Intermodulation in a superconducting radio-frequency cavity

Nitrogen-doped Niobium superconducting radio-frequency (SRF) cavities have the ultrahigh quality factor Q ~ 10⁹ – 10¹¹ and accelerating gradients up to 45 MV/m at the resonant frequencies f ~ 50 MHz – 4 GHz, and is expected to be applied to accelerators and quantum detectors to capture physics beyond the standard model. Recently, Bogorad et al. theoretically proposed a method for detecting axions and two photon interaction of low-energy quantum electrodynamics, i.e. the Euler-Heisenberg (EH) term, by measuring intermodulation in an SRF cavity [1]. The effective axion and EH current densities have cubic terms for the electromagnetic fields. Therefore, it is possible to generate intermodulation at frequency 2ω₁-ω₂ due to their cubic nonlinearity in an SRF cavity simultaneously pumped with two resonant frequencies ω₁ and ω₂.

There is another contribution from a cavity wall to intermodulation in an SRF cavity since supercurrents also have a cubic term for the vector potential [2]. This is called the nonlinear Meissner (NLM) effect, and has been performed several studies, both theoretical and experimental. Therefore, we calculate the number of signal photons at intermodulation frequency due to the NLM effect by solving the quasiclassical equations of superconductivity with Maxwell's equations, and discuss impact of the NLM effect on the axion and EH signals in Bogorad's setup [1].

[1] Z. Bogorad et al., Phys. Rev. Lett. 123, 021801 (2019).

[2] J. A. Sauls, Prog. Theor. Exp. Phys. 2022, 033I03 (2022).