WHAT ROLE CAN FOUR-WAVE MIXING TECHNIQUES PLAY IN COHERENT CONTROL?

Abstract

The role of four-wave mixing (FWM) techniques in coherent control is considered from the point of view of some of the most important developments in this field over the past years, namely multiphoton excitation, pump-dump methods, interference between coherent pulses, chirped laser pulses, and optimal control. FWM techniques provide a powerful platform for combining coherently multiple laser pulses. We explore the effectiveness of these techniques in controlling chemical reactions. The phase relationship between the pulses is maintained by detecting the signal in a phase-matching direction. The results presented show control over the observed dynamics from ground and excited state populations. The FWM signal results from the polarization of the sample following three different electric field interactions. The virtual echo sequence is achieved by the interactions of the sample with three consecutive electric fields characterized by exp[i(kx-ω t)], exp[-i(kx-ω t)] and exp[i(kx-ω t)]. This sequence allows control over the observed ground or excited state dynamics. With the photon echo pulse sequence, characterized by interactions with exp[-i(kx-ω t)], exp[i(kx-ω t)], and exp[i(kx-ω t)], we find that control of ground and excited state populations is not achieved. Differences between these two pulse sequences are shown experimentally and illustrated using wave packet simulations. Data obtained using the ‘mode suppression’ technique, in which the timing between the first and third laser pulses is fixed while the second pulse is scanned are presented. We show that this technique does not suppress the observed vibrational coherence from the ground or excited state but it yields an additional component to the signal that is independent of the vibrational coherence of the sample. Spectrally dispersed FWM is shown to be an ideal tool for studying intramolecular dynamics and this idea is applied to understanding the role of chirp in controlling molecule-laser interactions. All coherent control methods are affected by the rate of decoherence of the sample. Here we show how these rates are measured with FWM techniques. The measurements presented here illustrate how photon echo measurements yield the homogeneous relaxation rate while the virtual echo measurements yield the sum between homogeneous and inhomogeneous