Zero-Temperature Casimir Fluctuations and the Limits of Force Microscope Sensitivity

Abstract

It is predicted that in force microscopy the quantum fluctuations responsible for the Casimir force can be directly observed as temperature-independent force fluctuations having spectral density $9\pi /(40\ln (4/e))\hslash \delta k$, where $\hslash$ is Planck's constant and $\delta k$ is the observed change in spring constant as the microscope tip approaches a sample. For typical operating parameters the predicted force noise is of order $10^{-18}$ Newton in one Hertz of bandwidth. The Second Law is respected via the fluctuation-dissipation theorem. For small tip-sample separations the cantilever damping is predicted to increase as temperature is reduced, a behavior that is reminiscent of the Kondo effect.

Revised as submitted to PRL: (a) the predicted fluctuations are 8% larger, due to the correction of a minor algebraic error, (b) additional physical motivation is provided at each step of the calculation, (c) the figure is nicer. RevTeX, four pages, one embedded figure, uses epsf.sty