Josephson junction transmission lines as tunable artificial crystals

We investigate one-dimensional Josephson junction arrays with generalized unit cells as a circuit approach to engineer microwave band gaps. An array described by a lattice with a basis can be designed to have a gap in the electromagnetic spectrum, in full analogy to electronic band gaps in diatomic or many-atomic crystals. We derive the dependence of this gap on the array parameters in the linear regime, and suggest experimentally feasible designs to bring the gap below the single junction plasma frequency. The gap can be tuned in a wide frequency range by applying external flux, and it persists in the presence of small imperfections.Comment: 9 pages, 5 figure

The Role of Nonlinear Dynamics in Quantitative Atomic Force Microscopy

Various methods of force measurement with the Atomic Force Microscope (AFM) are compared for their ability to accurately determine the tip-surface force from analysis of the nonlinear cantilever motion. It is explained how intermodulation, or the frequency mixing of multiple drive tones by the nonlinear tip-surface force, can be used to concentrate the nonlinear motion in a narrow band of frequency near the cantilevers fundamental resonance, where accuracy and sensitivity of force measurement are greatest. Two different methods for reconstructing tip-surface forces from intermodulation spectra are explained. The reconstruction of both conservative and dissipative tip-surface interactions from intermodulation spectra are demonstrated on simulated data.Comment: 25 pages (preprint, double space) 7 figure