Application of sine-Gordon model in description of Josephson junction - present state of affairs
Keywords:
sine-Gordon equation, soliton, Josephson junctionAbstract
Josephson junctions find applications for construction of various devices in measuring, transmitting, receiving, and amplifying systems as well as classical and quantum computing devices. Some of the existing and future applications are related to shape engineering, which allows for adjustment of the parameters of the junction to the needs of various applications. The article includes review of both a description of the applications and theoretical considerations devoted to the Josephson junctions and their properties.
References
Ablowitz M.J., and H. Segur. Solitons and the Inverse Scattering Transform. Philadelphia: SIAM, 1981.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Anderson, P.W., and J.M. Rowell. "Probable Observation of the Josephson Tunnel Effect." Phys. Rev. Lett. 10, no. 6 (1963): 230-232.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Bednorz, J.G., and K.A. Müller. "Possible high Tc superconductivity in the Ba-La-Cu-O system." Z. Phys. B 64 (1986): 189-193.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Benabdallah, A., and J.G. Caputo, and A.C. Scott. "Exponentially tapered Josephson flux-flow oscillator." Phys. Rev. B 54 (1996): id. 16139.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Boixo, S., et al. "Characterizing quantum supremacy in near-term devices." Nat. Phys. 14 (2018): 595-600.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Bour, E. "Theorie de la deformation des surfaces." Journal de l’École impériale polytechnique 22, (1862): 1-148.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Braginski, A.I. "Superconductor Electronics: Status and Outlook." J. Supercond. Nov. Magn. 32 (2019): 23-44.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Caputo, J.-G., and D. Dutykh. "Nonlinear waves in networks: Model reduction for the sine-Gordon equation." Phys. Rev. E 90 (2014): id. 022912.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Chaloupka, H.J., and V.K. Kornev. "Antennae." In Handbook of Superconducting Materials. CRC Press, 2019.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Cherednichenko, S.V., et al. "Hotelectron bolometer terahertz mixers for the Herschel space observatory." Rev. Sci. Instrum. 79 (2008): id. 034501.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Dai, P., et al. "Synthesis and neutron powder diffraction study of the superconductor HgBa2Ca2Cu3O8+δ by Tl substitution." Physica C 243, no. 3-4 (1995): 201-206.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Dobrowolski, T. "The kink motion in a curved Josephson junction." Phys. Rev. E 79 (2009): id. 046601.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Dobrowolski, T. "The dynamics of the kink in curved large area Josephson junction." Discrete Contin. Dyn. Syst. Ser. S 4 (2011): 1095-1105.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Dobrowolski, T. "Curved Josephson Junction." Ann. Phys. (N.Y.) 327 (2012): 1336-1354.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Dobrowolski, T. "Possible curvature effects in Josephson Junction." Eur. Phys. J. B 86 (2013): id. 346.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Dobrowolski T., and A. Jarmoliński. "Perturbation scheme for fluxon in curved Josephson junction." Phys. Rev. E 96 (2017): id. 012214.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Dobrowolski T., and A. Jarmoliński. "Josephson junction with variable thickness of the dielectric layer." Phys. Rev. E 101 (2020): id. 052215.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Drozdov A.P., et al. "Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system." Nature 525 (2015): 73-76.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Drozdov, A.P., et al. "Superconductivity at 250 K in Lanthanum Hydride under High Pressures." Nature 569 (2019): 528-531.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Faddeev L.D., and L.A. Takhtajan. Hamiltonian Methods in the Theory of Solitons. Berlin; New York: Springer-Verlag, 1987.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Gallop, J., and L. Hao. "Applications: Other devices-metrology." In: Handbook of Superconducting Materials. CRC Press, 2019.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Gatlik, J., and T. Dobrowolski. "The impact of thermal noise on kink propagation through a heterogeneous system." Physica D 445 (2023): id. 133649.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Gingrich, E., et al. "Controllable 0-π Josephson junctions containing a ferromagnetic spin valve." Nat. Phys. 12 (2016): 564-567.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Glick, J.A., et al. "Spin-triplet supercurrent in JJs containing a synthetic antiferromagnet with perpendicular magnetic anisotropy." Phys. Rev. B 96 (2017): id.