A mode of atomic force microscopy (AFM) is demonstrated where an oscillating AFM cantilever having linear response is driven with two frequencies in the vicinity of a resonance. New frequencies in the response, known as intermodulation products, are generated when the linearity of the cantilever response is perturbed by the nonlinear tip-surface interaction. A rich structure of the intermodulation products is observed as a function of the probe-surface separation, indicating that it is possible to extract much more detailed information about the tip-surface interaction than is possible with the standard amplitude and phase imaging methods.
Experimental investigations of the nonlinear properties of superconducting niobium coplanar waveguide resonators are reported. The nonlinearity due to a current dependent kinetic inductance of the center conductor is strong enough to realize bifurcation of the nonlinear oscillator. When driven with two frequencies near the threshold for bifurcation, parametric amplification with a gain of +22.4 dB is observed.
Knowledge of surface forces is the key to understanding a large number of processes in fields ranging from physics to material science and biology. The most common method to study surfaces is dynamic atomic force microscopy (AFM). Dynamic AFM has been enormously successful in imaging surface topography, even to atomic resolution, but the force between the AFM tip and the surface remains unknown during imaging. Here we present a new approach that combines high-accuracy force measurements and high-resolution scanning. The method, called amplitude-dependence force spectroscopy (ADFS), is based on the amplitude dependence of the cantilever's response near resonance and allows for separate determination of both conservative and dissipative tip-surface interactions. We use ADFS to quantitatively study and map the nano-mechanical interaction between the AFM tip and heterogeneous polymer surfaces. ADFS is compatible with commercial atomic force microscopes and we anticipate its widespread use in taking AFM toward quantitative microscopy.
We describe a method of analysis which allows for reconstructing the nonlinear disturbance of a high Q harmonic oscillator. When the oscillator is driven with two or more frequencies, the nonlinearity causes intermodulation of the drives, resulting in a complicated spectral response. Analysis of this spectrum allows one to approximate the nonlinearity. The method, which is generally applicable to measurements based on resonant detection, increases the information content of the measurement without requiring a large detection bandwidth, and optimally uses the enhanced sensitivity near resonance to extract information and minimize error due to detector noise.
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