Skip to main content
SpringerLink
Log in

Phase Dynamics and Macroscopic Quantum Tunneling

  • Chapter
  • First Online:
Fundamentals and Frontiers of the Josephson Effect

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 286))

Abstract

We will review concepts, theory and experimental results on whether and in which conditions a quantum system, governed by a single macroscopic degree of freedom interacting with its environment, can tunnel out of a metastable state. The macroscopic quantum tunneling (MQT) experiments discussed in this chapter demonstrate that \(\varphi \) is indeed a quantum variable. Differently from the tunneling of a microscopic entity, coupling to the environment plays a major role in the macroscopic analog, and can be so strong that the motion in the classically accessible region is highly damped.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. H.A. Kramers, Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7, 284–304 (1940)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. M. Büttiker, E.P. Harris, R. Landauer, Thermal activation in extremely underdamped Josephson-junction circuits. Phys. Rev. B 28, 1268 (1983)

    Article  ADS  Google Scholar 

  3. P. Hanggi, P. Talkner, M. Borkovec, Reaction-rate theory: fifty years after Kramers. Rev. Mod. Phys. 62, 251 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  4. H. Grabert, U. Weiss, Crossover from thermal hopping to quantum tunneling. Phys. Rev. Lett. 53, 1787 (1984)

    Article  ADS  Google Scholar 

  5. Yu.M. Ivanchenko, L.A. Zilberman, Destruction of Josephson current by fluctuations, Zh. Esker. Teor. Fiz. 55, 2395–2402 (1968); Sov. Phys. JETP 28, 1272–1276 (1969)

    Google Scholar 

  6. A.O. Caldeira, A.J. Leggett, Influence of dissipation on quantum tunneling in macroscopic systems. Phys. Rev. Lett. 46, 211 (1981)

    Article  ADS  Google Scholar 

  7. A.O. Caldeira, A.J. Leggett, Quantum tunnelling in a dissipative system. Ann. Phys. 149, 374–456 (1993)

    Article  ADS  Google Scholar 

  8. A.O. Caldeira, An Introduction to Macroscopic Quantum Phenomena and Quantum Dissipation (Cambridge University Press, Cambridge, 2014)

    Book  Google Scholar 

  9. A. Barone, Y.N. Ovchinnikov, Macroscopic quantum tunneling in small- and large-dissipation regimes. J. Low Temp. Phys. 55, 297–302 (1984)

    Article  ADS  Google Scholar 

  10. V. Ambegaokar, U. Eckern, G. Schön, Quantum dynamics of tunneling between superconductors. Phys. Rev. Lett. 48, 1745 (1982)

    Article  ADS  Google Scholar 

  11. U. Eckern, G. Schön, V. Ambegaokar, Quantum dynamics of a superconducting tunnel junction. Phys. Rev. B 30, 6419 (1984)

    Article  ADS  Google Scholar 

  12. A.I. Larkin, Yu.N. Ovchinnikov, Quantum tunneling with dissipation. Zh. Esker. Teor. Pis. Red. 37, 322–325 (1969); JETP Lett. 37, 382–385 (1969)

    Google Scholar 

  13. H. Grabert, U. Weiss, P. Hanggi, Quantum tunneling in dissipative systems at finite temperatures. Phys. Rev. Lett. 52, 2193 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  14. G. Schön, A.D. Zaikin, Quantum description of dissipation in normal metals and short constrictions. Phys. Rev. B 40, 5231 (1989)

    Article  ADS  Google Scholar 

  15. J.M. Martinis, H. Grabert, Thermal enhancement of macroscopic quantum tunneling: derivation from noise theory. Phys. Rev. B 38, 2371 (1988)

    Article  ADS  Google Scholar 

  16. D. Waxman, A.J. Leggett, Dissipative quantum tunneling at finite temperatures. Phys. Rev. B 32, 4450 (1985)

    Article  ADS  Google Scholar 

  17. J. Kurkijärvi, Intrinsic fluctuations in a superconducting ring closed with a Josephson junction. Phys. Rev. B 6, 832 (1972)

    Article  ADS  Google Scholar 

  18. T.A. Fulton, L.N. Dunkleberger, Lifetime of the zero-voltage state in Josephson tunnel junctions. Phys. Rev. B 9, 4760 (1974)

    Article  ADS  Google Scholar 

  19. A. Garg, Escape-field distribution for escape from a metastable potential well subject to a steadily increasing bias field. Phys. Rev. B 51, 15592 (1995)

    Article  ADS  Google Scholar 

  20. L.D. Jackel, W.W. Webb, J.E. Lukens, S.S. Pei, Measurement of the probability distribution of thermally excited fluxoid quantum transitions in a superconducting ring closed by a Josephson junction. Phys. Rev. B 9, 115 (1974)

    Article  ADS  Google Scholar 

  21. R.F. Voss, R.A. Webb, Macroscopic quantum tunneling in 1-\(\mu \)m Nb Josephson junctions. Phys. Rev. Lett. 47, 265 (1981)

    Article  ADS  Google Scholar 

  22. L.D. Jackel, J.P. Gordon, E.L. Hu, R.E. Howard, L.A. Fetter, D.M. Tennant, R.W. Epworth, J. Kurkijärvi, Decay of the zero-voltage state in small-area, high-current-density Josephson junctions. Phys. Rev. Lett. 47, 697 (1981)

