Study of a cubic cavity resonator for gravitational waves detection in the microwave frequency range

The direct detection of gravitational waves (GWs) of frequencies above MHz has recently received considerable attention. In this work we present a precise study of the reach of a cubic cavity resonator to GWs in the microwave range, using for the first time tools allowing to perform realistic simulations. Concretely, the BI-RME 3D method, which allows to obtain not only the detected power but also the detected voltage (magnitude and phase), is used here. After analyzing three cubic cavities for different frequencies and working simultaneously with three different degenerate modes at each cavity, we conclude that the sensitivity of the experiment is strongly dependent on the polarization and incidence angle of the GW. The presented experiment can reach sensitivities up to $1 \cdot 10^{-19}$ at $100~$MHz, $2 \cdot 10^{-20}$ at $1~$GHz, and $6 \cdot 10^{-19}$ at $10~$GHz for optimal angles and polarizations, and where in all cases we assumed an integration time of $\Delta t=1~$ms. These results provide a strong case for further developing the use of cavities to detect GWs. Moreover, the possibility of analyzing the detected voltage (magnitude and phase) opens a new interferometric detection scheme based on the combination of the detected signals from multiple cavities.