  We theoretically study the pump-probe response of nonequilibrium BCS
superconductors coupled to optical phonons. For ultrashort pump pulses a
nonadiabatic regime emerges, which is characterized by oscillations of the
superconducting order parameter as well as by the generation of coherent
phonons. Using the density-matrix formalism, we compute the pump-probe response
in the nonadiabatic regime of the coupled Bogoliubov quasiparticle-phonon
system and determine the signatures of the order parameter and of the phonon
oscillations in the pump-probe conductivity. We find that the nonadiabatic
dynamics of the BCS superconductor reflects itself in oscillations of the
pump-probe response as functions of delay time between pump and probe pulses.
We argue that from the analysis of this oscillatory behavior both frequency and
decay time of the algebraically decaying order-parameter oscillations can be
inferred. Similarly, the coherent phonons are evidenced in the pump-probe
conductivity by oscillations with the frequency of the phonons. Remarkably, we
find that the oscillatory response in the pump-probe conductivity is resonantly
enhanced when the frequency of the order-parameter oscillations is tuned to the
phonon energy.
