Circuit Approach for Simulation of EM-quantum Components

Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 169)

Abstract

This Chapter is on the circuit approach to describe the quantummechanical phenomena. Being proposed by G. Kron many years ago, this technique is now a very powerful tool for modeling and design of hybrid electronics integrating the classical and quantum-mechanical components. The linear and non-linear Schrödinger equations are transformed into the first-order partial differential equations with respect to currents and voltages, and the obtained equivalent circuits are modeled using a commercially available simulator. The approach is pertinent for seamless simulation of the future-generation integration, although the main attention in this Chapter is paid to the modeling of trapped Bose-Einstein condensates. References -108. Figures -34. Pages -54.

Keywords

Equivalent Circuit Cold Atom Circuit Simulator Telegraph Equation Cold Matter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Tour, J.M.: Molecular Electronics. World Sci. (2003)Google Scholar
  2. 2.
    Deleonibus, S. (ed.): Electronic Device Architectures for the Nano-CMOS Era. World Sci. (2008)Google Scholar
  3. 3.
    Benci, V., Fortunato, D.: An eigenvalue problem for the Schrödinger-Maxwell equations. Topological Methods in Nonlinear Analysis 11, 283–293 (1998)MathSciNetMATHGoogle Scholar
  4. 4.
    Ginbre, B., Velo, G.: Long range scattering for the Maxwell-Schrödinger system with large magnetic field data and small Schrödinger data. Publ. RIMS, Kyoto Univ. 42, 421–459 (2006)CrossRefGoogle Scholar
  5. 5.
    Yang, J., Sui, W.: Solving Maxwell-Schrödinger equations for analyses of nano-scale devices. In: Proc. 37th Europ. Microw. Conf., pp. 154–157 (2007)Google Scholar
  6. 6.
    Pieratoni, B., Mencarelli, D., Rozzi, T.: A new 3-D transmission line matrix scheme for the combined Schrödinger-Maxwell problem in the electronic/electromagnetic characterization of nanodevices. IEEE Trans., Microwave Theory Tech. 56, 654–662 (2008)CrossRefGoogle Scholar
  7. 7.
    Pieratoni, B., Mencarelli, D., Rozzi, T.: Boundary immitance operators for the Schrödinger-Maxwell problem of carrier dynamics in nanodevices. IEEE Trans., Microwave Theory Tech. 57, 1147–1155 (2009)CrossRefGoogle Scholar
  8. 8.
    Mastorakis, N.E.: Solution of the Schrödinger-Maxwell equations via finite elements and genetic algorithms with Nelder-Mead. WSEAS Trans. Math. 8, 169–176 (2009)MathSciNetGoogle Scholar
  9. 9.
    Kron, G.: Electric circuit model of the Schrödinger equation. Phys. Rev. (1&2) (1945)Google Scholar
  10. 10.
    Sanada, H., Suzuki, M., Nagai, N.: Analysis of resonant tunneling using the equivalent transmission-line model. IEEE J. Q. Electron. 33, 731–741 (1977)CrossRefGoogle Scholar
  11. 11.
    Anwar, A.F.M., Khondker, A.N., et al.: Calculation of the transversal time in resonant tunneling devices. J. Appl. Phys. 65, 2761–2765 (1989)CrossRefGoogle Scholar
  12. 12.
    Kaji, R., Koshiba, M.: Equivalent network approach for guided electron waves in quantum-well structures and its application to electron-wave directional couplers. IEEE J. Quant. Electron 31, 1036–1043 (1994)CrossRefGoogle Scholar
  13. 13.
    Civalleri, P.P., Gilli, M., Bonnin, M.: Equivalent circuits for two-state quantum systems. Int. J. Circ. Theory Appl. 35, 265–280 (2007)CrossRefGoogle Scholar
  14. 14.
    Kouzaev, G.A.: Hertz vectors and the electromagnetic-quantum equations. Mod. Phys. Lett. B 24(24), 2117–2212 (2010)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Kouzaev, G.A.: Calculation of linear and non-linear Schrödinger equations by the equivalent network approach and envelope technique. Modern Phys. Lett. B 24, 29–38 (2010)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Matyas, A., Jirauschek, C., Perretti, P., et al.: Linear circuit models for on-chip quantum electrodynamics. IEEE Trans., Microw. Theory Tech. 59, 65–71 (2011)CrossRefGoogle Scholar
  17. 17.