    Article  ADS  Google Scholar 

  23. W. den Boer, R. de Bruyn Ouboter, Flux transition mechanisms in superconducting loops closed with a low capacitance point contact. Phys. B+C 98, 185–190 (1980); D.W. Bol, R. van Weelderen, R. de Bruyn Ouboter, On the conditional transition probabilities of the magnetic flux at low temperatures in a superconducting loop closed with a low-capacitance superconducting point contact. Phys. B+C 122, 1–7 (1983); D.W. Bol, J.J.F. Scheffer, W. Giele, R. de Bruyn Ouboter, Thermal activation in the quantum regime and macroscopic quantum tunnelling in the thermal regime in a metabistable system consisting of a superconducting ring interrupted by a weak junction: part I: thermal activation in the quantum regime. Phys. B+C 133, 196–209 (1985)

    Google Scholar 

  24. R.J. Prance, A.P. Long, T.D. Clarke, A. Widom, J.E. Mutton, J. Sacco, M.W. Potts, G. Negaloudis, F. Goodall, Macroscopic quantum electrodynamic effects in a superconducting ring containing a Josephson weak link. Nature 289, 543–549 (1981)

    Article  ADS  Google Scholar 

  25. I.M. Dimitrenko, V.A. Khlus, G.M. Tsoi, V.I. Shnyrkov, Quantum decay of metastable current states in rf SQUIDs. Fiz. Nizk. Temp. 11, 146–160 (1985); Sov. J. Low Temp. 11, 77–90 (1985)

    Google Scholar 

  26. S. Washburn, R.A. Webb, R.F. Voss, S.M. Farris, Effects of dissipation and temperature on macroscopic quantum tunneling. Phys. Rev. Lett. 54, 2712 (1981)

    Article  ADS  Google Scholar 

  27. D.B. Schartz, B. Sen, C.N. Archie, J.E. Lukens, Quantitative study of the effect of the environment on macroscopic quantum tunneling. Phys. Rev. Lett. 55, 1547 (1985)

    Article  ADS  Google Scholar 

  28. M.H. Devoret, J.M. Martinis, D. Esteve, J. Clarke, Resonant activation from the zero-voltage state of a current-biased Josephson junction. Phys. Rev. Lett. 53, 1260 (1984)

    Article  ADS  Google Scholar 

  29. M.H. Devoret, J.M. Martinis, J. Clarke, Measurements of macroscopic quantum tunneling out of the zero-voltage state of a current-biased Josephson junction. Phys. Rev. Lett. 55, 1908 (1985)

    Article  ADS  Google Scholar 

  30. J.M. Martinis, M.H. Devoret, J. Clarke, Experimental tests for the quantum behavior of a macroscopic degree of freedom: the phase difference across a Josephson junction. Phys. Rev. B 35, 4682 (1987)

    Article  ADS  Google Scholar 

  31. J. Clarke, A.N. Cleland, M.H. Devoret, D. Esteve, J.M. Martinis, Quantum mechanics of a macroscopic variable: the phase difference of a Josephson junction. Science 239, 992–997 (1988)

    Article  ADS  Google Scholar 

  32. H.W. Ott, Noise Reduction Techniques in Electronic Systems (Wiley Interscience, New York, 1988)

    Google Scholar 

  33. R. Morrison, Grounding and Shielding Techniques (Wiley Interscience, New York, 1998)

    Google Scholar 

  34. A.B. Zorin, The thermocoax cable as the microwave frequency filter for single electron circuits. Rev. Sci. Instrum. 66, 4296–4300 (1995)

    Article  ADS  Google Scholar 

  35. F.P. Milliken, J.R. Rozen, G.A. Keefe, R.H. Koch, 50 \(\Omega \) characteristic impedance low-pass metal powder filters. Rev. Sci. Instrum. 78, 024701–024705 (2007)

    Article  ADS  Google Scholar 

  36. D.A. Bennett, L. Longobardi, V. Patel, W. Chen, J.E. Lukens, rf-SQUID qubit readout using a fast flux pulse. Supercond. Sci. Tech. 20, 445 (2007)

    Article  ADS  Google Scholar 

  37. D. Esteve, M.H. Devoret, J.M. Martinis, Effect of an arbitrary dissipative circuit on the quantum energy levels and tunneling of a Josephson junction. Phys. Rev. B 34, 158 (1986)

    Article  ADS  Google Scholar 

  38. P. Silvestrini, S. Pagano, R. Cristiano, O. Liengme, K.E. Gray, Effect of dissipation on thermal activation in an underdamped Josephson junction: first evidence of a transition between different damping regimes. Phys. Rev. Lett. 60, 844 (1988)

    Article  ADS  Google Scholar 

  39. E. Turlot, D. Esteve, C. Urbina, J.M. Martinis, M.H. Devoret, S. Linkwitz, H. Grabert, Escape oscillations of a Josephson junction switching out of the zero-voltage state. Phys. Rev. Lett. 62, 1788 (1989)

    Article  ADS  Google Scholar 

  40. J.R. Kirtley, C.D. Tesche, W.J. Gallagher, A.W. Kleinsasser, R.L. Sandstrom, S.I. Raider, P.A. Fisher, Measurement of the intrinsic subgap dissipation in Josephson junctions. Phys. Rev. Lett. 61, 2372 (1988)

    Article  ADS  Google Scholar 

  41. M.G. Castellano, G. Torrioli, F. Chiarello, C. Cosmelli, P. Carelli, Return current in hysteretic Josephson junctions: experimental distribution in the thermal activation regime. J. Appl. Phys. 86, 6405–6411 (1999)

