Measurement of the effect of quantum phase slips in a Josephson junction chain

Journal name:
Nature Physics
Year published:
Published online

The interplay between superconductivity and Coulomb interactions has been studied for more than 20 years now1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. In low-dimensional systems, superconductivity degrades in the presence of Coulomb repulsion: interactions tend to suppress fluctuations of charge, thereby increasing fluctuations of phase. This can lead to the occurrence of a superconducting–insulator transition, as has been observed in thin superconducting films5, 6, wires7 and also in Josephson junction arrays4, 9, 11, 12, 13. The last of these are very attractive systems, as they enable a relatively easy control of the relevant energies involved in the competition between superconductivity and Coulomb interactions. Josephson junction chains have been successfully used to create particular electromagnetic environments for the reduction of charge fluctuations14, 15, 16. Recently, they have attracted interest as they could provide the basis for the realization of a new type of topologically protected qubit17, 18 or for the implementation of a new current standard19. Here we present quantitative measurements of quantum phase slips in the ground state of a Josephson junction chain. We tune in situ the strength of quantum phase fluctuations and obtain an excellent agreement with the tight-binding model initially proposed by Matveev and colleagues8.

At a glance


  1. Graphic representations describing the effect of phase slips in a six-junction chain, the resulting chain/'s energy and supercurrent and the measurement principle.
    Figure 1: Graphic representations describing the effect of phase slips in a six-junction chain, the resulting chain’s energy and supercurrent and the measurement principle.

    a, Schematic picture of the phase-biased Josephson junction chain. b, Representation of a phase slip in the chain. The filled diamonds show the initial configuration. The open diamonds show the phase configuration after a 2π flip of the phase on the third junction θ3. c, Energy levels of a Josephson junction chain with N=6 as a function of bias phase γ for different ratios EJ/EC. For EJ/EC=20 (black lines) no splitting is visible at the crossing points. For EJ/EC=3 (red lines) a gap emerges that increases rapidly with decreasing EJ/EC. The blue lines show the energy levels for EJ/EC=1.3. For each EJ/EC, the two lowest-lying states have been calculated by numerical diagonalization of the Hamiltonian (1). d, Current–phase relation for the ground state Eg(γ) for the same EJ/EC ratios as in c. The supercurrent is calculated from the derivative of the energy band: iS=(2e/planck)(Eg/γ). The chain current is reported in units of the critical current of a single chain junction i0=(2e/planck)EJ. e, Schematic picture of the chain shunted by the read-out junction. f, Escape potential for the Josephson junction chain with EJ/EC=3 in parallel with the read-out junction for three different flux biases φC in the read-out loop (see Fig. 2). The ground state of the chain clearly modifies the escape potential of the read-out junction.

  2. Measurement circuit.
    Figure 2: Measurement circuit.

    The six-SQUID chain is inserted in a superconducting loop. The flux ΦC created by on-chip coils controls the phase difference γ over the chain. The flux ΦS through the SQUIDs can be controlled independently by a second coil. We denote the phase difference over the read-out junction δ.

  3. Measured switching current (black diamonds) as a function of [phi]C over the chain for three different EJ/EC ratios.
    Figure 3: Measured switching current (black diamonds) as a function of φC over the chain for three different EJ/EC ratios.

    The measurement noise for each point is about 0.2 nA. The red lines represent theoretical calculations for the switching current using equations (3) and (2).

  4. Comparison between the measured and the calculated switching-current amplitude as a function of the EJ/EC ratio.
    Figure 4: Comparison between the measured and the calculated switching-current amplitude as a function of the EJ/EC ratio.

    Black diamonds: measured; red open circles: calculated. Note that the switching-current amplitude is divided by the flux-dependent critical current of a single SQUID i0, to reveal the effect of quantum-phase fluctuations. The top curve (blue open circles) shows the theoretical calculation of the switching-current amplitude in the absence of quantum phase fluctuations. The lines are guides for the eye.


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  1. Institut Néel, C.N.R.S. and Université Joseph Fourier, BP 166, 38042 Grenoble-cedex 9, France

    • I. M. Pop,
    • F. Lecocq,
    • Z. Peng,
    • B. Pannetier,
    • O. Buisson &
    • W. Guichard
  2. L. D. Landau Institute for Theoretical Physics, Kosygin street 2, Moscow 119334, Russia

    • I. Protopopov
  3. Institut fuer Nanotechnologie, Karlsruher Institut fuer Technologie, 76021 Karlsruhe, Germany

    • I. Protopopov


I.M.P. fabricated the sample and carried out the experiments. I.M.P., B.P., O.B. and W.G. designed the experiment, analysed the data and wrote the paper. I.M.P. and I.P. carried out the numerical calculations. Z.P. and F.L. contributed to the carrying out of experiments and sample fabrication. W.G. supervised the project. All authors discussed the results and commented on the manuscript at all stages.

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