  We present an alternative approach to pump-probe spectroscopy for measuring
fast charge dynamics with an atomic force microscope (AFM). Our approach is
based on coherent multifrequency lock-in measurement of the intermodulation
between a mechanical drive and an optical or electrical excitation. In response
to the excitation, the charge dynamics of the sample is reconstructed by
fitting a theoretical model to the measured frequency spectrum of the
electrostatic force near resonance of the AFM cantilever. We discuss the time
resolution, which in theory is limited only by the measurement time, but in
practice is of order one nanosecond for standard cantilevers and imaging
speeds. We verify the method with simulations and demonstrate it with a control
experiment, achieving a time resolution of $20~\mathrm{ns}$ in ambient
conditions, limited by thermal noise.