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Gol’tsman, G., et al. "Picosecond superconducting single photon optical detector." Appl. Phys. Lett. 79 (2001): 705-707.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Granata, C., and A. Vettoliere. "Nano superconducting Interference device: a powerful tool for nanoscale investigations." Phys. Rep. 614 (2016): 1-69.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Gulevich, D.R., and F.V. Kusmartsev. "Flux Cloning in Josephson Transmission Lines." Phys. Rev. Lett. 97 (2006): id. 017004.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Gulevich, D.R., and F.V. Kusmartsev. "Switching phenomena in an annular Josephson junction." Physica C 435 (2006): 87-91.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Gulevich, D.R., and F.V. Kusmartsev. "Fluxon Collider for Multiple Fluxon-Antifluxon Collisions." New J. Phys. 9 (2007): id. 59.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Gulevich, D.R., et al. "Josephson fluxon pump: Theoretical aspects and experimental implementation of elementary flux quanta generator with BSCCO." Physica C 468 (2008): 1903-1906.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Gulevich D.R., et al. "Shape waves in 2D Josephson junctions: Exact solutions and time dilation." Phys. Rev. Lett. 101 (2008): id. 127002.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Hansen, R.C., and R.E. Collin. Small Antenna Handbook. Hoboken, New Jersey: John Wiley & Sons, Inc., 2011.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Häussler, C., and J. Oppenländer, and N. Schopol. "Nonperiodic flux to voltage conversion of series arrays of dc superconducting quantum interference devices." J. Appl. Phys. 93 (2001): 1875-1879.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Il’in, K.S., et al. "Picosecond hotelectron energy relaxation in NbN superconducting photodetectors." Appl. Phys. Lett. 76 (2000): 2752-2754.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Inaba, T., et al. "Routine clinical heart examinations using SQUID magnetocardiography at University of Tsukuba Hospital." Supercond. Sci. Technol. 30 (2017): id. 114003.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Jarmoliński, A., and T. Dobrowolski. "The role of magnetic fields for curvature effects in Josephson junction." Physica B 514 (2017): 24-29.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Josephson, B.D. "Possible new effects in superconductive tunnelling." Phys. Lett. 1, no. 7 (1962): 251-253.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Josephson, B.D. "The discovery of tunnelling supercurrents." Rev. Mod. Phys. 46, no. 2 (1974): 251-254.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Kivshar, Y.S., and B.A. Malomed. "Dynamics of solitons in nearly integrable systems." Rev. Mod. Phys. 61 (1989): id. 763.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Kemp, A., and A. Wallraff, and A.V. Ustinov. "Josephson Vortex Qubit: Design, Preparation and Read-Out." Phys. Stat. Sol. B 233 (2002): 472-481.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Kemp, A., and A. Wallraff, and A.V. Ustinov. "Testing a state preparation and read-out protocolfor the vortex qubit." Physica C 368 (2002): 324-327.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Kohlmann, J. "Application to Josephson voltage standards." In: Josephson Junctions. History, Devices, and Applications. 359-383. New York: Jenny Stanford
##plugins.generic.googleScholarLinks.settings.viewInGS##
Publishing, 2017.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Kornev, V.K., et al. "Design and experimental evaluation of SQUIF arrays with linear voltage response." IEEE Trans. Apl. Supercond. 21 (2011): 394-398.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Korneev, A., et al. "Physics and operation of superconducting single-photon detectors." In: Superconductors at the Nanoscale: from Basic Research to Applications, 279-308. Berlin: De Gruyter Press, 2017.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Krause H.J., and M. Mück, and S. Tanaka. "SQUIDs in non-destructive evaluation." In: Applied Superconductivity: Handbook on Devices and Applications. Vol.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Wiley, 2015.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Lamb, G.L. Elements of Soliton Theory. Wiley, 1980.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Likharev, K.K., and O.A. Mukhanov, and V.K. Semenov. "Resistive singleflux quantum logic for the Josephson junction technology." In: SQUID ’85: Superconducting Quantum Interference Devices and Their Applications. 1103-1108. Berlin; New York: Walter de Gruyter, 1985.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Ling, Liming, and Xuan Sun. "On the elliptic-localized solutions of the sine-Gordon equation." Physica D: Nonlinear Phenomena 444 (2023): id. 133597.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Lutchyn, R.M., and J.D. Sau, and S. Das Sarma. "Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures."
