Impedance matching to axion dark matter: Considerations of the photon-electron interaction

We introduce the concept of impedance matching to axion dark matter by posing the question of why axion detection is difficult, even though there is enough power in each square meter of incident dark-matter flux to energize a LED light bulb. By quantifying backreaction on the axion field, we show that a small axion-photon coupling does not by itself prevent an order-unity fraction of the dark matter from being absorbed through optimal impedance match. We further show, in contrast, that the electromagnetic charges and the self-impedance of their coupling to photons provide the principal constraint on power absorption integrated across a search band. Using the equations of axion electrodynamics, we demonstrate stringent limitations on absorbed power in linear, time-invariant, passive receivers. Our results yield fundamental constraints, arising from the photon-electron interaction, on improving integrated power absorption beyond the cavity haloscope technique. The analysis also has significant practical implications, showing apparent tension with the sensitivity projections for a number of planned axion searches. We additionally provide a basis for more accurate signal power calculations and calibration models, especially for receivers using multi-wavelength open configurations such as dish antennas and dielectric haloscopes.