Casimir force inadequacy in explaining a strong attractive force in a micrometer-sized narrow-gap re-entrant cavity

TL;DR

This paper questions whether the Casimir force can explain the strong attractive force observed in a micrometer-sized narrow-gap re-entrant cavity, finding that the Casimir effect is too weak to account for the experimental results.

Contribution

The study provides detailed calculations showing the Casimir force is insufficient to explain the observed attraction, suggesting the need for alternative explanations.

Findings

Casimir force is orders of magnitude weaker than observed force

Observed force scales roughly with gap size as x^{-4}

Casimir effect cannot account for the strong attraction

Abstract

Pate et al. \cite{pate} investigated a macroscopic opto-mechanical system with a narrow-gap re-entrant cavity coupled to a SiN membrane resonator coated with Au or Nb. They observed a significant increase in the membrane's effective spring constant $k_{\rm eff}$ for sub-2-micron gaps $x$. This increase scales roughly with $x^{-4}$, suggesting an attractive force pulling the membrane towards the re-entrant Al post, with an $x^{-3}$ dependence. Attributing this force solely to the thermal Casimir effect is challenged by our detailed calculations (presented below). These calculations reveal that the Casimir force, at the investigated gap sizes, is orders of magnitude weaker than the observed force. This significant discrepancy necessitates an alternative explanation for the observed attraction.