Phase transition in a chain of quantum vortices

We consider interacting vortices in a quasi-one-dimensional array of Joseph son junctions with small capacitance. If the charging energy of a junction is of the order of the Josephson energy, the fluctuations of the supercondu cting order parameter in the system are considerable, and the Vortices beha ve as quantum particles. Their density may be tuned by an external magnetic held, and therefore one can control the commensurability of the one-dimens ional vortex lattice with the lattice of Josephson junctions. We show that the interplay between the quantum nature of a vortex and the long-range int eraction between the vortices leads to the existence of a specific commensu rate-incommensurate transition in a one-dimensional vortex lattice. In the commensurate phase an elementary excitation is a soliton with energy separa ted from the ground state by a finite gap. This gap vanishes in the incomme nsurate phase. Each soliton carries a fraction of a flux quantum; the propa gation of solitons leads to a finite resistance of the array. We find the d ependence of the resistance activation energy on the magnetic field and par ameters of the Josephson array. This energy consists of the above-mentioned gap, and also of a boundary pinning term, which is different in the commen surate and incommensurate phases. The developed theory allows us to explain quantitatively the available experimental data. [S0163-1829(99)00402-6].