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Abstract:

We present a research article which formulates the milestones for the understanding and characterization of holonomy and topology of a discrete-time quantum walk architecture, consisting of a unitary step given by a sequence of two non-commuting rotations in parameter space. Unlike other similar systems recently studied in detail in the literature, this system does not present continous 1D topological boundaries, it only presents a discrete number of Dirac points where the quasi-energy gap closes. At these discrete points, the topological winding number is not defined. Therefore, such discrete points represent topological boundaries of dimension zero, and they endow the system with a non-trivial topology. We illustrate the non-trivial character of the system by calculating the Zak phase. We discuss the prospects of this system, we propose a suitable experimental scheme to implement these ideas, and we present preliminary experimental data. © 2017 by the authors. Licensee MDPI, Basel, Switzerland.

Registro:

Documento: Artículo
Título:Topology and holonomy in discrete-time quantum walks
Autor:Puentes, G.
Filiación:Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Pabellon 1, Ciudad Universitaria, Buenos Aires, 1428, Argentina
3rd Institute of Physics, Research Center Scope and MPI for Solid State Research, University of Stuttgart, Stuttgart, 70569, Germany
Palabras clave:Holonomy; Quantum walks; Topology; Zak phase
Año:2017
Volumen:7
Número:5
DOI: http://dx.doi.org/10.3390/cryst7050122
Título revista:Crystals
Título revista abreviado:Crystals
ISSN:20734352
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_20734352_v7_n5_p_Puentes

Referencias:

