An improved synthetic signal injection routine for the Haloscope At Yale Sensitive To Axion Cold dark matter (HAYSTAC)

Microwave cavity haloscopes are among the most sensitive direct detection experiments searching for dark matter axions via their coupling to photons. When the power of the expected microwave signal due to axion-photon conversion is on the order of $10^{-24}$~W, having the ability to validate the detector response and analysis procedure by injecting realistic synthetic axion signals becomes helpful. Here we present a method based on frequency hopping spread spectrum for synthesizing axion signals in a microwave cavity haloscope experiment. It allows us to generate a narrow and asymmetric shape in frequency space that mimics an axion's spectral distribution, which is derived from a Maxwell-Boltzmann distribution. In addition, we show that the synthetic axion's power can be calibrated with reference to the system noise. Compared to the synthetic axion injection in HAYSTAC phase I, we demonstrated synthetic signal injection with a more realistic lineshape and calibrated power.