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Statistical theory of designed quantum transport across disordered networks

Mattia Walschaers1,2,*, Roberto Mulet1,3,†, Thomas Wellens1,‡, and Andreas Buchleitner1,4,§

  • 1Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany
  • 2Instituut voor Theoretische Fysica, University of Leuven, Celestijnenlaan 200D, B-3001 Heverlee, Belgium
  • 3Complex Systems Group, Department of Theoretical Physics, University of Havana, Cuba
  • 4Freiburg Institute for Advanced Studies, Albert-Ludwigs-Universität Freiburg, Albertstr. 19, D-79104 Freiburg, Germany

  • *mattia@itf.fys.kuleuven.be
  • †roberto.mulet@gmail.com
  • ‡thomas.wellens@physik.uni-freiburg.de
  • §a.buchleitner@physik.uni-freiburg.de
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Phys. Rev. E 91, 042137 – Published 28 April, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.042137

Abstract

We explain how centrosymmetry, together with a dominant doublet of energy eigenstates in the local density of states, can guarantee interference-assisted, strongly enhanced, strictly coherent quantum excitation transport between two predefined sites of a random network of two-level systems. Starting from a generalization of the chaos-assisted tunnelling mechanism, we formulate a random matrix theoretical framework for the analytical prediction of the transfer time distribution, of lower bounds of the transfer efficiency, and of the scaling behavior of characteristic statistical properties with the size of the network. We show that these analytical predictions compare well to numerical simulations, using Hamiltonians sampled from the Gaussian orthogonal ensemble.

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References (70)