    Kouzaev, G.A., Nazarov, I.V., Kalita, A.V.: Unconventional logic elements on the base of topologically modulated signals. El. Archive, http://xxx.arXiv.org/abs/physics/9911065
  18. 18.
    Kouzaev, G.A., Lebedeva, T.A.: Multivalued and quantum logic modeling by mode physics and topologically modulated signals. In: Proc. Int. Conf. Modelling and Simulation, Las Palmas de Grand Canaria, Spain, September 25-27 (2000), http://www.dma.ulpgc.es/ms2000
  19. 19.
    Kouzaev, G.A.: Predicate and pseudoquantum gates for amplitude-spatially modulated electromagnetic signals. In: Proc. 2001 IEEE Int. Symp. Intelligent Signal Processing and Commun. Systems, Nashville, Tennessee, USA, November 20-23 (2001)Google Scholar
  20. 20.
    Kouzaev, G.A.: Qubit logic modeling by electronic gates and electromagnetic signals. El. Archive (2001), http://xxx.arXiv.org/abs/quant-ph/0108012
  21. 21.
    Advanced Design System 2008. Agilent Corp. (2008)Google Scholar
  22. 22.
    A User Guide to Envelope Following Analysis Using Spectre RF. Cadence Corp. (2007)Google Scholar
  23. 23.
    Visscher, P.B.: A fast explicit algorithm for the time-dependent Schrödinger equation. Comp. Phys. 5/6, 596–598 (1991)Google Scholar
  24. 24.
    Frank, T.D.: Nonlinear Fokker-Planck Equations: Fundamentals and Applications. Springer, Berlin (2005) Google Scholar
  25. 25.
    Norbe, F.D., Rego-Monteiro, M.A., Tsallis, C.: A generalized nonlinear Schroedinger equation: Classical field-theoretic approach. Eur. Phys. Lett. 97(1-5), 41001 (2012)Google Scholar
  26. 26.
    Belevitch, V.: Classical Network Theory. Holden-Day (1968)Google Scholar
  27. 27.
    Galizkyi, V.M., Kornakov, B.M., Kogan, V.I.: Tasks to Solve in Quantum Mechanics (Zadachi po Kvantovoy Mekhanike), Nauka (1981) (in Russian)Google Scholar
  28. 28.
    Gross, E.P.: Structure of a quantized vortex in boson systems II. Nouvo Cimento 20, 454–457 (1961)MATHCrossRefGoogle Scholar
  29. 29.
    Pitaevskii, L.V.: Vortex lines in an imperfect Bose gas. Soviet Phys. JETP 13, 451–454 (1961)MathSciNetGoogle Scholar
  30. 30.
    Pitaevskii, L.P., Stringari, S.: Bose-Einstein Condensation. Clareton Press (2003) Google Scholar
  31. 31.
    Ueda, M.: Fundamentals and New Frontiers of Bose-Einstein Condensation. World Scientific (2010) Google Scholar
  32. 32.
    Vengalattore, M., Higbie, J.M., Leslie, S.R., et al.: High-Resolution Magnetometry with a spinor Bose-Einstein Condensate. Phys. Rev. Lett. 98, 200801 (2007)CrossRefGoogle Scholar
  33. 33.
    Simmonds, R.W., Marchenkov, A., Hoskinson, E., et al.: Quantum interference of super fluid 3He. Nature 412, 55–58 (2001)CrossRefGoogle Scholar
  34. 34.
    Seaman, T., Krämer, M., Anderson, D.Z., et al.: Atomtronics: ultracold-atom analogs of electronic devices. Phys. Rev. A 75, 023615 (2007)CrossRefGoogle Scholar
  35. 35.
    Stickney, J.A., Anderson, D.Z., Zozulya, A.A.: Transistorlike behavior of a Bose-Einstein condensate in a triple-well potential. Phys. Rev. A 75, 013608 (2007)CrossRefGoogle Scholar
  36. 36.