  • Berry, M.V., Classical adiabatic angles and quantal adiabatic phase (1985) J. Phys. A, 18, p. 15
  • Hannay, J., Angle variable holonomy in adiabatic excursion of an integrable Hamiltonian (1985) J. Phys. A, 18, p. 221
  • Zhang, Y., Tan, Y.-W., Stormer, H.L., Kim, P., Experimental observation of the quantum Hall effect and Berry’s phase in graphene (2005) Nature, 438, pp. 201-204
  • Delplace, P., Ullmo, D., Montambaux, G., Zak phase and the existence of edge states in graphene (2011) Phys. Rev. B, 84
  • Kane, C.L., Mele, E.J., Z 2 topological order and the quantum spin Hall effect (2005) Phys. Rev. Lett, 95
  • Delacretaz, G., Grant, E.R., Whetten, R.L., Wöste, L., Zwanziger, J.W., Fractional quantization of molecular pseudorotation in Na 3 (1986) Phys. Rev. Lett, 1986, p. 95
  • Nadj-Perge, S., Drozdov, I.K., Li, J., Chen, H., Jeon, S., Seo, J., Macdonald, A.H., Yazdani, A., Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor (2014) Science, 346, pp. 602-607
  • Simon, B., Holonomy, the quantum adiabatic theorem, and Berry’s phase (1983) Phys. Rev. Lett, 51
  • Kitagawa, T., Broome, M.A., Fedrizzi, A., Rudner, M.S., Berg, E., Kassal, I., Aspuru-Guzik, A., White, A.G., Observation of topologically protected bound states in photonic quantum walks (2012) Nat. Commun, 3, p. 882
  • Kitagawa, T., Rudner, M.S., Berg, E., Demler, E., Exploring topological phases with quantum walks (2010) Phys. Rev. A, 32
  • Provost, J., Vallee, G., Riemannian structure on manifolds of quantum states (1980) Comm. Math. Phys, 86, pp. 289-301
  • Bouchiat, C., Gibbons, G., Non-integrable quantum phase in the evolution of a spin-1 system: A physical consequence of the non-trivial topology of the quantum state-space (1988) J. Phys. France, 49, pp. 187-199
  • Page, D., Geometrical description of Berry’s phase (1987) Phys. Rev. A, 36, p. 3479
  • Berry, M.V., (1989) Geometric Phases in Physics, , Shapere, A., Wilczek, F., Eds., World Scientific: Singapore
  • Nakahara, M., (1990) Geometry, Topology and Physics, , CRC Press: Boca Raton, FL, USA
  • Aharonov, Y., Davidovich, L., Zagury, N., Quantum random walks (1993) Phys. Rev. A, 48, p. 1687
  • Crespi, A., Osellame, R., Ramponi, R., Giovannetti, V., Fazio, R., Sansoni, L., De Nicola, F., Mataloni, P., Anderson localization of entangled photons in an integrated quantum walk (2013) Nat. Photon, 7, pp. 322-328
  • Genske, M., Alt, W., Steffen, A., Werner, A.H., Werner, R.F., Meschede, D., Alberti, A., Electric quantum walks with individual atoms (2013) Phys. Rev. Lett, 110
  • Obuse, H., Kawakami, N., Topological phases and delocalization of quantum walks in random environments (2011) Phys. Rev. B, 84
  • Shikano, Y., Chisaki, K., Segawa, E., Konno, N., Emergence of randomness and arrow of time in quantum walks (2010) Phys. Rev. A, 81
  • Asbóth, J.K., Symmetries, topological phases, and bound states in the one-dimensional quantum walk (2012) Phys. Rev. B, 86
  • Obuse, H., Asboth, J.K., Nishimura, Y., Kawakami, N., Unveiling hidden topological phases of a one-dimensional Hadamard quantum walk (2015) Phys. Rev. B, 92
  • Cedzich, C., Grunbaum, F., Stahl, C., Velázquez, L., Werner, A., Werner, R., Bulk-edge correspondence of one-dimensional quantum walks (2016) J. Phys. A Math. Theor, 49
  • Wojcik, A., Luczak, T., Kurzynski, P., Grudka, A., Gdala, T., Bednarska-Bzdega, M., Trapping a particle of a quantum walk on the line (2012) Phys. Rev. A, 85
  • Moulieras, S., Lewenstein, M., Puentes, G., Entanglement engineering and topological protection in discrete-time quantum walks (2013) J. Phys. B, 46
  • Beenakker, C., Kouwenhoven, L.A., Road to reality with topological superconductors (2016) Nat. Phys, 12, pp. 618-621
  • Huber, S.D., Topological mechanics (2016) Nat. Phys, 12, pp. 621-623
  • Peano, V., Brendel, C., Schmidt, M., Marquardt, F., Topological Phases of Sound and Light, , Phys. Rev. X 2015, 5, 031011
  • Lu, L., Joannopoulos, J., Solijacic, M., Topological states in photonic systems (2016) Nat. Phys, 12, pp. 626-629
  • Xiao, M., Ma, G., Yang, Z., Sheng, P., Zhang, Z.Q., Chan, C.T., Geometric phase and band inversion in periodic acoustic systems (2015) Nat. Phys, 11, pp. 240-244
  • Bose, S., Quantum communication through an unmodulated spin chain (2003) Phys. Rev. Lett, 91
