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Coherent quantum phase slip


A hundred years after the discovery of superconductivity, one fundamental prediction of the theory, coherent quantum phase slip (CQPS), has not been observed. CQPS is a phenomenon exactly dual1 to the Josephson effect; whereas the latter is a coherent transfer of charges between superconducting leads2,3, the former is a coherent transfer of vortices or fluxes across a superconducting wire. In contrast to previously reported observations4,5,6,7,8 of incoherent phase slip, CQPS has been only a subject of theoretical study9,10,11,12. Its experimental demonstration is made difficult by quasiparticle dissipation due to gapless excitations in nanowires or in vortex cores. This difficulty might be overcome by using certain strongly disordered superconductors near the superconductor–insulator transition. Here we report direct observation of CQPS in a narrow segment of a superconducting loop made of strongly disordered indium oxide; the effect is made manifest through the superposition of quantum states with different numbers of flux quanta13. As with the Josephson effect, our observation should lead to new applications in superconducting electronics and quantum metrology1,10,11.

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Figure 1: The device.
Figure 2: Experimental data.
Figure 3: Spectroscopy of the system across a wide range of flux and frequency.


  1. 1

    Mooij, J. E. & Nazarov Superconducting nanowires as quantum phase-slip junctions. Nature Phys. 2, 169–172 (2006)

    ADS  CAS  Article  Google Scholar 

  2. 2

    Tinkham, M. Introduction to Superconductivity (McGraw-Hill, 1996)

    Google Scholar 

  3. 3

    Averin, D. V., Zorin, A. B. & Likharev, K. K. Bloch oscillations in small Josephson junction. Zh. Eksp. Teor. Fiz. 88, 407–412 (1984)

    Google Scholar 

  4. 4

    Giordano, N. Evidence for macroscopic quantum tunnelling in one-dimensional superconductors. Phys. Rev. Lett. 61, 2137–2140 (1988)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Bezryadin, A., Lau, C. N. & Tinkham, M. Quantum suppression of superconductivity in ultrathin nanowires. Nature 404, 971–974 (2000)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Zgirski, M., Riikonen, K.-P., Touboltsev, V. & Arutyunov Yu, K. Quantum fluctuations in ultranarrow superconducting aluminum nanowires. Phys. Rev. B 77, 054508 (2008)

    ADS  Article  Google Scholar 

  7. 7

    Lehtinen, J. S., Sajavaara, T., Arutyunov, K., Yu & Vasiliev, A. Evidence of quantum phase slip effect in titanium nanowires. Preprint at 〈〉 (2011)

  8. 8

    Hongisto, T. T. & Zorin, A. B. Single charge transistor based on superconducting nanowire in high impedance environment. Phys. Rev. Lett. 108, 097001 (2012)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Matveev, K. A., Larkin, A. I. & Glazman, L. I. Persistent current in superconducting nanorings. Phys. Rev. Lett. 89, 096802 (2002)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Hriscu, A. M. & Nazarov Model of a proposed superconducting phase slip oscillator: A method for obtaining few-photon nonlinearities. Phys. Rev. Lett. 106, 077004 (2011)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Hriscu, A. M. & Nazarov Coulomb blockade due to quantum phase-slips illustrated with devices. Phys. Rev. B 83, 174511 (2011)

    ADS  Article  Google Scholar 

  12. 12

    Vanevic, M. & Nazarov Quantum phase slips in superconducting wires with weak links. Preprint at 〈〉 (2011)

  13. 13

    Mooij, J. E. & Harmans, C. J. P. M. Phase-slip flux qubits. N. J. Phys. 7, 219 (2005)

    MathSciNet  Article  Google Scholar 

  14. 14

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

    ADS  CAS  Article  Google Scholar 

  15. 15

    Arutyunov, K., Golubev, D. S. & Zaikin, A. D. Superconductivity in one dimension. Phys. Rep. 464, 1–70 (2008)

    ADS  Article  Google Scholar 

  16. 16

    Manucharyan, V. E. et al. Phys. Rev. B 85, 024521 (2012)

    ADS  Article  Google Scholar 

  17. 17

    Pop, I. M. et al. Experimental demonstration of Aharonov-Casher interference in a Josephson junction circuit. Preprint at 〈〉 (2011)

