  We propose a two-frequency driving scheme in dynamic atomic force microscopy
that maximizes the interaction time between tip and sample. Using a stochastic
description of the cantilever dynamics, we predict large classical squeezing
and a small amount of skewness of the tip's phase-space probability
distribution. Strong position squeezing will require close contact between tip
and surface, while momentum squeezing would also be possible in the van der
Waals region of the tip-surface force. Employing a generalized Caldeira-Leggett
model, we predict that surface-dependent dissipative forces may be the dominant
source of quantum effects and propose a procedure to isolate quantum effects
from thermal fluctuations.
