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

Parametric amplification with weak-link nonlinearity in superconducting microresonators

Nonlinear kinetic inductance in a high Q superconducting coplanar waveguide microresonator can cause a bifurcation of the resonance curve. Near the critical pumping power and frequency for bifurcation, large parametric gain is observed for signals in the frequency band near resonance. We show experimental results on signal and intermodulation gain which are well described by a theory of the parametric amplification based on a Kerr nonlinearity. Phase dependent gain, or signal squeezing, is verified with a homodyne detection scheme.Comment: Submitted to Physica Scripta, topical issue: Nobel Symposium on Quantum Bits, 2009. 10 pages, 5 figures. Version 2 contains a few new sentences about the current-phase relation of weak link