Sensitivity of a Gigahertz Fabry-P\'erot Resonator for Axion Dark Matter Detection

Axions are hypothetical pseudo-Nambu Goldstone bosons that could explain the observed cold dark matter density and solve the strong CP problem of quantum chromodynamics (QCD). Haloscope experiments commonly employ resonant cavities to search for a conversion of axion dark matter into photons in external magnetic fields. As the expected signal power degrades with increasing frequency, this approach becomes challenging at frequencies beyond tens of Gigahertz. Here, we propose a novel haloscope design based on an open Fabry-P\'erot resonator. Operating a small-scale resonator at cryogenic temperatures and at modest magnetic fields should already lead to an unparalleled sensitivity for photon-axion couplings $g_{a\gamma} \gtrsim 3\times10^{-12}\,\mathrm{GeV}^{-1}$ at 35GHz. We demonstrate how this sensitivity could be further improved using graded-phase mirrors and sketch possibilities to probe benchmark models of the QCD axion.