Measurement of the Casimir effect under ultrahigh vacuum: Calibration method

Abstract

In this article, the authors present a strategy to measure the Casimir effect with an atomic force microscopy in an ultrahigh vacuum system. The key parameters including the absolute distance, the contact potential difference, and the calibration factor of the probe are determined by electrostatic interaction without contact. The strategy has been developed with the main purpose of performing a reliable relative measurement, that is, comparison of the Casimir force between different surfaces. As an example of the method, the authors estimate the accuracy and the precision of measurements performed on a Au sample.

Casimir Force Contrast Between Amorphous and Crystalline Phases of AIST

“…Prior to the force measurements in AIST films (Figure 2),12, 36 the measurement set‐up was tested by independent force measurements between Au coated spheres and Au thin films. As Figure indicates the force gradient scales qualitatively with separation distance as an average power law $ \nabla F\sim d^{- 3.61}$ .…”

“…Having established that the force set‐up is working properly, to perform a precise comparison of force measurements with theory several parameters have to be determined. These are the starting separation distance Z 0 , for the force measurement (corresponding here to the shortest separation), the cantilever spring constant k, and the contact potential difference V 0 ( Figure ) 36. The electrostatic calibration is performed by measuring the force gradient versus separation distance for two different applied bias voltages V b on the sphere yielding a gap voltage ΔV = V b – V 0 .…”

“…The electrostatic calibration is performed by measuring the force gradient versus separation distance for two different applied bias voltages V b on the sphere yielding a gap voltage ΔV = V b – V 0 . The contact potential V 0 may not be constant11, 36, 39, 40 but instead can depend on the separation distance Z between sphere and sample surface. Before data acquisition, the determination of V 0 is performed at only one distance Z 0 = 42.8 ± 0.5 nm for the amorphous, and Z 0 = 42.9 ± 0.4 nm for the crystalline AIST sample.…”

“…Before data acquisition, the determination of V 0 is performed at only one distance Z 0 = 42.8 ± 0.5 nm for the amorphous, and Z 0 = 42.9 ± 0.4 nm for the crystalline AIST sample. In order to perform the electrostatic calibration V b is then chosen so that ΔV = 0.5 V and ΔV = –0.5 V at Z = Z 0 36. The values of Z 0 and the spring constant k are obtained by fitting the average of the two electrostatic force measurements after subtraction of the Casimir contribution (ΔV = 0 V) 36.…”

Accurate flexural spring constant calibration of colloid probe cantilevers using scanning laser Doppler vibrometry

“…Examples of AFM colloid probes used to measure the physical and chemical interactions between surfaces include measurements of adhesion [2], meniscus forces [3], chemical interactions [4,5], and Casimir forces [6,7]. In these applications, the interest is in accurately measuring these forces; therefore, the spring constant of the cantilever must be accurately known.…”