Searches for high frequency gravitational waves using cavities based on the Gertsenshtein effect were recently proposed, building off existing axion dark matter experiments. In particular, the sensitivity of axion dark matter experiments using metamaterial plasmas (tunable plasma haloscopes) to gravitational waves has not been explored in detail. Here we perform a full analysis of gravitational wave detection in plasma haloscopes, showing that the baseline design of experiments such as ALPHA is several orders of magnitude less sensitive than previously thought. We show how simple changes to the experiment can recover that sensitivity and lead to a powerful gravitational wave detector in the order of (10-50) GHz frequency range.
Capdevilla et al. (Tue,) studied this question.