  Recent developments in the techniques of ultrafast pump-probe photoemission
have made possible the search for collective modes in strongly correlated
systems out of equilibrium. Including inelastic scattering processes and a
retarded interaction, we simulate time- and angle- resolved photoemission
spectroscopy (trARPES) to study the amplitude mode of a d-wave superconductor,
a collective mode excited through the nonlinear light-matter coupling to the
pump pulse. We find that the amplitude mode oscillations of the d-wave order
parameter occur in phase at a single frequency that is twice the
quasi-steady-state maximum gap size after pumping. We comment on the necessary
conditions for detecting the amplitude mode in trARPES experiments.
