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Confocal Annular Josephson Tunnel Junctions with Large Eccentricity

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Abstract

Confocal annular Josephson tunnel junctions (CAJTJs), which are the natural generalization of the circular annular Josephson tunnel junctions, have a rich nonlinear phenomenology due to the intrinsic non-uniformity of their planar tunnel barrier delimited by two closely spaced confocal ellipses. In the presence of a uniform magnetic field in the barrier plane, the periodically changing width of the elliptical annulus generates a asymmetric double-well for a Josephson vortex trapped in a long and narrow CAJTJ. The preparation and readout of the vortex pinned in one of the two potential minima, which are important for the possible realization of a vortex qubit, have been numerically and experimentally investigated for CAJTJs with the moderate aspect ratio 2:1. In this work, we focus on the impact of the annulus eccentricity on the properties of the vortex potential profile and study the depinning mechanism of a fluxon in more eccentric samples with aspect ratio 4:1. We also discuss the effects of the temperature-dependent losses as well as the influence of the current and magnetic noise.

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References

  1. F. Hund, Significance of molecular spectra. III. Notes on the oscillation and rotation spectra of molecules with more than two nuclei. Z. Phys. 43, 805 (1927)

    Article  ADS  Google Scholar 

  2. M.D. Dennison, G.E. Uhlenbeck, The two-minima problem and the ammonia molecule. Phys. Rev. 41, 313 (1932)

    Article  ADS  MATH  Google Scholar 

  3. E.L. Levy, I. Shomroni, J. Steinhauer, The a.c. and d.c. Josephson effects in a Bose–Einstein condensate. Nature 449, 579 (2007)

    Article  ADS  Google Scholar 

  4. T. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, M.K. Oberthaler, Nonlinear self-trapping of matter waves in periodic potentials. Phys. Rev. Lett. 94, 020403 (2005)

    Article  ADS  Google Scholar 

  5. M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, M.K. Oberthaler, Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction. Phys. Rev. Lett. 95, 010402 (2005)

    Article  ADS  Google Scholar 

  6. Y. Shin, G.B. Jo, M. Saba, T.A. Pasquini, W. Ketterle, D.E. Pritchard, Optical weak link between two spatially separated Bose–Einstein condensates. Phys. Rev. Lett. 95, 170402 (2005)

    Article  ADS  Google Scholar 

  7. B.V. Hall, S. Whitlock, R. Anderson, P. Hannaford, A.I. Sidorov, Condensate splitting in an asymmetric double well for atom chip based sensors. Phys. Rev. Lett. 98, 030402 (2007)

    Article  ADS  Google Scholar 

  8. Y. Makhlin, G. Schön, A. Shnirman, Josephson-junction qubits with controlled couplings. Nature 398, 305 (1999)

    Article  ADS  Google Scholar 

  9. J.E. Mooij, T.P. Orlando, L. Levitov, T. Tian, C.H. van derWal, S. Lloyd, Josephson persistent-current qubit. Nature 285, 1036 (1999)

    Google Scholar 

  10. J.R. Friedman, V. Patel, W. Chen, S.K. Tolpygo, J.E. Lukens, Quantum superposition of distinct macroscopic states. Science 406, 43 (2000)

    Google Scholar 

  11. J.Q. You, J.S. Tsai, F. Nori, Scalable quantum computing with Josephson charge qubits. Phys. Rev. Lett. 89, 197902 (2002)

    Article  ADS  Google Scholar 

  12. Y. Yu, S.Y. Han, X. Chu, S.I. Chu, Z. Wang, Coherent temporal oscillations of macroscopic quantum states in a Josephson junction. Science 296, 889 (2002)

    Article  ADS  Google Scholar 

  13. A. Wallraff, Y. Koval, M. Levitchev, M.V. Fistul, A.V. Ustinov, Annular long Josephson junctions in a magnetic field: engineering and probing the fluxon interaction potential. J. Low Temp. Phys. 118, 543 (2000)

    Article  ADS  Google Scholar 

  14. A. Wallraff, A. Lukashenko, J. Lisenfeld, A. Kemp, M.V. Fistul, Y. Koval, A.V. Ustinov, Quantum dynamics of a single vortex. Nature 425, 155 (2003)

    Article  ADS  Google Scholar 

  15. T. Kato, M. Imada, Macroscopic quantum tunneling of a fluxon in a long Josephson junction. J. Phys. Soc. Jpn. 64, 2963 (1996)