    Article  ADS  Google Scholar 

  42. M.G. Castellano, R. Leoni, G. Torrioli, F. Chiarello, C. Cosmelli, A. Costantini, G. Diambrini-Palazzi, P. Carelli, R. Cristiano, L. Frunzio, Switching dynamics of Nb/AlOx/Nb Josephson junctions: measurements for an experiment of macroscopic quantum coherence. J. Appl. Phys. 80, 2922–2928 (1996)

    Article  ADS  Google Scholar 

  43. A. Barone, R. Cristiano, P. Silvestrini, Supercurrent decay in underdamped Josephson junctions: nonstationary case. J. Appl. Phys. 58, 3822–3826 (1985)

    Article  ADS  Google Scholar 

  44. Yu.N. Ovchinnikov, A. Barone, A.A. Varlamov, Effect of magnetic field on macroscopic quantum tunneling escape time in small Josephson junctions. Phys. Rev. B 78, 054521 (2008); Y.N. Ovchinnikov, A. Barone, A.A. Varlamov, Macroscopic quantum tunneling in “Small” Josephson junctions in a magnetic field. Phys. Rev. Lett. 99, 037004 (2007)

    Google Scholar 

  45. A. Wallraff, T. Duty, A. Lukashenko, A.V. Ustinov, Multiphoton transitions between energy levels in a current-biased Josephson tunnel junction. Phys. Rev. Lett. 90, 370031 (2003)

    Article  Google Scholar 

  46. J.E. Marchese, M. Cirillo, N. Grønbech-Jensen, Classical analogs for Rabi-oscillations, Ramsey-fringes, and spin-echo in Josephson junctions. Eur. Phys. J. Spec. Top. 147, 333–342 (2007); N. Grønbech-Jensen, M. Cirillo, Rabi-type oscillations in a classical Josephson junction. Phys. Rev. Lett. 95, 067001 (2005); J.E. Marchese, M. Cirillo, N. Grønbech-Jensen, Classical analysis of phase-locking transients and Rabi-type oscillations in microwave-driven Josephson junctions. Phys. Rev. B 73, 174507 (2006)

    Google Scholar 

  47. B. Ivlev, G. Pepe, R. Latempa, A. Barone, F. Barkov, J. Lisenfeld, A.V. Ustinov, Extreme multiphoton phenomena in Josephson junctions: Euclidean resonance. Phys. Rev. B 72, 094507 (2005)

    Article  ADS  Google Scholar 

  48. A.I. Larkin, Yu.N. Ovchinnikov, Effect of level quantization on the lifetime of metastable states. Zh. Esker. Teor. Fiz. 91, 318–325 (1986); Sov. Phys. JETP 64, 185–189 (1986)

    Google Scholar 

  49. A.I. Larkin, Yu.N. Ovchinnikov, Current damping in superconducting junctions with nonequilibrium electron distribution functions. Zh. Esker. Teor. Fiz. 87, 1842–1856 (1984); Sov. Phys. JETP 60, 1060–1067 (1984)

    Google Scholar 

  50. P. Kopietz, S. Chakravarty, Lifetime of metastable voltage states of superconducting tunnel junctions. Phys. Rev. B 38, 97 (1988)

    Article  ADS  Google Scholar 

  51. R. Rouse, S. Han, J.E. Lukens, Observation of resonant tunneling between macroscopically distinct quantum levels. Phys. Rev. Lett. 75, 1614 (1995)

    Article  ADS  Google Scholar 

  52. E. Ben-Jacob, D.J. Bergman, B.J. Matkowsky, Z. Schuss, Lifetime of oscillatory steady states. Phys. Rev. A 26, 2805 (1982)

    Article  ADS  Google Scholar 

  53. Y.C. Chen, M.P.A. Fischer, A.J. Leggett, The return of a hysteretic Josephson junction to the zero-voltage state: I-V characteristic and quantum retrapping. J. Appl. Phys. 64, 3119 (1988)

    Article  ADS  Google Scholar 

  54. E. Ben-Jacob, D.J. Bergman, Y. Imry, B.J. Matkowsky, Z. Schuss, Thermal activation from the fluxoid and the voltage states of dc SQUIDs. J. Appl. Phys. 54, 6533–6542 (1983)

    Article  ADS  Google Scholar 

  55. F. Sharifi, J.L. Gavilano, D.J. Van Harlingen, Macroscopic quantum tunneling and thermal activation from metastable states in a dc SQUID. Phys. Rev. Lett. 61, 742 (1988)

    Article  ADS  Google Scholar 

  56. S. Han, J. Lapointe, J.E. Lukens, Thermal activation in a two-dimensional potential. Phys. Rev. Lett. 63, 1712 (1989)

    Article  ADS  Google Scholar 

  57. V. Lefevre-Seguin, E. Turlot, C. Urbina, D. Esteve, M.H. Devoret, Thermal activation of a hysteretic dc superconducting quantum interference device from its different zero-voltage states. Phys. Rev. B 46, 5507 (1992)

    Article  ADS  Google Scholar 

  58. S.-X. Li, Y. Yu, Y. Zhang, W. Qiu, S. Han, Quantitative study of macroscopic quantum tunneling in a dc SQUID: a system with two degrees of freedom. Phys. Rev. Lett. 89, 098301 (2002)

    Article  ADS  Google Scholar 

  59. F. Balestro, J. Claudon, J.P. Pekola, O. Buisson, Evidence of two-dimensional macroscopic quantum tunneling of a current-biased dc SQUID. Phys. Rev. Lett. 91, 158301 (2003)

