The parity effect in Josephson junction arrays

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 non-equilibrium quasiparticles. Due to the exponential increase in the number of relevant charge states with increasing length, in multi-junction arrays the parity effect manifests in qualitatively different ways to the two junction case. The role of charge disorder is also studied as this hides much of the parity physics which would otherwise be observed. Nonetheless, we see that the current through a multi-junction array at low bias is limited by the formation of meta-stable even-parity states.