    Ramanathan, A., Wright, K.C., Muniz, S.R., et al.: Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link. Phys. Rev. Lett. 106, 13041 (2001)Google Scholar
  37. 37.
    Farkas, M., Hudek, K.M., Salim, E.A., et al.: A compact, transportable, microchip-based system for high repetition rate production of Bose-Einstein condensates. App. Phys. Lett. 96, 093102 (2001)CrossRefGoogle Scholar
  38. 38.
    Cataliotti, F., Burger, S., Fort, C., et al.: Josephson junction arrays with Bose-Einstein condensates. Science 293, 843–846 (2001)CrossRefGoogle Scholar
  39. 39.
    Succi, S., Toschi, F., Tosi, M.P., et al.: Bose-Einstein condensates and the numerical solution of Gross-Pitaevskii equation. IEEE Comput. Sci. Eng. 7, 48–57 (2005)Google Scholar
  40. 40.
    Cerimele, M.M., Chiofalo, M.L., Pistella, F., et al.: Numerical solution of the Gross-Pitaevskii equation using an explicit finite-difference scheme: an application to trapped Bose-Einstein condensates. Phys. Rev. E 62, 1382–1389 (2000)CrossRefGoogle Scholar
  41. 41.
    Bao, W., Tang, W.: Ground-state solution of Bose-Einstein condensate by directly minimizing the energy functional. J. Comput. Phys. 187, 230–254 (2003)MathSciNetMATHCrossRefGoogle Scholar
  42. 42.
    Kron, G.: Numerical solution of ordinary and partial differential equations by means of equivalent circuits. J. Appl. Phys. 16, 172–186 (1945)MathSciNetMATHCrossRefGoogle Scholar
  43. 43.
    Kron, G.: Equivalent circuit of the field equations of Maxwell. In: Proc. I. R. E., pp. 289–299 (1944)Google Scholar
  44. 44.
    Dragoman, D., Dragoman, M.: Quantum-classical Analogies. Springer (2004) Google Scholar
  45. 45.
    Kouzaev, G.A.: Co-design of quantum and electronic integrations by available circuit simulators. In: Proc. 13th Int. Conf. Circuits, Rodos, Greece, pp. 152–156 (2009)Google Scholar
  46. 46.
    Holland, M.J., Jin, D.S., Chiofalo, M.L., et al.: Emergence of interaction effects in Bose-Einstein condensation. Phys. Rev. Lett. 78, 3801–3805 (1997)CrossRefGoogle Scholar
  47. 47.
    Bogolubov, N.: J. Phys 11, 23 (1947) (in Russian)MathSciNetGoogle Scholar
  48. 48.
    Pethick, C.J., Smith, H.: Bose-Einstein Condensation in Dilute Gases. Cambridge Press (2003) Google Scholar
  49. 49.
    Chevy, F., Dalibard, J.: Rotating Bose-Einstein condensates. Europhysicsnews 37, 12–16 (2006)Google Scholar
  50. 50.
    Rozanov, N.N., Rozhdestvenkyi, Y.V., Smirnov, V.A., et al.: Atomic “Needles” and “Bullets” of the Bose-Einstein condensate and forming of nano-size structures. Pisma v ZHETF- Lett. J. Exper. Theor. Phys. 77, 89–92 (2003) (in Russian)Google Scholar
  51. 51.
    Anderson, M.H., Ensher, J.R., Matthews, M.R., Wieman, C.E., Cornell, E.A.: Observation of Bose–Einstein condensation in a dilute atomic vapor. Science 269(5221), 198–201 (1995)CrossRefGoogle Scholar
  52. 52.
    Davis, K.B., Mewes, M.-O., Andrews, M.R., van Druten, N.J., Durfee, D.S., Kurn, D.M., Ketterle, W.: Bose–Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969–3973 (1995)CrossRefGoogle Scholar
  53. 53.
    Balykin, V.I., Minogin, V.G., Letokhov, V.S.: Electromagnetic trapping of cold atoms. Rep. Prog. Phys. 61, 1429–1510 (2000)CrossRefGoogle Scholar
  54. 54.