    Article  ADS  Google Scholar 

  60. S. Butz, A.K. Feofanov, K.G. Fedorov, H. Rotzinger, A.U. Thomann, B. Mackrodt, R. Dolata, V.B. Geshkenbein, G. Blatter, A.V. Ustinov, Flux-dependent crossover between quantum and classical behavior in a dc SQUID. Phys. Rev. Lett. 113, 247005 (2014)

    Article  ADS  Google Scholar 

  61. L. Longobardi, D. Massarotti, G. Rotoli, D. Stornaiuolo, G. Papari, A. Kawakami, G.P. Pepe, A. Barone, F. Tafuri, Quantum crossover in moderately damped epitaxial NbN/MgO/NbN junctions with low critical current density. Appl. Phys. Lett. 99, 062510 (2011)

    Article  ADS  Google Scholar 

  62. D. Massarotti, A. Pal, G. Rotoli, L. Longobardi, M.G. Blamire, F. Tafuri, Macroscopic quantum tunnelling in spin filter ferromagnetic Josephson junctions. Nat. Commun. 6, 7376 (2015)

    Article  ADS  Google Scholar 

  63. O. Buisson, F. Balestro, J.P. Pekola, F.W.J. Hekking, One-shot quantum measurement using a hysteretic dc SQUID. Phys. Rev. Lett. 90, 238304 (2003)

    Article  ADS  Google Scholar 

  64. A. Wallraff, A. Lukashenko, J. Lisenfeld, A. Kemp, M.V. Fistul, Y. Koval, A.V. Ustinov, Quantum dynamics of a single vortex. Nature 425, 125–128 (2003)

    Article  ADS  Google Scholar 

  65. R.L. Kautz, J.M. Martinis, Noise-affected I-V curves in small hysteretic Josephson junction. Phys. Rev. B 42, 9903 (1990)

    Article  ADS  Google Scholar 

  66. J.M. Kivioja, T.E. Nieminen, J. Claudon, O. Buisson, F.W.J. Hekking, J.P. Pekola, Observation of transition from escape dynamics to underdamped phase diffusion in a Josephson junction. Phys. Rev. Lett. 94, 247002 (2005)

    Article  ADS  Google Scholar 

  67. J. Männik, S. Li, W. Qiu, W. Chen, V. Patel, S. Han, J.E. Lukens, Crossover from Kramers to phase-diffusion switching in moderately damped Josephson junctions. Phys. Rev. B 71, 220509 (2005)

    Article  ADS  Google Scholar 

  68. V.M. Krasnov, T. Bauch, S. Intiso, E. Hürfeld, T. Akazaki, H. Takayanagi, P. Delsing, Collapse of thermal activation in moderately damped Josephson junctions. Phys. Rev. Lett. 95, 157002 (2005)

    Article  ADS  Google Scholar 

  69. J.M. Kivioja, T.E. Nieminen, J. Claudon, O. Buisson, F.W.J. Hekking, J.P. Pekola, Weak coupling Josephson junction as a current probe: effect of dissipation on escape dynamics. New J. Phys. 7, 179–200 (2005)

    Article  ADS  Google Scholar 

  70. V.M. Krasnov, T. Golod, T. Bauch, P. Delsing, Anticorrelation between temperature and fluctuations of the switching current in moderately damped Josephson junctions. Phys. Rev. B 76, 224517 (2007)

    Article  ADS  Google Scholar 

  71. J.C. Fenton, P.A. Warburton, Monte Carlo simulations of thermal fluctuations in moderately damped Josephson junctions: multiple escape and retrapping, switching- and return-current distributions, and hysteresis. Phys. Rev. B 78, 054526 (2008)

    Article  ADS  Google Scholar 

  72. M.-H. Bae, M. Sahu, H.-J. Lee, A. Bezryadin, Multiple-retrapping processes in the phase-diffusion regime of high-Tc intrinsic Josephson junctions. Phys. Rev. B 79, 104509 (2009)

    Article  ADS  Google Scholar 

  73. H.F. Yu, X.B. Zhu, Z.H. Peng, Y. Tian, D.J. Cui, G.H. Chen, D.N. Zheng, X.N. Jing, L. Lu, S.P. Zhao, S. Han, Quantum phase diffusion in a small underdamped Josephson junction. Phys. Rev. Lett. 107, 067004 (2011)

    Article  ADS  Google Scholar 

  74. L. Longobardi, D. Massarotti, G. Rotoli, D. Stornaiuolo, G. Papari, A. Kawakami, G.P. Pepe, A. Barone, F. Tafuri, Thermal hopping and retrapping of a Brownian particle in the tilted periodic potential of a NbN/MgO/NbN Josephson junction. Phys. Rev. B 84, 184504 (2011)

    Article  ADS  Google Scholar 

  75. Y. Yoon, S. Gasparinetti, M. Mottonen, J.P. Pekola, Capacitively enhanced thermal escape in underdamped Josephson junctions. J. Low Temp. Phys. 163, 164–169 (2011)

    Article  ADS  Google Scholar 

  76. H. Grabert, G.-L. Ingold, B. Paul, Phase diffusion and charging effects in Josephson junctions. Europhys. Lett. 44, 360–366 (1998)

    Article  ADS  Google Scholar 

  77. L. Longobardi, D. Massarotti, D. Stornaiuolo, L. Galletti, G. Rotoli, F. Lombardi, F. Tafuri, Direct transition from quantum escape to a phase diffusion regime in YBaCuO biepitaxial Josephson junctions. Phys. Rev. Lett. 109, 050601 (2012)