  1. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, Philadelphia, 1988).
  2. F. Dubin, R. Melet, T. Barisien, R. Grousson, L. Legrand, M. Schott, and V. Voliotis, Nat. Phys. 2, 32 (2006).
  3. Y. Imry, Introduction to Mesoscopic Physics (Oxford University Press, New York, 1997).
  4. T. Kottos and U. Smilansky, Ann. Phys. 274, 76 (1999).
  5. J. Madroñero, A. Ponomarev, A. R. Carvalho, S. Wimberger, C. Viviescas, A. Kolovsky, K. Hornberger, P. Schlagheck, A. Krug, A. Buchleitner, G. Rempe, and M. O. Scully, Adv. At. Mol. Opt. Phys. 53, 33 (2006).
  6. B. Hein and G. Tanner, Phys. Rev. Lett. 103, 260501 (2009).
  7. M. Christandl, N. Datta, A. Ekert, and A. J. Landahl, Phys. Rev. Lett. 92, 187902 (2004).
  8. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Nature (London) 390, 671 (1997).
  9. G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, C. Miniatura, and R. Kaiser, Phys. Rev. Lett. 83, 5266 (1999).
  10. T. Wellens, Appl. Phys. B 95, 189 (2009).
  11. M. Hartung, T. Wellens, C. A. Müller, K. Richter, and P. Schlagheck, Phys. Rev. Lett. 101, 020603 (2008).
  12. F. Jörder, K. Zimmermann, A. Rodriguez, and A. Buchleitner, Phys. Rev. Lett. 113, 063004 (2014).
  13. G. Modugno, Rep. Prog. Phys. 73, 102401 (2010).
  14. S. Wimberger, I. Guarneri, and S. Fishman, Nonlinearity 16, 1381 (2003).
  15. E. Collini and G. D. Scholes, J. Phys. Chem. A 113, 4223 (2009).
  16. G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Mancal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, Nature (London) 446, 782 (2007).
  17. T. Mančal, N. Christensson, V. Lukeš, F. Milota, O. Bixner, H. F. Kauffmann, and J. Hauer, J. Phys. Chem. Lett. 3, 1497 (2012).
  18. M. Walschaers, J. Fernandez-de-Cossio Diaz, R. Mulet, and A. Buchleitner, Phys. Rev. Lett. 111, 180601 (2013).
  19. T. Ritz, R. Wiltschko, P. Hore, C. Rodgers, K. Stapput, P. Thalau, C. Timmel, and W. Wiltschko, Biophys. J. 96, 3451 (2009).
  20. G. Scholes, T. Mirkovic, D. Turner, F. Fassioli, and A. Buchleitner, Energy Environ. Sci. 5, 9374 (2012).
  21. M. Hercher, Appl. Opt. 7, 951 (1968).
  22. E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).
  23. P. W. Anderson, Phys. Rev. 109, 1492 (1958).
  24. T. Scholak, F. Mintert, T. Wellens, and A. Buchleitner, Semicond. Semimet. 83, 1 (2010).
  25. T. P. J. Krüger, C. Ilioaia, M. P. Johnson, E. Belgio, P. Horton, A. V. Ruban, and R. van Grondelle, Biophys. J. 105, 1018 (2013).
  26. R. Hildner, D. Brinks, J. B. Nieder, R. J. Cogdell, and N. F. van Hulst, Science 340, 1448 (2013).
  27. S. Mostarda, F. Levi, D. Prada-Gracia, F. Mintert, and F. Rao, Nat. Commun. 4, 2296 (2013).
  28. M. B. Plenio and S. F. Huelga, New J. Phys. 10, 113019 (2008).
  29. M. Mohseni, P. Rebentrost, S. Lloyd, and A. Aspuru-Guzik, J. Phys. Chem. Lett. 129, 174106 (2008).
  30. J. Moix, J. Wu, P. Huo, D. Coker, and J. Cao, J. Phys. Chem. Lett. 2, 3045 (2011).
  31. T. Scholak, F. de Melo, T. Wellens, F. Mintert, and A. Buchleitner, Phys. Rev. E 83, 021912 (2011).
  32. T. Zech, R. Mulet, T. Wellens, and A. Buchleitner, New J. Phys. 16, 055002 (2014).
  33. M. L. Mehta, Random Matrices (Elsevier/Academic Press, Amsterdam, 2004).
  34. T. Scholak, T. Wellens, and A. Buchleitner, Phys. Rev. A 90, 063415 (2014).
  35. A. Broadbent and E. Kashefi, Theo. Comp. Sci. 410, 2489 (2009).
  36. A. M. Childs, Phys. Rev. Lett. 102, 180501 (2009).
  37. C. S. Hamilton, R. Kruse, L. Sansoni, C. Silberhorn, and I. Jex, Phys. Rev. Lett. 113, 083602 (2014).
  38. The requirement that the initial and final states, |in〉 and |out〉, be localized on individual sites, is, however, not a strictly necessary ingredient for our subsequent conclusions.
  39. A. Cantoni and P. Butler, Lin. Algebra Appl. 13, 275 (1976).
  40. T. Zech, M. Walschaers, T. Scholak, R. Mulet, T. Wellens, and A. Buchleitner, Fluct. Nois. Lett. 12, 1340007 (2013).
  41. O. Bohigas, in Chaos and Quantum Physics, edited by M.-J. Giannoni, A. Voros, and J. Zinn-Justin, Les Houches Lectures, Vol. Session LII (North-Holland, Amsterdam, 1989).
  42. Note that we here employ a reference time which is 10 times larger than in Refs. [24, 31]. However, this does not alter the qualitative result; also see Ref. [46].
  43. E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge Univ. Press, Cambridge, 2007).
  44. F. Haake, Quantum Signatures of Chaos (Springer-Verslag, Berlin Heidelberg, 2010).
  45. F. Haake and K. Życzkowski, Phys. Rev. A 42, 1013 (1990).
  46. T. Scholak, T. Wellens, and A. Buchleitner, J. of Phys. B: At. Mol. Opt. Phys. 44, 184012 (2011).
  47. S. Tomsovic and D. Ullmo, Phys. Rev. E 50, 145 (1994).
  48. A. Buchleitner, I. Guarneri, and J. Zakrzewski, Europhys. Lett. 44, 162 (1998).
  49. P. Schlagheck and A. Buchleitner, Eur. Phys. J. D 22, 401 (2003).
  50. S. Wimberger and A. Buchleitner, J. Phys. A: Math. Gen. 34, 7181 (2001).
  51. J. Zakrzewski, D. Delande, and A. Buchleitner, Phys. Rev. E 57, 1458 (1998).
  52. J. Madroñero and A. Buchleitner, Phys. Rev. Lett. 95, 263601 (2005).
  53. J. Madroñero, P. Schlagheck, L. Hilico, B. Grémaud, D. Delande, and A. Buchleitner, Europhys. Lett. 70, 183 (2005).
  54. S. M. Falke, C. A. Rozzi, D. Brida, M. Maiuri, M. Amato, E. Sommer, A. De Sio, A. Rubio, G. Cerullo, E. Molinari, and C. Lienau, Science 344, 1001 (2014).
  55. F. Leyvraz and D. Ullmo, J. Phys. A: Math. Gen. 29, 2529 (1996).
  56. G. López, P. A. Mello, and T. H. Seligman, Z. Phys. A 302, 351 (1981).
  57. G. Ergün and Y. V. Fyodorov, Phys. Rev. E 68, 046124 (2003).
  58. E. F. Fama and R. Roll, J. Am. Stat. Assoc. 63, 817 (1968).
  59. H. S. Seung, H. Sompolinsky, and N. Tishby, Phys. Rev. A 45, 6056 (1992).
  60. L. de Haan and A. Ferreira, Extreme Value Theory: An Introduction, Springer Series in Operations Research and Financial Engineering (Springer, New York, 2007).
  61. F. C. Leone, L. S. Nelson, and R. B. Nottingham, Technometrics 3, 543 (1961).
  62. M. Abramowitz and I. Stegan, Handbook of Mathematical Functions (Dover Publications, New York, 1965).
  63. P. S. Laplace, Stat. Sci. 1, 364 (1986).
  64. S. Mostarda, F. Levi, D. Prada-Gracia, F. Mintert, and F. Rao, arXiv:1312.1833.
  65. O. Brodier, P. Schlagheck, and D. Ullmo, Phys. Rev. Lett. 87, 064101 (2001).
  66. O. Brodier, P. Schlagheck, and D. Ullmo, Ann. Phys. 300, 88 (2002).
  67. E. Farhi and S. Gutmann, Phys. Rev. A 58, 915 (1998).
  68. J. Roland and N. J. Cerf, Phys. Rev. A 71, 032330 (2005).
  69. P. I. Bunyk, E. M. Hoskinson, M. W. Johnson, E. Tolkacheva, F. Altomare, A. J. Berkley, R. Harris, J. P. Hilton, T. Lanting, A. J. Przybysz, and J. Whittaker, IEEE Trans. Appl. Superconductivity 24, 1700110 (2014).
  70. T. Lanting, A. J. Przybysz, A. Y. Smirnov, F. M. Spedalieri, M. H. Amin, A. J. Berkley, R. Harris, F. Altomare, S. Boixo, P. Bunyk, N. Dickson, C. Enderud, J. P. Hilton, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, R. Neufeld, T. Oh, I. Perminov, C. Rich, M. C. Thom, E. Tolkacheva, S. Uchaikin, A. B. Wilson, and G. Rose, Phys. Rev. X 4, 021041 (2014).

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Phys. Rev. E 91, 042137– Published 28 April, 2015
  • Received 9 September 2014

©2015 American Physical Society

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