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Advances in multi-photon processes and spectroscopy

WHAT HAVE WE LEARNED FROM THE PHASE LAG IN COHERENT CONTROL EXPERIMENTS?

Robert J. Gordon, Jeanette A. Fiss, Ani Khachatrian, Kaspars Truhins, Langchi Zhu, Tamar Seideman

Published Dec 1, 2000• 0 citations
Publisher

Abstract

In coherent control experiments the product signal intensity is modulated by interference between two excitation paths. This modulation is produced by varying the relative phase of the electromagnetic fields used to excited the target. It is observed that the modulated signals for different channels may be out of phase with respect to each other. The phase lag between different channels is energy dependent and contains information about the dynamics of the system. This paper explores different mechanisms that produce such phase lags and assesses what may be learned from them.

DOI
10.1142/9789812791948_0007

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In coherent control experiments the product signal intensity is modulated by interference between two excitation paths. This modulation is produced by varying the relative phase of the electromagnetic fields used to excited the target. It is observed that the modulated signals for different channels may be out of phase with respect to each other. The phase lag between different channels is energy dependent and contains information about the dynamics of the system. This paper explores different mechanisms that produce such phase lags and assesses what may be learned from them.
The phase lag associated with coherent control by two-pathway excitation in the presence of autoionizing and/or predissociating resonances is studied experimentally and theoretically. For a mixture of HI and DI, the phase lag $\ensuremath{\Delta}\ensuremath{\delta}$ between the two-parent ion signals vanishes to within experimental accuracy, whereas for an HI/H2S\mathrm{HI}/{\mathrm{H}}_{2}\mathrm{S}HI/H2​S mixture, $|\ensuremath{\Delta}\ensuremath{\delta}|$ reaches a maximum in the vicinity of the HI $5s\ensuremath{\sigma}$ resonance. These and previous observations are all explained within a single theoretical model which clarifies the origins of the phase lag in different atomic and molecular systems.
We report the observation of coherent control of the ionization rate in four-photon resonant, five-photon ionization schemes in Kr and Xe. The intermediate resonance is excited via different interfering channels involving four-photon absorption of the fundamental laser frequency ( ionization) as well as one third harmonic and one fundamental frequency photon absorption ( excitation), a particular aspect of the scheme being that interference occurs at a virtual level. By varying the relative phase of the two electromagnetic fields, a large modulation depth has been observed which is due to the chosen non-linear excitation scheme. In the Xe excitation experiment the interference between the different channels could be additionally probed through the modulation of the third-harmonic signal.
Laser light has been used as a probe of atoms, molecules, and solids since the invention of the laser. The use of laser light in a more active role, to modify and process surfaces, and initiate chemical reactions, followed shortly thereafter. But usually it is the intensity and the directionality of the laser light that is employed, not necessarily its coherence, and not particularly the fact that it has a well-defined phase. 'Coherence control' can be broadly understood as the set of processes whereby light modifies matter in a way that is critically dependent on the incident light beams possessing well-defined phases. While in a laser matter is manipulated to produce light of the desired properties, in coherent control light is manipulated -- in particular, its phase and intensity is adjusted -- to produce a material response of the desired type. Of the various coherent control processes that are currently being investigated, some involve a transition in the material medium from an initial state to a final state by two or more possible processes. With each of these is associated a quantum mechanical amplitude, and hence the probability for the transition can show interference effects between the two amplitudes, just as in the familiar two-slit interference experiment the probability for the electron to be observed at a given position involves a probability that is the square of the sum of two amplitudes. In quantum interference control (QUIC), the relative phase of the two amplitudes is adjusted by adjusting the relative phase of two polarizations of a single beam, or the relative phase of two beams at different frequencies. It is this particular type of coherent control that is of interest in this communication.
Systematic analysis is carried out for molecular phase in (ω1,ω3) coherent control scheme. Two mechanisms for nonzero molecular phase are proposed. It is shown that the imaginary part of the three-photon transition operator, which is due to the contribution of the intermediate continuua, can give different phase factors for the one- and three-photon transition amplitudes, yielding very important effects of molecular phase in (ω1,ω3) coherent control. We also show that the interactions between the final continuum states can result in nonzero molecular phase, when the intermediate states are discrete. These findings are discussed in relation to Gordon and co-workers’ recent observations [Zhu et al., Science 270, 77 (1995)] on phase lag.
We show how the spatial phase of a focused laser beam may be used as a tool for controlling the branching ratio of a chemical reaction. Guoy discovered [Acad. Sci., Paris, C. R. 110, 1250 (1890)] that when an electromagnetic wave passes through a focus its phase increases by pi. In a coherent control scheme involving the absorption of n photons of frequency omega(m) and m photons of frequency omega(n), the overall phase shift produced by the Gouy phase is (n-m)pi. At any given point in space, this phase shift is identical for all reaction products. Nevertheless, if the yields for different reaction channels have different intensity dependencies, the Gouy phase produces a net phase lag between the products that varies with the axial coordinate of the laser focus. We obtain here analytical and numerical values of this phase as the laser focus is scanned across the diameter of the molecular beam, taking into account the Rayleigh range and astigmatism of the laser beam and saturation of the transition. We also show that the modulation depth of the interference pattern may be increased by optimizing the relative intensities of the two fields.