Pulse-Bandwidth Dependence of Coherent Phase Control of Resonance-Mediated (2+1) Three-Photon Absorption

We study in detail coherent phase control of femtosecond resonance-mediated (2+1) three-photon absorption and its dependence on the spectral bandwidth of the excitation pulse. The regime is the weak-field regime of third perturbative order. The corresponding interference mechanism involves a group of three-photon excitation pathways that are on resonance with the intermediate state and a group of three-photon excitation pathways that are near resonant with it. The model system of the study is atomic sodium (Na), for which experimental and numerical-theoretical results are obtained. Prominent among the results is our finding that with simple proper pulse shaping an increase in the excitation bandwidth leads to a corresponding increase in the enhancement of the three-photon absorption over the absorption induced by the (unshaped) transform-limited pulse. For example, here, a 40-nm bandwidth leads to an order-of-magnitude enhancement over the transform-limited absorption.