  • Christandl, M., Datta, N., Ekert, A., Landahl, A.J., Perfect state transfer in quantum spin networks (2004) Phys. Rev. Lett, 92
  • Plenio, M.B., Huelga, S.F., Dephasing-assisted transport: Quantum networks and biomolecules (2008) New J. Phys, 10
  • Spring, J., Boson sampling on a photonic chip (2013) Science, 339, pp. 798-801
  • Broome, M.A., Fedrizzi, A., Rahimi-Keshari, S., Dove, J., Aaronson, S., Ralph, T.C., White, A.G., Photonic boson sampling in a tunable circuit (2013) Science, 339, pp. 794-798
  • Tillmann, M., Dakic, B., Heilmann, R., Nolte, S., Szameit, A., Walther, P., Experimental boson sampling (2013) Nat. Photon, 7, pp. 540-544
  • Crespi, A., Integrated multimode interferometers with arbitrary designs for photonic boson sampling (2013) Nat. Photon, 7, pp. 545-549
  • Spagnolo, N., Efficient experimental validation of photonic boson sampling against the uniform distribution (2014) Nat. Photon, 8, pp. 615-620
  • Carolan, J., On the experimental verification of quantum complexity in linear optics. Nat (2014) Photon, 8, pp. 621-626
  • Childs, A.M., Universal computation by quantum walk (2009) Phys. Rev. Lett, 102
  • Aiello, A., Puentes, G., Voigt, D., Woerdman, J.P., Maximally entangled mixed-state generation via local operations (2007) Phys. Rev. A, 75
  • Puentes, G., Voigt, D., Aiello, A., Woerdman, J.P., Universality in depolarized light scattering (2006) Opt. Lett, 30, pp. 3216-3218
  • Peruzzo, A., Quantum walks of correlated photons (2010) Science, 329, pp. 1500-1503
  • Poulios, K., Quantum walks of correlated photon pairs in two-dimensional waveguide arrays (2014) Phys. Rev. Lett, 332
  • Schreiber, A., Gabris, A., Rohde, P.P., Laiho, K., Stefanak, M., Potocek, V., Hamilton, C., Silberhorn, C., A 2D quantum walk simulation of two-particle dynamics (2012) Science, 336, pp. 55-58
  • Nielsen, M., Chuang, I., (2000) Quantum Computation and Quantum Information, , Cambridge University Press: Cambridge, UK
  • Schreiber, A., Cassemiro, K.N., Potocek, V., Gábris, A., Mosley, P.J., Ersson, E., Jex, I., Silberhorn, C., Photons walking the line: A quantum walk with adjustable coin operations (2010) Phys. Rev. Lett, 104
  • Schreiber, A., Cassemiro, K.N., Potocek, V., Gabris, A., Jex, I., Silberhorn, C., Decoherence and disorder in quantum walks: From ballistic spread to localization (2011) Phys. Rev. Lett, 106
  • Broome, M.A., Fedrizzi, A., Lanyon, B.P., Kassal, I., Aspuru-Guzik, A., White, A.G., Discrete single-photon quantum walks with tunable decoherence (2010) Phys. Rev. Lett, 104
  • Zahringer, F., Kirchmair, G., Gerritsma, R., Solano, E., Blatt, R., Roos, C.F., Realization of a quantum walk with one and two trapped ions (2010) Phys. Rev. Lett, 104
  • Longhi, S., Zak phase of photons in optical waveguide lattices (2013) Opt. Lett, 38, pp. 3716-3719
  • Fruchart, M., Unveiling hidden topological phases of a one-dimensional Hadamard quantum walk (2015) Phys. Rev. B, 92
  • Rudner, M.S., Lindner, N.H., Berg, E., Levin, M., Anomalous edge states and the bulk-edge correspondence for periodically driven two-dimensional systems (2013) Phys. Rev. X, 3
  • Atala, M., Aidelsburger, M., Barreiro, J., Abanin, D., Kitagawa, T., Demler, E.I., Direct measurement of the Zak phase in topological Bloch bands (2013) Nat. Phys, 9, pp. 795-800
  • Loredo, J.C., Broome, M.A., Smith, D.H., White, A.G., Observation of entanglement-dependent two-particle holonomic phase (2014) Phys. Rev. Lett, 112
  • Brun, T.A., Carteret, H.A., Ambainis, A., Quantum to classical transition for random walks (2003) Phys. Rev. Lett, 91

Citas:

---------- APA ----------
(2017) . Topology and holonomy in discrete-time quantum walks. Crystals, 7(5).
http://dx.doi.org/10.3390/cryst7050122
---------- CHICAGO ----------
Puentes, G. "Topology and holonomy in discrete-time quantum walks" . Crystals 7, no. 5 (2017).
http://dx.doi.org/10.3390/cryst7050122
---------- MLA ----------
Puentes, G. "Topology and holonomy in discrete-time quantum walks" . Crystals, vol. 7, no. 5, 2017.
http://dx.doi.org/10.3390/cryst7050122
---------- VANCOUVER ----------
Puentes, G. Topology and holonomy in discrete-time quantum walks. Crystals. 2017;7(5).
http://dx.doi.org/10.3390/cryst7050122