Attosecond pulse trains as multi-color coherent control

We present a general description of the interaction between multi-color laser pulses and atoms and molecules, focusing on the experimentally relevant example of infrared (IR) pulses overlapped with attosecond pulse trains (APTs). This formulation reveals explicitly and analytically the role of the delay between the IR pulse and APT as a coherent control parameter. Our formulation also shows the nearly equivalent roles of the delay and the carrier-envelope phase in controlling the interference between different multiphoton pathways. We illustrate these points by investigating the single ionization of He and introduce dressed adiabatic hyperspherical potentials to aid the discussion. We confirm the predictions with a full-dimensional, two-electron solution of the time-dependent Schr\"odinger equation.