, Germany
  4.Institute of Theoretical Physics, Technische Universität Dresden, 01062 Dresden, Germany
- Author bio：
  
  Yong-Jian Han (smhan@ustc.edu.cn)
  Chuan-Feng Li (cfli@ustc.edu.cn)
- Funds：
- DOI：10.1038/s41377-019-0237-8
  中图分类号：
- 纸质出版日期：2020，
  
  网络出版日期：2020-01-20，
  
  收稿日期：2019-06-11，
  
  修回日期：2019-12-18，
  
  录用日期：2019-12-18
- Accepted：
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Measuring a dynamical topological order parameter in quantum walks[J]. LSA, 2020,9(1):60-70.

Xu, X. Y. et al. Measuring a dynamical topological order parameter in quantum walks. Light: Science & Applications, 9, 60–70 (2020).
Measuring a dynamical topological order parameter in quantum walks[J]. LSA, 2020,9(1):60-70. DOI： 10.1038/s41377-019-0237-8.

Xu, X. Y. et al. Measuring a dynamical topological order parameter in quantum walks. Light: Science & Applications, 9, 60–70 (2020). DOI： 10.1038/s41377-019-0237-8.

摘要

Abstract

Quantum processes of inherent dynamical nature

such as quantum walks

defy a description in terms of an equilibrium statistical physics ensemble. Until now

identifying the general principles behind the underlying unitary quantum dynamics has remained a key challenge. Here

we show and experimentally observe that split-step quantum walks admit a characterization in terms of a dynamical topological order parameter (DTOP). This integer-quantized DTOP measures

at a given time

the winding of the geometric phase accumulated by the wavefunction during a quantum walk. We observe distinct dynamical regimes in our experimentally realized quantum walks

and each regime can be attributed to a qualitatively different temporal behavior of the DTOP. Upon identifying an equivalent manybody problem

we reveal an intriguing connection between the nonanalytic changes of the DTOP in quantum walks and the occurrence of dynamical quantum phase transitions.

关键词

Keywords

references

Anderson, P. W. Absence of diffusion in certain random lattices.Phys. Rev.109, 1492-1505 (1958)..

Islam, R. et al. Measuring entanglement entropy in a quantum many-body system.Nature528, 77-83 (2015)..

Kaufman, A. M. et al. Quantum thermalization through entanglement in an isolated many-body system.Science353, 794-800 (2016)..

Simon, B. Holonomy, the quantum adiabatic theorem, and berry's phase.Phys. Rev. Lett.51, 2167-2170 (1989)..

Berry, M. V. Quantal phase factors accompanying adiabatic changes.Proc. R. Soc. A Math. Phys. Eng. Sci.392, 45-57 (1984)..

Xu, J. S. et al. Simulating the exchange of Majorana zero modes with a photonic system.Nat. Commun.7, 13194 (2016)..

Eisert, J., Friesdorf, M.&Gogolin, C. Quantum many-body systems out of equilibrium.Nat. Phys.11, 124-130 (2015)..

Aharonov, Y., Davidovich, L.&Zagury, N. Quantum random walks.Phys. Rev. A48, 1687-1690 (1993)..

Childs, A. M. Universal computation by quantum walk.Phys. Rev. Lett.102, 180501 (2009)..

Childs, A. M., Gosset, D.&Webb, Z. Universal computation by multiparticle quantum walk.Science339, 791-794 (2013)..

Long, G. L. Grover algorithm with zero theoretical failure rate.Phys. Rev. A64, 022307 (2001)..

Schreiber, A. et al. A 2D quantum walk simulation of two-particle dynamics.Science336, 55-58 (2012)..

Sansoni, L. et al. Two-particle bosonic-fermionic quantum walk via integrated photonics.Phys. Rev. Lett.108, 010502 (2012)..

Poulios, K. et al. Quantum walks of correlated photon pairs in two-dimensional waveguide arrays.Phys. Rev. Lett.112, 143604 (2014)..

Preiss, P. M. et al. Strongly correlated quantum walks in optical lattices.Science347, 1229-1233 (2015)..

Chen, Z. H., Zhou, Y.&Shen, J. T. Photon antibunching and bunching in a ring-resonator waveguide quantum electrodynamics system.Opt. Lett.41, 3313-3316 (2016)..

Chen, Z. H., Zhou, Y.&Shen, J. T. Exact dissipation model for arbitrary photonic Fock state transport in waveguide QED systems.Opt. Lett.42, 887-890 (2017)..

Chen, Z. H., Zhou, Y.&Shen, J. T. Entanglement-preserving approach for reservoir-induced photonic dissipation in waveguide QED systems.Phys. Rev. A98, 053830 (2018)..

Zhou, Y. et al. Efficient two-photon excitation by photonic dimers.Opt. Lett.44, 475-478 (2019)..

Schreiber, A. et al. Decoherence and disorder in quantum walks: from ballistic spread to localization.Phys. Rev. Lett.106, 180403 (2011)..

Crespi, A. et al. Anderson localization of entangled photons in an integrated quantum walk.Nat. Photonics7, 322-328 (2013)..

Kitagawa, T. et al. Exploring topological phases with quantum walks.Phys. Rev. A82, 033429 (2010)..

Kitagawa, T. Topological phenomena in quantum walks: elementary introduction to the physics of topological phases.Quantum Inf. Process.11, 1107-1148 (2012)..

Kitagawa, T. et al. Observation of topologically protected bound states in photonic quantum walks.Nat. Commun.3, 882 (2012)..

Obuse, H.&Kawakami, N. Topological phases and delocalization of quantum walks in random environments.Phys. Rev. B84, 195139 (2011)..

