Signatures of collective modes in fifth harmonic generation of BCS superconductor

Recent advances in the field of THz spectroscopy allow for controlled experiments to measure signatures of collective excitations in the conventional s-wave superconductor in the fifth harmonic generation current (FHG). Here, we analyze this process theoretically within the Anderson pseudospin formalism and use a periodic multicycle pulse setup, where the driving electromagnetic field points in the direction of a lattice vector. We investigate the interplay of the Higgs mode contribution to the fifth harmonic generation current and compare it to other contributing mechanisms, such as charge density fluctuations (CDF). Similar to the third harmonic generating current we show that the signal in the FHG is also dominated by the CDF. Most importantly, we predict a double peak signature in the frequency dependence of the intensity amplitude of the FHG current with one peak located at Ω = Δ₀ (4Ω = 4Δ₀) and another one at Ω = Δ₀/2 (4Ω = 2Δ₀). The resonant enhancement in the latter case is indicative of the higher order coupling to the Higgs mode or CDF, while the former is reminiscent of the THG describing the coupling of CDF and the Higgs mode with 2 single photons.