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

The interplay between superconductivity and Coulomb interactions has been studied for more than 20 years now1–13. 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 arrays4,9,11–13. 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 fluctuations14–16. 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. In superconducting circuits, each electrical element such as an inductor, a capacitor or the Josephson element can add a degree of freedom. In the case of small circuits, by applying Devoret’s circuit theory20, a complete analytical description that takes into account all degrees of freedom can be obtained. However, when the circuits contain an increasing number of elements, as for example Josephson junction chains, even numerical solutions of the problem become difficult to obtain when taking into account all degrees of freedom. Nevertheless, our measurements demonstrate that the ground state of a phase-biased Josephson junction chain (see Fig. 1a) can be described by a single degree of freedom. Although the chain is a multidimensional object, the effect of quantum phase slips can be described by a single variable,m, that counts the number of phase slips in the chain. We start by giving a short introduction on the low-energy properties of a Josephson junction chain analysed in terms of quantum phase slips8. Let us consider the Josephson junction chain shown in Fig. 1a. The chain contains N junctions and is biased with a phase γ . We denote EJ the Josephson energy of a single junction and EC = e2/2C its charging energy. Here we consider EJ EC. Let Qi be the charge on each junction and θi the phase difference. In the nearest-neighbour-capacitance limit, the Hamiltonian can be written as: