Coherent dynamics and pump-probe spectra of BCS superconductors

The density matrix formalism is employed to calculate pump-probe spectra of BCS superconductors in the coherent regime. Two dynamical regimes, one adiabatic and one nonadiabatic, can be clearly distinguished. In the adiabatic regime, the modulus of the BCS order parameter can be identified with half the gap in the probe spectra. In the nonadiabatic regime, the order parameter oscillates in real time, whereas the gap observed in the spectra reflects its temporal average. The transition between these regimes is accompanied by a qualitative change of the intensity dependence of the dynamical gap renormalization. Furthermore, a hole-burning effect occurs if the spectral shape of the pump pulse is sufficiently sharp. A probe pulse preceding the pump pulse leads to spectral oscillations, and both the gap before and after the pump pulse are visible in the probe spectra.