Reducing the frequency of the Higgs mode in a helical superconductor coupled to an LC-circuit

We show that the amplitude, or Higgs mode of a superconductor with strong spin-orbit coupling and an exchange field, couples linearly to the electromagnetic field. Furthermore, by coupling such a superconductor to an LC resonator, we demonstrate that the Higgs resonance becomes a regular mode at frequencies smaller than the quasiparticle energy threshold $2\Delta$. We finally propose and discuss a possible experiment based on microwave spectroscopy for an unequivocal detection of the Higgs mode. Our approach may allow visualizing Higgs modes also in more complicated multiband superconductors with a coupling between the charge and other electronic degrees of freedom.