  18. 18

    Arutyunov, K., Hongisto, T. T., Lehtinen, J. S., Leino, L. I. & Vasiliev, A. L. Quantum phase-slip phenomenon in ultra-narrow superconducting nanorings. Sci. Rep. 2, 293 (2012)

    ADS  Article  Google Scholar 

  19. 19

    Astafiev, O. et al. Resonance fluorescence of a single artificial atom. Science 327, 840–843 (2010)

    ADS  CAS  Article  Google Scholar 

  20. 20

    Zaikin, A. D., Golubev, D. S., van Otterlo, A. & Zimanyi, G. T. Quantum phase slips and transport in ultrathin superconducting wires. Phys. Rev. Lett. 78, 1552–1555 (1997)

    ADS  CAS  Article  Google Scholar 

  21. 21

    Golubev, D. S. & Zaikin, A. D. Quantum tunneling of the order parameter in superconducting nanowires. Phys. Rev. B 014504 (2001)

  22. 22

    Finkel’stein, A. M. Suppression of superconductivity in homogeneously disordered systems. Physica B 197, 636–648 (1994)

    ADS  Article  Google Scholar 

  23. 23

    Feigel'man, M. V., Ioffe, L. B., Kravtsov, V. E. & Cuevas, E. Fractal superconductivity near localization threshold. Ann. Phys. 325, 1390–1478 (2010)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Feigel'man, M. V., Ioffe, L. B., Kravtsov, V. E. & Yuzbashyan, E. A. Eigenfunction fractality and pseudogap state near the superconductor-insulator transition. Phys. Rev. Lett. 98, 027001 (2007)

    ADS  CAS  Article  Google Scholar 

  25. 25

    Feigel'man, M. V., Ioffe, L. B. & Mezard, M. Superconductor-insulator transition and energy localization. Phys. Rev. B 82, 184534 (2010)

    ADS  Article  Google Scholar 

  26. 26

    Sacépé, B. et al. Localization of preformed Cooper pairs in disordered superconductors. Nature Phys. 7, 239–244 (2011)

    ADS  Article  Google Scholar 

  27. 27

    Sacépé, B. et al. Pseudogap in a thin film of a conventional superconductor. Nature Commun. 1, 140 (2010)

    Article  Google Scholar 

  28. 28

    Johansson, A., Sambandamurthy, G., Shahar, D., Jacobson, N. & Tenne, R. Nanowire acting as superconducting quantum device. Phys. Rev. Lett. 95, 116805 (2005)

    ADS  CAS  Article  Google Scholar 

  29. 29

    Wallraff, A. et al. Approaching unit visibility for control of a superconducting qubit with dispersive readout. Phys. Rev. Lett. 95, 060501 (2005)

    ADS  CAS  Article  Google Scholar 

  30. 30

    Abdumalikov, A. A., Astafiev, O. V., Nakamura, Y., Pashkin & Tsai, J. S. Vacuum Rabi splitting due to strong coupling of a flux qubit and a coplanar-waveguide resonator. Phys. Rev. B 78, 180502 (2008)

    ADS  Article  Google Scholar 

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We are grateful to M. Feigel’man, J. Mooij and Y. Nazarov for discussions. This work was supported by Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST), MEXT KAKENHI “Quantum Cybernetics”, Ministry of Science and Education of Russian Federation grant 2010-1.5-508-005-037. L.B.I. was supported by ARO W911NF-09-1-0395, DARPA HR0011-09-1- 0009 and NIRT ECS-0608842. D.S. and O.C. were supported by Minerva Fund.

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O.V.A. planned the experiment, designed and fabricated the samples, performed measurements and data analysis. L.B.I. came up with the idea of using materials close to the SIT and provided theoretical support. S.K. fabricated the sample and contributed to understanding the data . Yu.A.P. participated in discussions of the experiment. K.Yu.A. triggered the research direction and suggested the realization of the phase-slip qubit. D.S. and O.C. fabricated the InO x films. J.S.T. discussed the data and provided support for the work within the FIRST and KAKENHI projects. O.V.A. wrote the manuscript with feedback from all authors, including significant contributions from L.B.I. and K.Yu.A.

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Correspondence to O. V. Astafiev.

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The authors declare no competing financial interests.

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Astafiev, O., Ioffe, L., Kafanov, S. et al. Coherent quantum phase slip. Nature 484, 355–358 (2012).

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