    Article  ADS  Google Scholar 

  78. F. Tafuri, J.R. Kirtley, Weak links in high critical temperature superconductors. Rep. Prog. Phys. 68, 2573–2663 (2005)

    Article  ADS  Google Scholar 

  79. Y.V. Fominov, A.A. Golubov, M.Y. Kupriyanov, Decoherence due to nodal quasiparticles in d-wave qubits. Pis’ma v Zh. Eksp. Teor. Fiz. 77, 691–695 (2003); JETP Lett. 77, 587–591 (2003); M.H.S. Amin, A.Y. Smirnov, Quasiparticle Decoherence in d-Wave Superconducting Qubits. Phys. Rev. Lett. 92, 017001 (2004)

    Article  ADS  Google Scholar 

  80. S. Kawabata, S. Kashiwaya, Y. Asano, Y. Tanaka, Macroscopic quantum tunneling and quasiparticle dissipation in d-wave superconductor Josephson junctions. Phys. Rev. B 70, 132505 (2004); S. Kawabata, S. Kashiwaya, Y. Asano, Y. Tanaka, Effect of zero-energy bound states on macroscopic quantum tunneling in high-Tc superconductor junctions. Phys. Rev. B 72, 052506 (2005); T. Yokoyama, S. Kawabata, T. Kato, Y. Tanaka, Theory of macroscopic quantum tunneling in high-T\(_c\) \(c\)-axis Josephson junctions. Phys. Rev. B 76, 134501 (2007)

    Google Scholar 

  81. T. Bauch, F. Lombardi, F. Tafuri, A. Barone, G. Rotoli, P. Delsing, T. Claeson, Macroscopic quantum tunneling in \(d\)-wave YBa\(_{2}\)Cu\(_{3}\)O\(_{7-x}\) Josephson junctions. Phys. Rev. Lett. 94, 087003 (2005)

    Article  ADS  Google Scholar 

  82. T. Bauch, T. Lindström, F. Tafuri, G. Rotoli, P. Delsing, T. Claeson, F. Lombardi, Quantum dynamics of a d-wave Josephson junction. Science 311, 57–60 (2006)

    Article  ADS  Google Scholar 

  83. G. Rotoli, T. Bauch, T. Lindstrom, D. Stornaiuolo, F. Tafuri, F. Lombardi, Classical resonant activation of a Josephson junction embedded in an LC circuit. Phys. Rev. B 75, 144501 (2007)

    Article  ADS  Google Scholar 

  84. S. Kawabata, T. Bauch, T. Kato, Theory of two-dimensional macroscopic quantum tunneling in YBa\(_{2}\)Cu\(_{3}\)O\(_{7-x}\) Josephson junctions coupled to an LC circuit. Phys. Rev. B 80, 174513 (2009)

    Article  ADS  Google Scholar 

  85. D. Massarotti, L. Longobardi, L. Galletti, D. Stornaiuolo, D. Montemurro, G.P. Pepe, G. Rotoli, A. Barone, F. Tafuri, Escape dynamics in moderately damped Josephson junctions. Low Temp. Phys. 38, 263 (2012); Fiz. Nizk. Temp. 38, 336–347 (2012)

    Google Scholar 

  86. D. Massarotti, D. Stornaiuolo, P. Lucignano, L. Galletti, D. Born, G. Rotoli, F. Lombardi, L. Longobardi, A. Tagliacozzo, F. Tafuri, Breakdown of the escape dynamics in Josephson junctions. Phys. Rev. B 92, 054501 (2015)

    Article  ADS  Google Scholar 

  87. D. Stornaiuolo, G. Papari, N. Cennamo, F. Carillo, L. Longobardi, D. Massarotti, A. Barone, F. Tafuri, High quality factor HTS Josephson junctions on low loss substrates. Supercond. Sci. Tech. 24, 045008–045013 (2011)

    Article  ADS  Google Scholar 

  88. D. Stornaiuolo, G. Rotoli, K. Cedergren, D. Born, T. Bauch, F. Lombardi, F. Tafuri, Submicron YBaCuO biepitaxial Josephson junctions: d-wave effects and phase dynamics. J. Appl. Phys. 107, 113901–113606 (2010)

    Article  ADS  Google Scholar 

  89. D. Stornaiuolo, G. Rotoli, D. Massarotti, F. Carillo, L. Longobardi, F. Beltram, F. Tafuri, Resolving the effects of frequency-dependent damping and quantum phase diffusion in YBa\(_{2}\)Cu\(_{3}\)O\(_{7-x}\) Josephson junctions. Phys. Rev. B 87, 134517 (2013)

    Article  ADS  Google Scholar 

  90. E. Il’ichev, M. Grajcar, R. Hlubina, R.P.J. IJsselsteijn, H.E. Hoenig, H.-G. Meyer, A. Golubov, M.H.S. Amin, A.M. Zagoskin, A.N. Omelyanchouk, M.Yu. Kupriyanov, Degenerate ground state in a mesoscopic YBa\(_{2}\)Cu\(_{3}\)O\(_{7-x}\) grain boundary Josephson junction. Phys. Rev. Lett. 86, 5369 (2001)

    Article  ADS  Google Scholar 

  91. A.Y. Tzalenchuk, T. Lindström, S.A. Charlebois, E.A. Stepantsov, Z. Ivanov, A.M. Zagoskin, Mesoscopic Josephson junctions of high-Tc superconductors. Phys. Rev. B 68, 100501 (2003)

