Coherent control of multiphoton transitions with femtosecond pulse shaping

We explore the effects of ultrafast shaped pulses for two-level systems that do not have a single-photon resonance, by developing a multiphoton density-matrix approach. We take advantage of the fact that the dynamics of the intermediate virtual states are absent within our laser pulse time scales. Under these conditions, the multiphoton results are similar to those for a single photon, and it is possible to extend the single-photon coherent control ideas to develop multiphoton coherent control.