  A neutral quantum particle with magnetic moment encircling a static electric
charge acquires a quantum mechanical phase (Aharonov-Casher effect). In
superconducting electronics the neutral particle becomes a fluxon that moves
around superconducting islands connected by Josephson junctions. The full
understanding of this effect in systems of many junctions is crucial for the
design of novel quantum circuits. Here we present measurements and quantitative
analysis of fluxon interference patterns in a six Josephson junction chain. In
this multi-junction circuit the fluxon can encircle any combination of charges
on five superconducting islands, resulting in a complex pattern. We compare the
experimental results with predictions of a simplified model that treats fluxons
as independent excitations and with the results of the full diagonalization of
the quantum problem. Our results demonstrate the accuracy of the fluxon
interference description and the quantum coherence of these arrays.
