  The complex Kohn variational method is extended to compute light-driven
electronic transitions between continuum wavefunctions in atomic and molecular
systems. This development enables the study of multiphoton processes in the
perturbative regime for arbitrary light polarization. As a proof of principle,
we apply the method to compute the photoelectron spectrum arising from the
pump-probe two-photon ionization of helium induced by a sequence of extreme
ultraviolet and infrared-light pulses. We compare several two-photon ionization
pump-probe spectra, resonant with the (2s2p)1P1o Feshbach resonance, with
independent simulations based on the atomic B-spline close- coupling STOCK
code, and find good agreement between the two approaches. This new finite-pulse
perturbative approach is a step towards the ab initio study of weak-field
attosecond processes in poly-electronic molecules.
