Nonlinear Atomic Force Microscopy: Squeezing and Skewness of Micro-Mechanical Oscillators interacting with a Surface

TL;DR

This paper introduces a two-frequency driving scheme in atomic force microscopy that enhances tip-sample interaction and predicts classical squeezing and skewness in the cantilever's phase space, with implications for quantum effects.

Contribution

It presents a novel two-frequency driving approach and a stochastic model predicting classical squeezing and skewness, along with a method to distinguish quantum effects from thermal noise.

Findings

Large classical squeezing of the tip's phase space predicted.

Surface-dependent dissipation may induce quantum effects.

Close contact enhances position squeezing, van der Waals forces enable momentum squeezing.

Abstract

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.