Laser-imposed phase in resonant absorption of an isolated attosecond pulse

We calculate resonant absorption line shapes in helium atoms subject to the combination of an attosecond pulse of XUV radiation and a delayed, few-cycle infrared (IR) laser pulse. We are in particular interested in how the resonant features evolve with the delay between the fields and with increasing IR intensity. We first compare the single-atom absorption calculated by a nonperturbative solution of the time-dependent Schr\"odinger equation (TDSE) to a simple model in which the resonant absorption is modified only by a laser-imposed phase (LIP) that originates in the instantaneous ac Stark shift of the resonant state. We find that the LIP model can explain many features of the resonant absorption, including the direction of the resonance energy shift and the onset of dispersive line shapes with increasing IR intensity. We also find, however, that the LIP model predicts the energy shifts and the line shapes only qualitatively when the resonant states are strongly IR coupled to nearby states. We then use a coupled solution of the Maxwell wave equation and the TDSE to examine how the line shapes are modified by propagation effects at helium densities such that the resonant absorption is strong. We find that when the resonant absorption saturates, their line shapes are strongly modified due to reshaping of the attosecond pulse time profile during propagation. This in turn alters the ultrafast absorption and emission dynamics.