##plugins.generic.googleScholarLinks.settings.viewInGS##
Phys. Rev. Lett. 105 (2010): id. 077001.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Manheimer, M.A. "Cryogenic computing complexity program: phase 1: introduction." IEEE Trans. Appl. Supercond. 25 (2015): id. 1301704.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Miki, S., and M. Fujiwara, and R.B. Jin. "Quantum information networks with superconducting nanowire single-photon detectors." In: Superconducting Device
##plugins.generic.googleScholarLinks.settings.viewInGS##
in Quantum Optics. Cham; Heidelberg; New York; Dordrecht; London: Springer International Publishing Switzerland, 2016.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Monaco, R. "Engineering double-well potentials with variable-width annular Josephson tunnel junctions." J. Phys. Condens. Matter 28 (2016): id. 445702.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Monaco R., and J. Mygind, and V.P. Koshelets. "Development of a Josephson vortex two-state system based on a confocal annular Josephson junction." Supercond. Sci. Technol. 31 (2018): id. 025003.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Nakajima, K., and Y. Onodera,and Y. Ogawa. "Logic design of Josephson network." J. Appl. Phys. 47 (1976): 1620-1627.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Niedzielski, B., et al. "S/F/S Josephson junctions with single-domain ferromagnets for memory applications." Supercond. Sci. Technol. 28 (2015): id. 085012.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Nowak, H. "SQUIDs in biomagnetism." In: Applied Superconductivity: Handbook on Devices and Applications. Vol. 2. 992-1019. Wiley, 2015.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Oates, D.E. "Microwave resonators and filters." In: Handbook of Superconducting Materials. CRC Press, 2019.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Olver, P.J. Applications of Lie Groups to Differential Equations. New York: Springer New York, 1986.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Oreg, Y., and G. Refael, and F. von Oppen. "Helical liquids and Majorana bound states in quantum wires." Phys. Rev. Lett. 105 (2010): id. 177002.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Rogers, C., and W.K. Schief. University, Bäcklund and Darboux Transformations, Geometry and Modern Applications in Soliton Theory. Cambridge: Cambridge
##plugins.generic.googleScholarLinks.settings.viewInGS##
University Press 2002.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Schilling, A., et al. "Superconductivity above 130 K in the Hg-Ba-Ca-Cu-O system." Nature 363 (1993): 56-58.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Seidel, P. (ed.) Applied Superconductivity: Handbook on Devices and Applications. Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA, 2015.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Service R.F. "At last, room temperature superconductivity achieved." Science 370, no. 6514 (2020): 273-274.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Snider, E., et al. "Room-temperature superconductivity in a carbonaceous sulfurhydride." Nature 586 (2020): 373-377.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Sobolewski, R. "Optical sensors." In: Handbook of Superconducting Materials. CRC Press, 2019.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Stolz, R. "Geophysical exploration." In: Applied Superconductivity: Handbook on Devices and Applications. Vol. 2. 1020-1041. Wiley, 2015.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Ullom, J.N., and D.A. Bennett. "Review of superconducting transition-edge sensors for X-ray and gamma-ray spectroscopy." Supercond. Sci. Technol. 28 (2015): id. 084003.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Van Duzer, T., et al. "64-kb hybrid Josephson-CMOS 4 Kelvin RAM with 400 ps access time and 12 mW read power." IEEE Trans. Appl. Supercond. 23 (2013): id.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Wiedenmann, J., et al. "4π-periodic Josephson supercurrent in HgTe-based topological Josephson junctions." Nat. Comm. 7 (2016): id. 10303.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Yu, H.F., et al. "Quantum and classical resonant escapes of a strongly driven Josephson junction." Phys. Rev. B 81 (2010): 144518.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Zhang, H., et al. "Quantized Majorana conductance." Nature 556 (2018): 74-79.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Wydawnictwo Naukowe Uniwersytetu Komisji Edukacji Narodowej

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.