Haldane Gap and Fractional Oscillations in Gated Josephson Arrays

An analogy between the twisted quantum xxz model and a gated Josephson junction array is used to predict sharp structure in the critical currents versus gate voltage, and fractional ac Josephson frequencies. We prove selection rules for level crossings which imply fractional periodicities of ground states with varying Aharonov-Bohm flux. Extrapolated numerical diagonalization on ladders indicates a Haldane gap at moderate easy-plane anisotropy, with vanishing superfluid stiffness. Physical parameters for experimental realization of these novel effects are proposed.