    Article  ADS  Google Scholar 

  92. E. Goldobin, D. Koelle, R. Kleiner, A.I. Buzdin, Josephson junctions with second harmonic in the current-phase relation: properties of \(\varphi \) junctions. Phys. Rev. B 76, 224523 (2007)

    Article  ADS  Google Scholar 

  93. K. Inomata, S. Sato, K. Nakajima, A. Tanaka, Y. Takano, H.B. Wang, M. Nagao, H. Hatano, S. Kawabata, Macroscopic quantum tunneling in a d-wave high-Tc BiSrCaCuO superconductor. Phys. Rev. Lett. 95, 107005 (2005)

    Article  ADS  Google Scholar 

  94. X.Y. Jin, J. Lisenfeld, Y. Koval, A. Lukashenko, A.V. Ustinov, P. Mueller, Enhanced macroscopic quantum tunneling in BiSrCaCuO intrinsic Josephson-junction stacks. Phys. Rev. Lett. 96, 177003 (2006)

    Article  ADS  Google Scholar 

  95. P.A. Warburton, A.R. Kuzhakhmetov, G. Burnell, M.G. Blamire, H. Schneidewind, Decoupling of a current-biased intrinsic Josephson junction from its environment. Phys. Rev. B 67, 184513 (2003)

    Article  ADS  Google Scholar 

  96. A. Franz, Y. Koval, D. Vasyukov, P. Müller, H. Schneidewind, D.A. Ryndyk, J. Keller, C. Helm, Thermal fluctuations in ultrasmall intrinsic Josephson junctions. Phys. Rev. B 69, 014506 (2004)

    Article  ADS  Google Scholar 

  97. D. Vion, M. Götz, P. Joyez, D. Esteve, M.H. Devoret, Thermal activation above a dissipation barrier: switching of a small Josephson junction. Phys. Rev. Lett. 77, 3435 (1996)

    Article  ADS  Google Scholar 

  98. P. Joyez, D. Vion, M. Götz, M. Devoret, D. Esteve, The Josephson effect in nanoscale tunnel junctions. J. Supercond. 12, 757–766 (1999)

    Article  ADS  Google Scholar 

  99. M. Iansiti, A.T. Johnson, W.F. Smith, H. Rogalla, C.J. Lobb, M. Tinkham, Charging energy and phase delocalization in single very small Josephson tunnel junctions. Phys. Rev. Lett. 59, 489 (1987); M. Iansiti, M. Tinkham, A.T. Johnson, W.F. Smith, C.J. Lobb, Charging effects and quantum properties of small superconducting tunnel junctions. Phys. Rev. B 39, 6465 (1989)

    Article  ADS  Google Scholar 

  100. J. Ankerhold, Overdamped quantum phase diffusion and charging effects in Josephson junctions. Europhys. Lett. 67, 280–286 (2004)

    Article  ADS  Google Scholar 

  101. U. Weiss, H. Grabert, Quantum diffusion of a particle in a periodic potential with ohmic dissipation. Phys. Lett. 108A, 63–67 (1985)

    Article  ADS  Google Scholar 

  102. J. Ankerhold, H. Grabert, P. Pechukas, Quantum Brownian motion with large friction. Chaos 15, 026106–026115 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  103. P. Hänggi, F. Marchesoni, Artificial Brownian motors: controlling transport on the nanoscale. Rev. Mod. Phys. 81, 387 (2009)

    Article  ADS  Google Scholar 

  104. L. Machura, M. Kostur, P. Talkner, J. Luczka, P. Hänggi, Quantum diffusion in biased washboard potentials: strong friction limit. Phys. Rev. E 73, 031105 (2006)

    Article  ADS  Google Scholar 

  105. B. Jäck, J. Senkpiel, M. Etzkorn, J. Ankerhold, C.R. Ast, K. Kern, Quantum Brownian motion at strong dissipation probed by superconducting tunnel junctions. Phys. Rev. Lett. 119, 147702 (2017)

    Article  ADS  Google Scholar 

  106. F.S. Bergeret, A.F. Volkov, K.B. Efetov, Odd triplet superconductivity and related phenomena in superconductor-ferromagnet structures. Rev. Mod. Phys. 77, 1321 (2005)

    Article  ADS  Google Scholar 

  107. A.I. Buzdin, Proximity effects in superconductor-ferromagnet heterostructures. Rev. Mod. Phys. 77, 935 (2005)

    Article  ADS  Google Scholar 

  108. M. Eschrig, Spin-polarized supercurrents for spintronics. Phys. Today 64, 43–48 (2011)

    Article  ADS  Google Scholar 

  109. J. Linder, J.W.A. Robinson, Superconducting spintronics. Nat. Phys. 11, 307–315 (2015)

    Article  Google Scholar 

  110. K. Senapati, M.G. Blamire, Z.H. Barber, Spin-filter Josephson junctions. Nat. Mater. 10, 849–852 (2011)

    Article  ADS  Google Scholar 

  111. A. Pal, Z.H. Barber, J.W.A. Robinson, M.G. Blamire, Pure second harmonic current-phase relation in spin-filter Josephson junctions. Nat. Commun. 5, 3340 (2014)

    Article  ADS  Google Scholar 

  112. A. Pal, K. Senapati, Z.H. Barber, M.G. Blamire, Electric field dependent spin polarization in GdN spin filter tunnel junctions. Adv. Mater. 25, 5581 (2013)