    Chu, S.: Laser manipulations of atoms and particles. Science 253, 861–866 (1991)CrossRefGoogle Scholar
  55. 55.
    Cohen-Tannoudji, C., Guerry-Odelin, D.: Advances in Atomic Physics: an Overview. World Scientific (2011)Google Scholar
  56. 56.
    Phillips, W.D.: Nobel lecture: Laser cooling and trapping of neutral atoms. Rev. Mod. Phys. 70, 721–741 (1998)CrossRefGoogle Scholar
  57. 57.
    Friedman, N., Kaplan, A., Davidson, N.: Dark optical traps for cold atoms. Adv. Atomic, Molec., Opt. Phys. 48, 99–151 (2002)CrossRefGoogle Scholar
  58. 58.
    Noh, H.-R., Jhe, W.: Atom optics with hollow optical systems. Phys. Reports 372, 269–317 (2002)CrossRefGoogle Scholar
  59. 59.
    Kuhr, S., Alt, W., Schrader, D., et al.: Deterministic delivery of a single atom. Science 293, 278–280Google Scholar
  60. 60.
    Mandel, A., Greiner, M., Widera, A., et al.: Controlled collisions for multi-particle entanglement of optically trapped atoms. Nature 425, 937–940 (2003)CrossRefGoogle Scholar
  61. 61.
    Schrader, D., Dotsenko, I., Khudaverdyan, M., et al.: Neutral atom quantum register. Phys. Rev. Lett. 93(1-4), 150501Google Scholar
  62. 62.
    Bloch, I.: Exploring quantum matter with ultracold atoms in optical lattices. J. Phys. B 38, S629–S643 (2005)CrossRefGoogle Scholar
  63. 63.
    Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultra-cold gases. Rev. Mod. Phys., 885–964 (2008)Google Scholar
  64. 64.
    Bergman, T., Erez, G., Metcalf, H.J.: Magnetostatic trapping fields for neutral atoms. Phys. Rev. A 35, 1535–1546 (1987)CrossRefGoogle Scholar
  65. 65.
    AMPERES Program Guide. Integrated Software Eng. Inc. (2006)Google Scholar
  66. 66.
    Sand, K.J.: On the design and simulation of electromagnetic traps and guides for ultra-cold matter. PhD Thesis, NTNU, Trondheim, Norway, 252 p (2010)Google Scholar
  67. 67.
    Kouzaev, G.A., Sand, K.J.: RF controllable Ioffe-Pritchard trap for cold dressed atoms. Modern Phys. Lett. B 21, 59–68 (2007)MATHCrossRefGoogle Scholar
  68. 68.
    Thomas, N.R., Foot, C.J., Wilson, A.C.: Double-well magnetic trap for Bose-Einstein condensates. ArXiv: cond-mat/01108169 (2001)Google Scholar
  69. 69.
    Tiecke, T.G., Kemmann, M., Buggle, C., et al.: Bose-Einstein condensation in a magnetic double-well potential. ArXiv: cond-mat/0211604 (2002)Google Scholar
  70. 70.
    Rechel, J., Hansel, W., Hommelholf, P., et al.: Applications of integrated magnetic microtraps. Appl. Phys. B 72, 81–89 (2001)CrossRefGoogle Scholar
  71. 71.
    Jones, M.P.A., Vale, C.J., Sahagun, D., et al.: Cold atoms probe the magnetic field near a wire. J. Phys. B 37, L15–L20 (2004)CrossRefGoogle Scholar
  72. 72.
    Crookston, M.B., Baker, P.M., Robinson, M.P.: A microstrip ring trap for cold atoms. J. Phys. B 38, 3227–3289 (2005)CrossRefGoogle Scholar
  73. 73.
    Koukharenko, E., Mktadir, Z., Kraft, M., et al.: Microfabrication of gold wires for atom guides. Sensors and Actuators A 115, 600–607Google Scholar
  74. 74.
    Henkel, Wilkens, M.: Heating of trapped atoms near thermal surfaces. Europhys. Lett. 47, 414–420 (1999)CrossRefGoogle Scholar
  75. 75.
