One-dimensional Josephson junction chains (1D-JJs) are paradigmatic systems to tudy the correlations between different elements in superconducting nano-devices realized with several Josephson junctions. Their use has been proposed for the realization of a qubit topologically protected against decoherence , for the realization of a tunable parametric amplifier in narrow frequency ranges , for the realization of a fundamental current standard in quantum metrology , and for designing controlled inductive electromagnetic environments in quantum circuitry.
The quantum ground state of the chain is ruled by the competition between the Josephson effect and the electrostatic interactions which contrast the charge transfer. This effect corresponds to an increase of the quantum fluctuations of the local phase of the condensate on the islands . Indeed, in the thermodynamic limit, the theory predicted a quantum superconductor-insulator phase transition .
However the experimental devices designed for the above-mentioned applications are generally composed by a finite number of superconducting elements. I will discuss the effect of quantum phase fluctuations in 1D-JJ chains of finite length. Some comparisons with experiments will be also presented.
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