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 ...
An on-demand single-photon source is a key element in a series of prospective quantum technologies and applications. Here we demonstrate the operation of a tuneable on-demand microwave photon source based on a fully controllable superconducting artificial atom strongly coupled to an open-ended transmission line. The atom emits a photon upon excitation by a short microwave π-pulse applied through a control line. The intrinsically limited device efficiency is estimated to be in the range 65–80% in a wide frequency range from 7.75 to 10.5 GHz continuously tuned by an external magnetic field. The actual demonstrated efficiency is also affected by the excited state preparation, which is about 90% in our experiments. The single-photon generation from the single-photon source is additionally confirmed by anti-bunching in the second-order correlation function. The source may have important applications in quantum communication, quantum information processing and sensing.
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