    Fermani, R., Scheel, S., Knight, P.L.: Trapping cold atoms near carbon nanotubes: Thermal spin flips and Casimir-Polder potential. Phys. Rev. A 75(1-7), 062905 (2007)CrossRefGoogle Scholar
  76. 76.
    Bostroem, M., Sernelius, B.E., Brevik, I., et al.: Retardation turns the van der Waals attraction into a Casimir repulsion as close as 3 nm. Phys. Rev. A 85(1-4), 010701Google Scholar
  77. 77.
    Kouzaev, G.A., Sand, K.J.: 3D multicell designs for registering of Bose-Einstein condensate clouds. Modern Phys. Lett. 22(25), 2469–2479 (2008)CrossRefGoogle Scholar
  78. 78.
    Shi, Y.: Entanglement between Bose-Einstein condensates. Int. J. Modern. Phys. B 15, 3007–3030 (2001)CrossRefGoogle Scholar
  79. 79.
    Yalabik, M.C.: Nonlinear Schrödinger equation for quantum computation. Modern Physics Lett. B 20, 1099–1106 (2006)MATHCrossRefGoogle Scholar
  80. 80.
    Albiez, M., Gati, R., Foeling, J., et al.: Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction. Phys. Rev. Lett. 95(1-4), 010402 (2005)CrossRefGoogle Scholar
  81. 81.
    Levy, S., Lahoud, E., Shomroni, I., et al.: The a.c. and d.c. Josephson effects in a Bose-Einstein condensate. Nature 449, 579–583 (2007)CrossRefGoogle Scholar
  82. 82.
    Muskat, E.: Dressed neutrons. Phys. Rev. Lett. 58, 2047–2050 (1987)CrossRefGoogle Scholar
  83. 83.
    Zobay, O., Garraway, B.M.: Two-dimensional atom trapping in field-induced adiabatic potentials. Phys. Rev. Lett. 86, 1195–1198 (2001)CrossRefGoogle Scholar
  84. 84.
    Colombe, Y., Knyazchyan, E., Morizot, O., et al.: Ultracold atoms confined in rf-induced two-dimensional trapping potentials. arXiv:quant-ph/0403006Google Scholar
  85. 85.
    Courteille, P.W., Deh, B., Fortag, J., et al.: Highly versatile atomic micro traps generated by multifrequency magnetic field modulation. arXiv:quant-ph/0512061Google Scholar
  86. 86.
    Schumm, T., Hofferberth, S., Andersson, L.M., et al.: Matter-wave interferometry in a double well on an atom chip. Nature Physics 1, 57–62 (2005)CrossRefGoogle Scholar
  87. 87.
    Lesanovsky, I., Schumm, T., Hofferberth, S., et al.: Adiabatic radio frequency potentials for coherent manipulation of matter waves. ArXiv:physics/0510076Google Scholar
  88. 88.
    Ol’shanii, M.A., Ovchinnikov, Y.V., Letokhov, V.S.: Laser guiding of atoms in a hollow optical fiber. Opt. Commun. 98, 77–79 (1993)CrossRefGoogle Scholar
  89. 89.
    Renn, M.J., Mongomery, D., Vdovin, O., et al.: Laser-Guided atoms in hollow-core optical fibers. Phys. Rev. Lett. 75, 3253–3256 (1995)CrossRefGoogle Scholar
  90. 90.
    Renn, M.J., Donley, E.A., Cornell, E.A., et al.: Evanescent-wave guiding of atoms in hollow optical fibers. Phys. Rev. A 53, R648–R651 (1996)CrossRefGoogle Scholar
  91. 91.
    Song, Y., Milam, D., Hill III, W.T.: Long, narrow all-light atom guide. Opt. Lett. 24, 1805–1807 (1999)CrossRefGoogle Scholar
  92. 92.
    Myatt, C.J., Newbury, N.R., Ghrist, R.W., et al.: Multiply loaded magneto-optical trap. Opt. Lett. 21, 290–292Google Scholar
  93. 93.
