Experimental critical current patterns in Josephson junction ladders

We present an experimental and theoretical study of the magnetic-field dependence of the critical current of Josephson junction ladders. At variance with the well-known case of a one-dimensional (1D) parallel array of Josephson junctions the magnetic-field patterns display a single minimum even for very low values of the self-inductance parameter ${\ensuremath{\beta}}_{\mathrm{L}}.$ Experiments performed changing both the geometrical value of the inductance and the critical current of the junctions show a good agreement with numerical simulations. We argue that the observed magnetic-field patterns are due to a peculiar mapping between the isotropic Josephson ladder and the 1D parallel array with the self-inductance parameter ${\ensuremath{\beta}}_{\mathrm{L}}^{\mathrm{eff}}={\ensuremath{\beta}}_{\mathrm{L}}+2.$