Obuse, H. et al. Unveiling hidden topological phases of a one-dimensional Hadamard quantum walk.Phys. Rev. B92, 045424 (2015)..

Asbóth, J. K. Symmetries, topological phases, and bound states in the one-dimensional quantum walk.Phys. Rev. B86, 195414 (2012)..

Asbóth, J. K.&Obuse, H. Bulk-boundary correspondence for chiral symmetric quantum walks.Phys. Rev. B88, 121406 (2013)..

Asbóth, J. K., Tarasinski, B.&Delplace, P. Chiral symmetry and bulk-boundary correspondence in periodically driven one-dimensional systems.Phys. Rev. B90, 125143 (2014)..

Rakovszky, T.&Asbóth, J. K. Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk.Phys. Rev. A92, 052311 (2015)..

Cedzich, C. et al. Bulk-edge correspondence of one-dimensional quantum walks.J. Phys. A Math. Theor.49, 21LT01 (2016)..

Cardano, F. et al. Statistical moments of quantum-walk dynamics reveal topological quantum transitions.Nat. Commun.7, 11439 (2016)..

Cardano, F. et al. Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons.Nat. Commun.8, 15516 (2017)..

Xiao, L. et al. Observation of topological edge states in parity-time-symmetric quantum walks.Nat. Phys.13, 1117-1123 (2017)..

Zhan, X. et al. Detecting topological invariants in nonunitary discrete-time quantum walks.Phys. Rev. Lett.119, 130501 (2017)..

Ramasesh, V. V. et al. Direct probe of topological invariants using bloch oscillating quantum walks.Phys. Rev. Lett.118, 130501 (2017)..

Flurin, E. et al. Observing topological invariants using quantum walks in superconducting circuits.Phys. Rev. X7, 031023 (2017)..

Xu, X. Y. et al. Measuring the winding number in a large-scale chiral quantum walk.Phys. Rev. Lett.120, 260501 (2018)..

Zeuner, J. M. et al. Observation of a topological transition in the bulk of a non-hermitian system.Phys. Rev. Lett.115, 040402 (2015)..

Wang, Y. et al. Direct observation of topology from single-photon dynamics.Phys. Rev. Lett.122, 193903 (2019)..

Pancharatnam, S. Generalized theory of interference, and its applications.Proc. Indian Acad. Sci. A44, 247-262 (1956)..

Samuel, J.&Bhandari, R. General setting for berry's phase.Phys. Rev. Lett.60, 2339-2342 (1988)..

Wang, Q. Q. et al. Dynamic-disorder-induced enhancement of entanglement in photonic quantum walks.Optica5, 1136-1140 (2018)..

Manouchehri, K.&Wang, J. B.Physical Implementation of Quantum Walks(Springer, Berlin, 2014).

Su, W. P. et al. Solitons in polyacetylene.Phys. Rev. Lett.42, 1698-1701 (1979)..

Hasan, M. Z.&Kane, C. L.Colloquium: topological insulators.Rev. Mod. Phys.82, 3045-3067 (2010)..

Budich, J. C.&Heyl, M. Dynamical topological order parameters far from equilibrium.Phys. Rev. B93, 085416 (2016)..

Heyl, M., Polkovnikov, A.&Kehrein, S. Dynamical quantum phase transitions in the transverse-Field Ising model.Phys. Rev. Lett.110, 135704 (2013)..

Heyl, M. Dynamical quantum phase transitions: a review.Rep. Prog. Phys.81, 054001 (2018)..

Jurcevic, P. et al. Direct observation of dynamical quantum phase transitions in an interacting many-body system.Phys. Rev. Lett.119, 080501 (2017)..

Zhang, J. et al. Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator.Nature551, 601-604 (2017)..

Bernien, H. et al. Probing many-body dynamics on a 51-atom quantum simulator.Nature551, 579-584 (2017)..

Fläschner, N. et al. Observation of dynamical vortices after quenches in a system with topology.Nat. Phys.14, 265-268 (2018)..

Guo, X. Y. et al. Observation of a dynamical quantum phase transition by a superconducting qubit simulation.Phys. Rev. Appl.11, 044080 (2019)..

Wang, K. K. et al. Simulating dynamic quantum phase transitions in photonic quantum walks.Phys. Rev. Lett.122, 020501 (2019)..

Smale, S. et al. Observation of a transition between dynamical phases in a quantum degenerate Fermi gas.Sci. Adv.5, eaat1568 (2019)..

Tian, T. et al. Observation of dynamical phase transitions in a topological nanomechanical system.Phys. Rev. B100, 024310 (2019)..

Vajna, S.&Dóra, B. Topological classification of dynamical phase transitions.Phys. Rev. B91, 155127 (2015)..

Mendl, C. B.&Budich, J. C. Stability of dynamical quantum phase transitions in quenched topological insulators: from multi-band to disordered systems.Phys. Rev. B100, 224307 (2019)..

Kitaev, A. Y. Fault-tolerant quantum computation by anyons.Ann. Phys.303, 2-30 (2003)..

Suzuki, S., Inoue, J. I.&Chakrabarti, B. K.Quantum Ising Phases and Transitions in Transverse Ising Models.2nd edn (Springer, Berlin, 2013).

Tang, H. et al. Experimental two-dimensional quantum walk on a photonic chip.Sci. Adv.4, eaat3174 (2018)..

Kwiat, P. G.&Chiao, R. Y. Observation of a nonclassical Berry's phase for the photon.Phys. Rev. Lett.66, 588-591 (1991)..

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