    Goepfert, A., Lison, F., Schutze, R., et al.: Efficient magnetic guiding and deflection of atomic beams with moderate velocities. Appl. Phys. B 69, 217–222Google Scholar
  94. 94.
    Key, M., Hughes, I.G., Rooijakkers, W., et al.: Propagation of cold atoms along a miniature magnetic guide. Phys. Rev. Lett. 84, 1371–1373 (2000)CrossRefGoogle Scholar
  95. 95.
    Teo, B.K., Raithel, G.: Loading mechanism for atomic guides. Phys. Rev. A 63(1-4), 031402 (2001)CrossRefGoogle Scholar
  96. 96.
    Yung-Kuo, L.: Problems and Solutions on Electromagnetism. World Scientific (1993)Google Scholar
  97. 97.
    Subbotin, M.V., Balykin, V.I., Laryushin, D.L., et al.: Laser controlled atom waveguide as a source of ultracold atoms. Opt. Commun. 139, 107 (1997)CrossRefGoogle Scholar
  98. 98.
    Greiner, M., Bloch, I., Haensh, T.W., et al.: Magnetic transport of trapped cold atoms over a large distance. Phys. Rev. A 63(1-4), 0131401 (2001)Google Scholar
  99. 99.
    Kouzaev, G.A., Sand, K.J.: Inter-wire transfer of cold dressed atoms. Modern Phys. Lett. B 21, 1653–1665 (2007)CrossRefGoogle Scholar
  100. 100.
    Weinstein, J.D., Librecht, K.G.: Microscopic magnetic traps for neutral particles. Phys. Rev. A 52, 4004–4009 (1995)CrossRefGoogle Scholar
  101. 101.
    Thywissen, J.J., Olshanii, M., Zabow, G., et al.: Microfabricated magnetic waveguides for neutral atoms. Eur. Phys. J. D 7, 361–367 (1999)CrossRefGoogle Scholar
  102. 102.
    Allwood, D.A., Schrefl, T., Hrkac, G., et al.: Mobile atom traps using nanowires. Appl. Phys. Lett. 89(1-3), 014102 (2006)CrossRefGoogle Scholar
  103. 103.
    Dekker, N.H., Lee, C.S., Lorent, V., et al.: Guiding neutral atoms on a chip, vol. 84, pp. 1124–1127 (2000)Google Scholar
  104. 104.
    Tonyshkin, A., Prentiss, M.: Straight macroscopic magnetic guide for cold atom interferometer. J. Appl. Phys. 108(1-5), 094904 (2010)CrossRefGoogle Scholar
  105. 105.
    Bongs, K., Burger, S., Dettmer, S., et al.: Waveguide for Bose-Einstein condensates. Phys. Rev. A 63(1-4), 031602 (2001)CrossRefGoogle Scholar
  106. 106.
    Treutlein, P., Hommelhoff, P., Steinmetz, T., et al.: Coherence in microstrip traps. Phys. Rev. Lett. 92(1-4), 203005 (2004)CrossRefGoogle Scholar
  107. 107.
    Treutlein, P., Steinmetz, T., Colombe, Y., et al.: Quantum information processing in optical lattices and magnetic microtraps. Fortschr. Phys. 54, 702–718 (2006)CrossRefGoogle Scholar
  108. 108.
    Boehi, P., Riedel, M.F., Hoffrogge, J., et al.: Coherent manipulation of Bose-Einstein condensates with state-dependent microwave potentials on an atom chip. Nature Physics 5, 592–597 (2009)CrossRefGoogle Scholar
  109. 109.
    Sun, Y., Tan, W., Jiang, H.-T., et al.: Metamaterial analog of quantum interference: From electromagnetically induced transparency to absorbtion. EPLA 98, 6407 (1-6) (2012)Google Scholar
  110. 110.
    Rangelow, A.A., Suchowski, H., Silberberg, Y., et al.: Wireless adiabatic power transfer. Annals of Phys. 326, 626–633 (2011)CrossRefGoogle Scholar

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© Springer-Verlag GmbH Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Electronics and Telecommunications Norwegian University of Science and TechnologyTrondheimNorway

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