    Article  ADS  Google Scholar 

  16. J.H. Kim, R.P. Dhungana, K.-S. Park, Decoherence in Josephson vortex quantum bits: Long-Josephson-junction approach to a two-state system. Phys. Rev. B 73, 214506 (2006)

    Article  ADS  Google Scholar 

  17. E. Goldobin, A. Sterck, D. Koelle, Josephson vortex in a ratchet potential: theory. Phys. Rev. E 63, 031111 (2001)

    Article  ADS  Google Scholar 

  18. C. Nappi, S. Pagano, Fluxon dynamics in non uniform width Josephson transmission lines, in National Workshop on Nonlinear Dynamics, ed. by M. Costato, A. Degasperis, M. Milani (Italian Physical Society, Bologna, 1995), p. 261

    Google Scholar 

  19. A. Benabdallah, J.G. Caputo, A.C. Scott, Exponentially tapered Josephson flux-flow oscillator. Phys. Rev. B 54, 16139 (1996)

    Article  ADS  Google Scholar 

  20. R. Monaco, Confocal annular Josephson tunnel junctions. J. Low Temp. Phys. 184, 979 (2016)

    Article  ADS  Google Scholar 

  21. A. Davidson, B. Dueholm, B. Kryger, N.F. Pedersen, Experimental investigation of trapped sine-Gordon solitons. Phys. Rev. Lett. 55, 2059 (1985)

    Article  ADS  Google Scholar 

  22. A. Davidson, B. Dueholm, N.F. Pedersen, Experiments on soliton motion in annular Josephson-junctions. J. Appl. Phys. 60, 1447 (1986)

    Article  ADS  Google Scholar 

  23. A.V. Ustinov, T. Doderer, R.P. Huebener, N.F. Pedersen, B. Mayer, V.A. Oboznov, Dynamics of sine-Gordon solitons in the annular Josephson junction. Phys. Rev. Lett. 69, 1815 (1992)

    Article  ADS  Google Scholar 

  24. N. Grönbech-Jensen, P.S. Lomdahl, M.R. Samuelsen, Phase-locking of long annular Josephson-junctions coupled to an external RF magnetic-field. Phys. Lett. A 154, 14 (1991)

    Article  ADS  Google Scholar 

  25. A.V. Ustinov, Observation of a radiation-induced soliton resonance in a Josephson ring. JETP Lett. 64, 191 (1996)

    Article  ADS  Google Scholar 

  26. N. Martucciello, J. Mygind, V.P. Koshelets, A.V. Shchukin, L.V. Filippenko, R. Monaco, Fluxon dynamics in long annular Josephson tunnel junctions. Phys. Rev. B 57, 5444 (1998)

    Article  ADS  Google Scholar 

  27. R. Monaco, Engineering double-well potentials with variable-width annular Josephson tunnel junctions. J. Phys. Condens. Matter 28, 445702 (2016)

    Article  Google Scholar 

  28. R. Monaco, J. Mygind, V.P. Koshelets, Development of a Josephson vortex twostate system based on a confocal annular Josephson junction. Supercond. Sci. Technol. 31, 025003 (2018)

    Article  ADS  Google Scholar 

  29. N. Martucciello, R. Monaco, Annular Josephson tunnel junctions in an external magnetic field: the statics. Phys. Rev. B 53, 3471 (1996)

    Article  ADS  Google Scholar 

  30. N. Martucciello, C. Soriano, R. Monaco, Annular Josephson tunnel junctions in an external magnetic field: the dynamics. Phys. Rev. B 55, 15157 (1997)

    Article  ADS  Google Scholar 

  31. D.W. McLaughlin, A.C. Scott, Perturbation analysis of fluxon dynamics. Phys. Rev. A 18, 1652 (1978)

    Article  ADS  Google Scholar 

  32. J.C. Swihart, Field solution for a thin-film superconducting strip transmission line. J. Appl. Phys. 21, 461–469 (1961)

    Article  ADS  Google Scholar 

  33. R.L. Peterson, J.W. Ekin, Critical-current diffraction patterns of grain-boundary Josephson weak links. Phys. Rev. B 42, 8014 (1990)

    Article  ADS  Google Scholar 

  34. C. Nappi, R. Monaco, Critical current diffraction pattern of elliptic annular Josephson tunnel junctions. Physica C 520, 36 (2016)

