Parity effect in Josephson junction arrays

Abstract

We study the parity effect and transport due to quasiparticles in circuits comprised of many superconducting islands. We develop a general approach and show that it is equivalent to previous methods for describing the parity effect in their more limited regimes of validity. As an example we study transport through linear arrays of Josephson junctions in the limit of negligible Josephson energy and observe the emergence of the parity effect with decreasing number of nonequilibrium quasiparticles. Due to the exponential increase in the number of relevant charge states with increasing length, in multijunction arrays the parity effect manifests in qualitatively different ways to the two-junction..