# On the Casimir effect between superconductors

## TL;DR

This paper calculates the Casimir effect between superconductors, showing the transition effect is too small to detect with current experiments but could be observed with improved sensitivity and different material configurations.

## Contribution

It provides theoretical predictions for the Casimir force change during superconducting transition and suggests experimental setups to observe this effect.

## Key findings

- Transition effect is over 250 times smaller than current experimental sensitivity.
- Using a Au-NbTiN cavity could enhance the effect to detectable levels.
- An order of magnitude increase in sensitivity could enable observation of the transition effect.

## Abstract

A recent experiment [R. A. Norte et al. Phys. Rev. Lett. {\bf 121}, 030405 (2018)] probed the variation of the Casimir force between two closely spaced thin Al films, as they transition into a superconducting state, observing a null result. We present here computations of the Casimir effect for superconductors, based on the Mattis-Bardeen formula for their optical response. We show that for the Al cavity used in the experiment the effect of the transition is over two hundred and fifty times smaller than the experimental sensitivity, in agreement with the observed null result. We demonstrate that a large enhancement of the effect can be achieved by using a cavity consisting of a Au mirror and a superconducting NbTiN film. We estimate that the effect of the superconducting transition would be observable with the proposed Au-NbTiN configuration, if the sensitivity of the apparatus could be increased by an order of magnitude.