    Article  Google Scholar 

  35. G. Carapella, F. Russo, R. Latempa, G. Costabile, Preparation and readout of a Josephson vortex in a double-well potential. Phys. Rev. B 70, 092502 (2004)

    Article  ADS  Google Scholar 

  36. R. Cristiano, L. Frunzio, R. Monaco, C. Nappi, S. Pagano, Investigation of subgap structures in high-quality Nb/AlOx/Nb tunnel-junctions. Phys. Rev. B 49, 429 (1994)

    Article  ADS  Google Scholar 

  37. N.F. Pedersen, D. Welner, Analytical results for the fluxon-antifluxon annihilation process in Josephson-junctions. Phys. Rev. B 29, 2551 (1985)

    Article  ADS  Google Scholar 

  38. M. Lisitskiy, D. Massarotti, L. Galletti, L. Longobardi, G. Rotoli, M. Russo, F. Tafuri, B. Ruggiero, Bias current ramp rate dependence of the crossover temperature from Kramers to phase diffusion switching in moderately damped NbN/AlN/NbN Josephson junctions. J. Appl. Phys. 116, 043905 (2014)

    Article  ADS  Google Scholar 

  39. A.N. Price, A. Kemp, D.R. Gulevich, F.V. Kusmartsev, A.V. Ustinov, Vortex qubit based on an annular Josephson junction containing a microshort. Phys. Rev. B 81, 014506 (2010)

    Article  ADS  Google Scholar 

  40. A fluxon can be depinned by both a positive or a negative bias current; for the negative depinning currents, \(\gamma _{d-}^{L,R}\), it was found that \(\gamma _{d-}(h_{||})= -\gamma _{d+}(-h_{||})\) and \(\gamma _{d-}(h_{\bot })= -\gamma _{d+}(h_{\bot })\). It follows that the determination of the fluxon state can also be accomplished through the measurement of a negative current switch

  41. R. Monaco, M. Aaroe, J. Mygind, R.J. Rivers, V.P. Koshelets, Experiments on spontaneous vortex formation in Josephson tunnel junctions. Phys. Rev. B 74, 144513 (2006)

    Article  ADS  Google Scholar 

  42. R. Monaco, M. Aaroe, J. Mygind, R.J. Rivers, V.P. Koshelets, Spontaneous fluxon production in annular Josephson tunnel junctions in the presence of a magnetic field. Phys. Rev. B 77, 054509 (2008)

    Article  ADS  Google Scholar 

  43. L.V. Filippenko, S.V. Shitov, P.N. Dmitriev, A.B. Ermakov, V.P. Koshelets, J.R. Gao, Integrated superconducting receiver: fabrication and yield. IEEE Trans. Appl. Supercond. 11, 816 (2001)

    Article  ADS  Google Scholar 

  44. R. Monaco, V.P. Koshelets, A. Mukhortova, J. Mygind, Self-field effects in window-type Josephson tunnel junctions. Supercond. Sci. Technol. 26, 055021 (2013)

    Article  ADS  Google Scholar 

  45. S. Pagano, M.P. Soerensen, P.L. Christiansen, R.D. Parmentier, Stability of fluxon motion in long Josephson-junctions at high bias. Phys. Rev. B 38, 4677 (1988)

    Article  ADS  Google Scholar 

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Acknowledgements

RM and JM acknowledge the support from the Danish Council for Strategic Research under the program the Danish National Research Foundation (bigQ). LVF acknowledges support from the Russian Foundation for Basic Research, 416 Grant No. 17-52-12051.

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Authors and Affiliations

  1. CNR-ISASI, Institute of Applied Sciences and Intelligent Systems “E. Caianello”, Comprensorio Olivetti, 80078, Pozzuoli, Italy

    Roberto Monaco

  2. DTU Physics, B309, Technical University of Denmark, 2800, Lyngby, Denmark

    Jesper Mygind

  3. Kotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Mokhovaya 11, Bldg 7, Moscow, Russia, 125009

    Lyudmila V. Filippenko

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  1. Roberto Monaco
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Correspondence to Roberto Monaco.

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Monaco, R., Mygind, J. & Filippenko, L.V. Confocal Annular Josephson Tunnel Junctions with Large Eccentricity. J Low Temp Phys 192, 315–329 (2018). https://doi.org/10.1007/s10909-018-1977-1

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  • DOI: https://doi.org/10.1007/s10909-018-1977-1

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