Probing an ultralight QCD axion with electromagnetic quadratic interaction

The axion-gluon coupling is the defining feature of the QCD axion. This feature induces additional and qualitatively different interactions of the axion with standard model particles-quadratic couplings. Previously, hadronic quadratic couplings have been studied and experimental implications have been explored especially in the context of atomic spectroscopy and interferometry. We investigate additional quadratic couplings to the electromagnetic field and electron mass. These electromagnetic quadratic couplings are generated at the loop level from threshold corrections and are expected to be present in the absence of fine-tuning. While they are generally loop-suppressed compared to the hadronic ones, they open up new ways to search for the QCD axion, for instance via optical atomic clocks. Moreover, due to the velocity spread of the dark matter field, the quadratic nature of the coupling leads to low-frequency stochastic fluctuations. These distinctive low-frequency fluctuations offer a new way to search for heavier axions. We provide an analytic expression for the power spectral density of this low-frequency background and briefly discuss experimental strategies for a low-frequency stochastic background search.