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Chapter 16: Design of Femtosecond Pulse Sequences to Control Reactions

Animation — Courtesy of Yaron silberberg
Multiple pathway Interference. Feynman's path integral approach to quantum mechanics leads naturally to thinking of quantum interference as arising from multiple dynamical paths that lead from the same initial to the same final state. The simplest example involves an initial state, two intermediate states, and a single final state. By controlling the phase with which each of the two intermediate states contributes to the final state, one may control constructive vs. destructive interference in the final states. This is the basis of the Brumer-Shapiro approach to coherent control. With advances in the technology of amplitude and phase shaping of femtosecond pulses, one can have a virtual infinity of interfering pathways, all ending up at the same final state. The figure below shows a schematic energy-level diagrams of nonresonant, two-photon processes. Note that there is a continuum of pairs of frequencies under the pulse envelope such that the two photon resonance frequency. The existence of multiple paths to the same final state that can all be excited by the same pulse envelope gives rise to the possibility of quantum interference and a rich assortment of coherent control strategies. The movie shows the Fourier transform relationship between the frequency-sculpted spectrum (left), the temporal pulse sequence , (right), and the two-photon power spectrum (bottom).
The movie assumes that , where , is increasing linearly in time, and H is the Heaviside function.

open in new window — Courtesy of Yaron silberberg
Multiple pathway Interference. Feynman's path integral approach to quantum mechanics leads naturally to thinking of quantum interference as arising from multiple dynamical paths that lead from the same initial to the same final state. The simplest example involves an initial state, two intermediate states, and a single final state. By controlling the phase with which each of the two intermediate states contributes to the final state, one may control constructive vs. destructive interference in the final states. This is the basis of the Brumer-Shapiro approach to coherent control. With advances in the technology of amplitude and phase shaping of femtosecond pulses, one can have a virtual infinity of interfering pathways, all ending up at the same final state. The figure below shows a schematic energy-level diagrams of nonresonant, two-photon processes. Note that there is a continuum of pairs of frequencies under the pulse envelope such that the two photon resonance frequency. The existence of multiple paths to the same final state that can all be excited by the same pulse envelope gives rise to the possibility of quantum interference and a rich assortment of coherent control strategies. The movie shows the Fourier transform relationship between the frequency-sculpted spectrum (left), the temporal pulse sequence , (right), and the two-photon power spectrum (bottom).
The movie assumes that , where , is increasing linearly in time, and H is the Heaviside function.