Superconducting Microwave Detector Technology for Ultra-Light Dark Matter Haloscopes and other Fundamental Physics Experiments: Background Theory (Part I)

We consider how superconducting microwave detector technology might be applied to the readout of cavity-axion haloscopes and similar fundamental physics experiments. Expressions for the sensitivity of two detection schemes are derived: 1) a dispersive spectrometer, and 2) a direct-conversion/homodyne receiver using detectors as mixing elements. In both cases the semi-classical/Poisson-mixture approach is used to account for quantum effects. Preliminary sensitivity calculations are performed to guide future development work. These suggest the homodyne scheme offers a near-term solution for realising near-quantum-noise limited receivers with improved usability compared with parametric amplifiers. Similarly, they show that the dispersive spectrometer offers a potential way to beat the quantum noise limit, but that significant technological development work is needed to do so.