Spectral fingerprints of the non-linear dynamics of driven superconductors with dissipation

We study the out-of-equilibrium dynamics of a BCS superconductor in the presence of a periodic drive with a frequency $\omega_d$ larger than the equilibrium superconducting gap and an external bath providing dissipation. Similar to the dissipationless case, a subset of quasiparticles, resonant with the drive, synchronizes and produces interesting non-linear phenomena. For small dissipation Rabi-Higgs oscillations [Collado et al. Phys. Rev. B 98, 214519 (2018)] can be observed as a transient effect. At long-times in contrast, dissipation leads to a steady state with a population imbalance that increases quadratically for small drives and saturates for large drives as in non-linear quantum optics. We show also that second harmonic generation is allowed for a drive which acts on the BCS coupling constant. We also compute the intensity of time- and angle-resolved photo-emission spectroscopy (tr-ARPES) and time-resolved tunneling spectra. The excited quasiparticle population appears as a decrease (increase) in the photo-emission intensity at energy $-\omega_d/2$ ($+\omega_d/2$) measured from the chemical potential. The tunneling intensity shows a time-dependent depression at $\pm\omega_d/2$ due to the lacking of spectral density and population unbalance causing Pauli blockade. We predict that at short times, compared to the energy relaxation time, both experiments will show oscillations with the Rabi-Higgs frequency.

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