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

Abstract

The interplay between superconductivity and Coulomb interactions has been studied for more than twenty years now 1-13 . 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 films 5,6 , wires 7 and also in Josephson junction arrays 9,11-13 . The latter 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 fluctuations [14][15][16] . Recently, they have attracted interest as they could provide the basis for the realization of a new type of topologically protected qubit 17,18 or for the implementation of a new current standard 19 . Here we present measurements that show clearly the effect of quantum phase slips on the ground state of a Josephson junction chain. We tune in situ the strength of quantum phase fluctuations and obtain for the first time an excellent agreement with the tight-binding model initially proposed by Matveev et al. 8 .The Hamiltonian for the theoretical description of superconducting circuits can be conveniently obtained by applying Devoret's circuit theory 20 . Here, each electrical element such as an inductance, a capacitor or the Josephson element can add a degree of freedom. In the case of circuits with a small number of electrical elements, 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. 1(a)) can be described by a single degree of freedom. Although the chain is a multi-dimensional 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 lowenergy properties of a Josephson junction chain which have been studied in terms of quantum phase slips by Matveev et al. 8 . Let us consider the Josephson junction chain depicted in Fig. 1(a). The chain contains N junctions and is biased with a phase γ. We denote E J the Josephson energy of a single junction and E C = e 2 2C its charging energy. Here we consider E J E C . Let Q i be the charge on each junction and θ i the phase difference. In the nearest-neighbor-capacitance limit the Hamiltonian can be written as:Ignoring the charging energy for the moment, we find the classical ground state, that satisfies the constraint on the phase N i=1 θ i ...

Insulating Josephson Junction Chains as Pinned Luttinger Liquids

“…The prototypical Bose-Hubbard model without disorder predicts a Beresinskii-KosterlitzThouless quantum phase transition between superfluid and Mott insulator. Experimental implementation using arrays of Josephson junctions has been explored [6][7][8], however, the possibility of the insulating glass has not been considered.One-dimensional arrays of Josephson junctions are notable for application as a fundamental current standard [9,10], which is based on synchronisation of a 'dual' Josephson effect, envisioned to arise from coherent quantum tunnelling of flux quanta, or so-called quantum phase slips [11][12][13][14][15]. Unlike the Mott insulator, the insulating glass is compressible, therefore AC synchronisation of charge may not be possible.…”

Spectroscopic Evidence of the Aharonov-Casher Effect in a Cooper Pair Box

“…The quantum phase slips (QPS) in the junctions can be viewed as the charge-sensitive fluxon tunneling [9,10] provided the conditions discussed below are satisfied. Microwave experiments [11] have demonstrated that dephasing of a fluxonium, a small Josephson junction shunted by a 1D Josephson chain, can be due to the effect of fluctuating charges on the QPS in the chain.…”

Kondo resonance of a microwave photon

“…The superconducting system comprises an artificial spin or double-island charge qubit [7][8][9] interacting with the zero-point fluctuations of two long onedimensional transmission lines envisioned from tunable one-dimensional Josephson junction arrays [10][11][12]. In order to maximize the elastic transmission of a microwave photon, the spin-1/2 object is built from a superconducting double Cooper-pair box where spin up and spin down states refer to the two degenerate charge states (0, 1) and (1, 0), respectively corresponding to one additional Cooper pair on either island [13].…”