We present an experimental and theoretical analysis of the self-and cross-Kerr effect of extended plasma resonances in Josephson junction chains. We calculate the Kerr coefficients by deriving and diagonalizing the Hamiltonian of a linear circuit model for the chain and then adding the Josephson non-linearity as a perturbation. The calculated Kerr-coefficients are compared with the measurement data of a chain of 200 junctions. The Kerr effect manifests itself as a frequency shift that depends linearly on the number of photons in a resonant mode. By changing the input power on a low signal level, we are able to measure this shift. The photon number is calibrated using the self-Kerr shift calculated from the sample parameters. We then compare the measured cross-Kerr shift with the theoretical prediction, using the calibrated photon number.

We present a novel shadow evaporation technique for the realization of junctions and capacitors. The design by e-beam lithography of strongly asymmetric undercuts on a bilayer resist enables in situ fabrication of junctions and capacitors without the use of the well-known suspended bridge (Dolan 1977 Appl. Phys. Lett. 31 337-9). The absence of bridges increases the mechanical robustness of the resist mask as well as the accessible range of the junction size, from 10(-2) µm(2) to more than 10(4) µm(2). We have fabricated Al/AlO(x)/Al Josephson junctions, phase qubit and capacitors using a 100 kV e-beam writer. Although this high voltage enables a precise control of the undercut, implementation using a conventional 20 kV e-beam is also discussed. The phase qubit coherence times, extracted from spectroscopy resonance width, Rabi and Ramsey oscillation decays and energy relaxation measurements, are longer than the ones obtained in our previous samples realized by standard techniques. These results demonstrate the high quality of the junction obtained by this bridge-free technique.