Projected Sensitivity of DMRadio-m$^3$: A Search for the QCD Axion Below $1\,\mu$eV

The QCD axion is one of the most compelling candidates to explain the dark matter abundance of the universe. With its extremely small mass ($\ll 1\,\mathrm{eV}/c^2$), axion dark matter interacts as a classical field rather than a particle. Its coupling to photons leads to a modification of Maxwell's equations that can be measured with extremely sensitive readout circuits. DMRadio-m$^3$ is a next-generation search for axion dark matter below $1\,\mu$eV using a $>4$ T static magnetic field, a coaxial inductive pickup, a tunable LC resonator, and a DC-SQUID readout. It is designed to search for QCD axion dark matter over the range $20\,\mathrm{neV}\lesssim m_ac^2\lesssim 800\,\mathrm{neV}$ ($5\,\mathrm{MHz}