Article

Observation of topologically protected bound states in photonic quantum walks

  • Nature Communications 3, Article number: 882 (2012)
  • doi:10.1038/ncomms1872
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Abstract

Topological phases exhibit some of the most striking phenomena in modern physics. Much of the rich behaviour of quantum Hall systems, topological insulators, and topological superconductors can be traced to the existence of robust bound states at interfaces between different topological phases. This robustness has applications in metrology and holds promise for future uses in quantum computing. Engineered quantum systems—notably in photonics, where wavefunctions can be observed directly—provide versatile platforms for creating and probing a variety of topological phases. Here we use photonic quantum walks to observe bound states between systems with different bulk topological properties and demonstrate their robustness to perturbations—a signature of topological protection. Although such bound states are usually discussed for static (time-independent) systems, here we demonstrate their existence in an explicitly time-dependent situation. Moreover, we discover a new phenomenon: a topologically protected pair of bound states unique to periodically driven systems.

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References

  1. 1.

    Zur Theorie der Phasenumwandlungen. Phys. Z. Sowjetunion 11, 26–27 (1937).

  2. 2.

    et al. Experimental realization of a three-dimensional topological insulator, Bi2Te3. Science 325, 178–181 (2009).

  3. 3.

    et al. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nat. Phys. 5, 398–402 (2009).

  4. 4.

    , , , & Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008).

  5. 5.

    & Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).

  6. 6.

    , , , & Non-Abelian statistics and topological quantum information processing in ID wire networks. Nat. Phys. 7, 412–417 (2011).

  7. 7.

    et al. Observation of topological order in a superconducting doped topological insulator. Nat. Phys. 6, 855–859 (2010).

  8. 8.

    & Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

  9. 9.

    & Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).

  10. 10.

    & Solitons with fermion number. Phys. Rev. D. 13, 3398–3409 (1976).

  11. 11.

    , , & Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775 (2009).

  12. 12.

    , & Fractional quantum hall states of atoms in optical lattices. Phys. Rev. Lett. 94, 086803 (2005).

  13. 13.

    , , , & Spin Hall effects for cold atoms in a light-induced gauge potential. Phys. Rev. Lett. 97, 240401 (2006).

  14. 14.

    & Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms. New J. Phys. 5, 56 (2003).

  15. 15.

    , , , & Cold atoms in non-Abelian gauge potentials: from the Hofstadter 'moth' to lattice gauge theory. Phys. Rev. Lett. 95, 010403 (2005).

  16. 16.

    , & Quantum random walks. Phys. Rev. A 48, 1687 (1993).

  17. 17.

    , , & Topological characterization of periodically driven quantum systems. Phys. Rev. B. 82, 235114 (2010).

  18. 18.

    et al. Majorana fermions in equilibrium and in driven cold-atom quantum wires. Phys. Rev. Lett. 106, 220402 (2011).

  19. 19.

    , & Floquet topological insulator in semiconductor quantum wells. Nat. Phys. 7, 490–495 (2011).

  20. 20.

    et al. Quantum walk in position space with single optically trapped atoms. Science 325, 174–177 (2009).

  21. 21.

    et al. Realization of a quantum walk with one and two trapped ions. Phys. Rev. Lett. 104, 100503 (2010).

  22. 22.

    et al. Quantum walk of a trapped ion in phase space. Phys. Rev. Lett. 103, 090504 (2009).

  23. 23.

    et al. Photons walking the line: A quantum walk with adjustable coin operations. Phys. Rev. Lett. 104, 050502 (2010).

  24. 24.

    et al. Discrete single-photon quantum walks with tunable decoherence. Phys. Rev. Lett. 104, 153602 (2010).

  25. 25.

    , , & Exploring topological phases with quantum walks. Phys. Rev. A. 82, 033429 (2010).

  26. 26.

    & Topological origin of zero-energy edge states in particle-hole symmetric systems. Phys. Rev. Lett. 89, 077002 (2002).

  27. 27.

    , & Solitons in polyacetylene. Phys. Rev. Lett. 42, 1698–1701 (1979).

  28. 28.

    , & Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin. Phys. Rev. Lett. 106, 080502 (2011).

  29. 29.

    , , & Topological insulators and superconductors: tenfold way and dimensional hierarchy. New J. Phys. 12, 065010 (2010).

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Acknowledgements

We thank B.P. Lanyon, B.J. Powell and T.C. Stace for discussions. We acknowledge financial support from the ARC Centres of Excellence for Engineered Quantum Systems (Project number CE110001013) and Quantum Computation and Communication Technology (Project number CE110001027), Discovery and Federation Fellow programs and an IARPA-funded US Army Research Office contract. T.K., M.S.R., E.B. and E.D. thank DARPA OLE program, CUA, NSF under DMR-07-05472, AFOSR Quantum Simulation MURI, and the ARO-MURI on Atomtronics. T.K. thanks the Kodama foundation. I.K. and A.A.-G. thank the Dreyfus and Sloan Foundations, ARO under W911-NF-07-0304 and DARPA's Young Faculty Award N66001-09-1-2101-DOD35CAP. A.A.-G. acknowledges funding from the National Science Foundation under award number CHE-1037992.

Author information

Author notes

    • Takuya Kitagawa
    •  & Matthew A. Broome

    These authors contributed equally to this work.

Affiliations

  1. Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.

    • Takuya Kitagawa
    • , Mark S. Rudner
    • , Erez Berg
    •  & Eugene Demler
  2. ARC Centre for Engineered Quantum Systems and ARC Centre for Quantum Computation and Communication Technology, School of Mathematics and Physics, University of Queensland, Brisbane 4072, Australia.

    • Matthew A. Broome
    • , Alessandro Fedrizzi
    • , Ivan Kassal
    •  & Andrew G. White
  3. Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA.

    • Ivan Kassal
    •  & Alán Aspuru-Guzik

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Contributions

M.A.B. and A.F. designed and performed experiments, collected and analyzed data, and wrote the paper. T.K., M.S.R., and E.B. developed the concepts, conceived the design of experiments, provided theoretical tools, analyzed the data and wrote the paper. I.K. provided theoretical support and wrote the paper. E.D., A.A.G, and A.G.W. supervised the project and edited the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Takuya Kitagawa or Matthew A. Broome.

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