Polarimetric searches for axion dark matter and high-frequency gravitational waves using optical cavities

We revisit birefringence effects associated with the evolution of the polarization of light as it propagates through axion dark matter or the background of a passing gravitational wave (GW). We demonstrate that this can be described by a unified formalism, highlighting a synergy between searches for axions and high-frequency GWs. We show that by exploiting this framework, the optical cavities used by the ALPS II experiment can potentially probe axion masses in the range $m_a \sim 10^{-9} - 10^{-6} \, \mathrm{eV}$, offering competitive sensitivity with existing laboratory and astrophysical searches. Also building on this approach, we propose using these optical cavities to search for high-frequency GWs by measuring changes in the polarization of their laser. This makes it a promising method for exploring, in the near future, GWs with frequencies above $100$ MHz and strain sensitivities on the order of $10^{-14} \, \mathrm{Hz}^{-1/2}$. Such sensitivity allows the exploration of currently unconstrained parameter space, complementing other high-frequency GW experiments. This work contributes to the growing community investigating novel approaches for high-frequency GW detection.