    Article  Google Scholar 

  113. A.K. Feofanov, V.A. Oboznov, V.V. Bol’ginov, J. Lisenfeld, S. Poletto, V.V. Ryazanov, A.N. Rossolenko, M. Khabipov, D. Balashov, A.B. Zorin, P.N. Dmitriev, V.P. Koshelets, A.V. Ustinov, Implementation of superconductor/ferromagnet/ superconductor \(\pi \)-shifters in superconducting digital and quantum circuits. Nat. Phys. 6, 593–597 (2010)

    Article  Google Scholar 

  114. L. Trifunovic, Long-range superharmonic Josephson current. Phys. Rev. Lett. 107, 047001–047005 (2011)

    Article  ADS  Google Scholar 

  115. C. Richard, M. Houzet, J.S. Meyer, Superharmonic long-range triplet current in a diffusive Josephson junction. Phys. Rev. Lett. 110, 217004–217008 (2013)

    Article  ADS  Google Scholar 

  116. H. Sickinger, A. Lipman, M. Weides, R.G. Mints, H. Kohlstedt, D. Koelle, R. Kleiner, E. Goldobin, Experimental evidence of a \(\varphi \) Josephson junction. Phys. Rev. Lett. 109, 107002 (2012)

    Article  ADS  Google Scholar 

  117. E. Goldobin, R. Kleiner, D. Koelle, R.G. Mints, Phase retrapping in a pointlike \(\varphi \) Josephson junction: the butterfly effect. Phys. Rev. Lett. 111, 057004–057007 (2013)

    Article  ADS  Google Scholar 

  118. R. Menditto, H. Sickinger, M. Weides, H. Kohlstedt, M. Zonda, T. Novotný, D. Koelle, R. Kleiner, E. Goldobin, Phase retrapping in a \(\varphi \) Josephson junction: onset of the butterfly effect. Phys. Rev. B 93, 174506–174512 (2016)

    Article  ADS  Google Scholar 

  119. I. Petković, M. Aprili, Phase dynamics of ferromagnetic Josephson junctions. Phys. Rev. Lett. 102, 157003 (2009)

    Article  ADS  Google Scholar 

  120. H. Courtois, Ph Gandit, D. Mailly, B. Pannetier, Long-range coherence in a mesoscopic metal near a superconducting interface. Phys. Rev. Lett. 76, 130–133 (1996)

    Article  ADS  Google Scholar 

  121. P. Dubos, H. Courtois, B. Pannetier, F.K. Wilhelm, A.D. Zaikin, G. Schön, Josephson critical current in a long mesoscopic S-N-S junction. Phys. Rev. B 63, 064502–064507 (2001)

    Article  ADS  Google Scholar 

  122. A.A. Golubov, M. Kupriyanov, E. Il’Ichev, The current-phase relation in Josephson junctions. Rev. Mod. Phys. 76, 411 (2004)

    Article  ADS  Google Scholar 

  123. D.S. Antonenko, M.A. Skvortsov, Quantum decay of the supercurrent and intrinsic capacitance of Josephson junctions beyond the tunnel limit. Phys. Rev. B 92, 214513 (2015)

    Article  ADS  Google Scholar 

  124. H. Courtois, M. Meschke, J.T. Peltonen, J.P. Pekola, Origin of hysteresis in a proximity Josephson junction. Phys. Rev. Lett. 101, 067002 (2008)

    Article  ADS  Google Scholar 

  125. A.V. Galaktionov, A.D. Zaikin, Fluctuations of the Josephson current and electron-electron interactions in superconducting weak links. Phys. Rev. B 82, 184520–184525 (2010)

    Article  ADS  Google Scholar 

  126. D. Massarotti, N. Banerjee, R. Caruso, G. Rotoli, M.G. Blamire, F. Tafuri, Electrodynamics of Josephson junctions containing strong ferromagnets. Phys. Rev. B 98, 144516 (2018)

    Google Scholar 

  127. J.W.A. Robinson, J.D.S. Witt, M.G. Blamire, Controlled injection of spin-triplet supercurrents into a strong ferromagnet. Science 329, 59–61 (2010)

    Article  ADS  Google Scholar 

  128. G.-H. Lee, D. Jeong, J.-H. Choi, Y.-J. Doh, H.-J. Lee, Electrically tunable macroscopic quantum tunneling in a graphene-based Josephson junction. Phys. Rev. Lett. 107, 146605 (2011)

    Article  ADS  Google Scholar 

  129. L. Angers, F. Chiodi, G. Montambaux, M. Ferrier, S. Gureron, H. Bouchiat, J.C. Cuevas, Proximity dc squids in the long-junction limit. Phys. Rev. B 77, 165408 (2008)

    Article  ADS  Google Scholar 

  130. A.W. Kleinsasser, R.A. Buhrman, High-quality submicron niobium tunnel junctions with reactive-ion-beam oxidation. Appl. Phys. Lett. 37, 841–843 (1980)

    Article  ADS  Google Scholar 

  131. R.E. Miller, W.H. Mallison, A.W. Kleinsasser, K.A. Delin, E.M. Macedo, Niobium trilayer Josephson tunnel junctions with ultrahigh critical current densities. Appl. Phys. Lett. 63, 1423–1425 (1993)

    Article  ADS  Google Scholar 

  132. W.A. Little, Decay of persistent currents in small superconductors. Phys. Rev. 156, 396–403 (1967)

    Article  ADS  Google Scholar 

  133. J.S. Langer, V. Ambegaokar, Intrinsic resistive transition in narrow superconducting channels. Phys. Rev. 164, 498 (1967); D.E. McCumber, B.I. Halperin, Time scale of intrinsic resistive fluctuations in thin superconducting wires. Phys. Rev. B 1, 1054 (1970)

    Article  ADS  Google Scholar 

  134. D.S. Golubev, A.D. Zaikin, Thermally activated phase slips in superconducting nanowires. Phys. Rev. B 78, 144502 (2008)

    Article  ADS  Google Scholar 

  135. N. Shah, D. Pekker, P.M. Goldbart, Inherent stochasticity of superconductor-resistor switching behavior in nanowires. Phys. Rev. Lett. 101, 207001 (2008)

    Article  ADS  Google Scholar 

  136. E. Hoskinson, Y. Sato, I. Hahn, R.E. Packard, Transition from phase slips to the Josephson effect in a superfluid \(^4\)He weak link. Nat. Phys. 2, 23–26 (2006)

    Article  Google Scholar 

  137. K.K. Likharev, Superconducting weak links. Rev. Mod. Phys. 51, 101 (1979)

    Article  ADS  Google Scholar 

  138. A.V. Galaktionov, D.S. Golubev, A.D. Zaikin, Andreev levels as a quantum dissipative environment. Phys. Rev. B 96, 134509 (2017)

    Article  ADS  Google Scholar 

  139. D.S. Golubev, A.D. Zaikin, Anomalous switching current distributions in superconducting weak links. IEEE Trans. Appl. Supercond. 28, 1–5 (2018)

    Article  Google Scholar 

  140. N. Giordano, Evidence for macroscopic quantum tunneling in one-dimensional superconductors. Phys. Rev. Lett. 61, 2137 (1988)

    Article  ADS  Google Scholar 

  141. A. Bezryadin, Superconductivity in Nanowires (Wiley, New York, 2012)

    Book  Google Scholar 

  142. H. Bartlof, Fluctuation Mechanisms in Superconductors (Wiley, New York, 2015)

    Google Scholar 

  143. A. Bezryadin, C.N. Lau, M. Tinkham, Quantum suppression of superconductivity in ultrathin nanowires. Nature 404, 971–974 (2000); C.N. Lau, N. Markovic, M. Bockrath, A. Bezryadin, M. Tinkham, Quantum phase slips in superconducting nanowires. Phys. Rev. Lett. 87, 217003 (2001); M. Tinkham, J.U. Free, C.N. Lau, N. Markovic, Hysteretic I-V curves of superconducting nanowires. Phys. Rev. B 68, 134515 (2003); A. Rogachev, A.T. Bollinger, A. Bezryadin, Influence of high magnetic fields on the superconducting transition of one-dimensional Nb and MoGe nanowires. Phys. Rev. Lett. 94, 017004 (2005)

    Google Scholar 

  144. F. Altomare, A.M. Chang, M.R. Melloch, Y. Hong, C.W. Tu, Evidence for macroscopic quantum tunneling of phase slips in long one-dimensional superconducting Al wires. Phys. Rev. Lett. 97, 017001 (2006); Y. Chen, Y.-H. Lin, S.D. Snyder, A.M. Goldman, A. Kamenev, Dissipative superconducting state of non-equilibrium nanowires. Nat. Phys. 10, 567–571 (2014)

    Google Scholar 

  145. M. Sahu, M.H. Bae, A. Rogachev, D. Pekker, T.C. Wei, N. Shah, P.M. Goldbart, A. Bezryadin, Individual topological tunnelling events of a quantum field probed through their macroscopic consequence. Nat. Phys. 5, 503–508 (2009)

    Article  Google Scholar 

  146. P. Li, P.M. Wu, Y. Bomze, I.V. Borzenets, G. Finkelstein, A.M. Chang, Switching currents limited by single phase slips in one-dimensional superconducting Al nanowires. Phys. Rev. Lett. 107, 137004 (2011)

    Article  ADS  Google Scholar 

  147. P. Li, P.M. Wu, Y. Bomze, I.V. Borzenets, G. Finkelstein, A.M. Chang, Retrapping current, self-heating, and hysteretic current-voltage characteristics in ultranarrow superconducting aluminum nanowires. Phys. Rev. B 84, 184508 (2011)

    Article  ADS  Google Scholar 

  148. X.D.A. Baumans, V.S. Zharinov, E. Raymenants, S.B. Alvarez, J.E. Scheerder, J. Brisbois, D. Massarotti, R. Caruso, F. Tafuri, E. Janssens, V.V. Moshchalkov, J. Van de Vondel, A.V. Silhanek, Statistics of localized phase slips in tunable width planar point contacts. Sci. Rep. 7, 44569 (2017)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica “E.Pancini”, Universitá di Napoli Federico II, Complesso Universitario Monte Sant’Angelo Via Cinthia 26, 80126, Napoli, Italy

    Davide Massarotti & Francesco Tafuri

Authors
  1. Davide Massarotti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francesco Tafuri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Davide Massarotti .

Editor information

Editors and Affiliations

  1. Dipartimento di Fisica “E.Pancini”, Università di Napoli Federico II, Napoli, Italy

    Francesco Tafuri

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Massarotti, D., Tafuri, F. (2019). Phase Dynamics and Macroscopic Quantum Tunneling. In: Tafuri, F. (eds) Fundamentals and Frontiers of the Josephson Effect. Springer Series in Materials Science, vol 286. Springer, Cham. https://doi.org/10.1007/978-3-030-20726-7_11

Download citation

Publish with us

Policies and ethics

Search

Navigation