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The Journal of Chemical Physics

On the molecular phase in coherent control

Sungyul Lee

Published Aug 22, 1997• 19 citations
Publisher

Abstract

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.

DOI
10.1063/1.474632

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Molecular phases are computed near the resonances in the (ω1,ω3) coherent control scheme for excitations to predissociating final states. We show that the phase factors for the one- and three-photon transition amplitudes are identical, giving a vanishing molecular phase, when the intermediate manifolds consist only of discrete states and when the final continuum states do not interact. The phase lag between the dissociation products identically vanishes across the resonance in this case. On the other hand, when there is contribution of the intermediate continuum states, the imaginary part of the three-photon transition operator can give different phase factors for the one- and three-photon transition amplitudes, yielding very important effects of the molecular phase in (ω1,ω3) coherent control. It is also shown that couplings between the final continuum states can give different molecular phase for different product channels in the absence of the effects of the intermediate continuum states, exhibiting the phase lag of the products near resonances. We demonstrate that the phase lag may show minimum near the top of the resonance, as was observed in Gordon and co-workers’ recent observations [Zhu et al., Science 270, 77 (1995)] on the phase lag in HI coherent control experiments, indicating that the observed phase lag is due to the effects of the molecular phase.

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•Jan 1, 2008•0 citations
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.
Molecular phases are computed near the resonances in the (ω1,ω3) coherent control scheme for excitations to predissociating final states. We show that the phase factors for the one- and three-photon transition amplitudes are identical, giving a vanishing molecular phase, when the intermediate manifolds consist only of discrete states and when the final continuum states do not interact. The phase lag between the dissociation products identically vanishes across the resonance in this case. On the other hand, when there is contribution of the intermediate continuum states, the imaginary part of the three-photon transition operator can give different phase factors for the one- and three-photon transition amplitudes, yielding very important effects of the molecular phase in (ω1,ω3) coherent control. It is also shown that couplings between the final continuum states can give different molecular phase for different product channels in the absence of the effects of the intermediate continuum states, exhibiting the phase lag of the products near resonances. We demonstrate that the phase lag may show minimum near the top of the resonance, as was observed in Gordon and co-workers’ recent observations [Zhu et al., Science 270, 77 (1995)] on the phase lag in HI coherent control experiments, indicating that the observed phase lag is due to the effects of the molecular phase.
Coherent control schemes are interference-based procedures for the control of quantum mechanical systems informed by a careful analysis of the physical conditions on interference. In this thesis, the coherent control approach is applied to experimental phase control in the condensed phase. Specifically, coherent control schemes are proposed as mechanisms for experimental manifestations of phase interference. First, a simulation of a ``black box'' feedback control experiment using realistic pulse shaping is shown to automatically find a specific, previously devised coherent control scheme. Qualitative features of experiments performed in this way are reproduced. Second, an analysis of interference in one-photon phase control yields an upper bound on the duration of phase effects. One-photon phase control was previously shown to be possible only over the transient (as opposed to steady-state) value of observables. The bound described here quantifies this statement and provide a rigorous definition of ``transient'' control. We propose that phase control beyond this bound, as reported in a number of weak-field experimental and computational studies, is the result of previously unaccounted for multiphoton effects. Third, we analyze a recent experiment showing phase control of the macroscopic current emanating from living brain cells photostimulated by two-photon absorption. We propose mechanisms for the phase dependence of the current that operate over fifteen orders of magnitude in time, from the femtosecond dynamics of light-matter interactions to the macroscopic dynamics of neuron current. Significantly, coherent control is extended to the case of systems repeatedly interacting with pulses of light; we show that macroscopic control is obtained, in this case, from the multi-pulse accumulation of small phase effects. Research into multiphoton control led to the development of a novel algorithm to compute higher order perturbation theory integrals, presented in the final chapter of this thesis. The Fourier-Laplace Inversion of the Perturbation Theory (FLIPT) method is a highly efficient, numerically exact, ``black box'' integration algorithm. The FLIPT method exploits the specific structure of the multidimensional perturbation theory integrals to obtain an exponential improvement in performance over standard quadrature.
Coherent control provides a quantum interference based method for controlling atomic and molecular dynamics. We report two experimental observations of different ways to achieve such a control in atomic photoionization continuum. One is the photoionization of sodium atoms, initially prepared in the 3P1/2 excited state, by a non resonant three-photon interaction with 1064-nm laser light and by a one-photon interaction with the third-harmonic field, at 355 nm. Interference between the two transition paths allows the control of the total ionization rate by varying the relative phase of the laser fields. The second experiment is the observation of the modification of the ionization continua of xenon through laser induced continuum structure (LICS). The multiphoton radiative decay of the xenon ground state into the two electronic continua, that correspond to the two fine structure levels of the ground state of the xenon ion, is varied by electromagnetically embedding a bound state of the atom into the two continua. Both experiments are performed on an atomic beam apparatus which uses a time-of-flight spectrometer for energy analyzing the emitted photoelectrons.
The phase lag between the ionization and dissociation products of HI and DI molecules obtained by one- and three-photon excitation was measured as a function of excitation energy in the vicinity of a molecular resonance. The phase lag was observed to have an asymmetric profile with a deep minimum near the center of the resonance. A strong isotope effect was also observed. A theoretical analysis, using projection operators to partition the Lippmann-Schwinger equation, showed that a molecular phase is responsible for the energy dependence of the phase lag.
The four-wave mixing produced with two ultrashort phase-locked !-3! laser pulses propagating coherently in a two-level system in the infrared spectral region is shown to depend on the pulses relative phase. The Maxwell-Bloch equations are solved beyond the rotating-wave approximation to account for field frequencies which are largely detuned from the atomic resonance. The relative phase dominating the efficiency of the coupling to the 5! anti-Stokes Raman component is determined by sign of the total ac Stark shift induced in the system, in such a way that the phase influence disappears precisely where the ac Stark effect due to both pulses is compensated. This fundamental quantum interference effect can be the basis for nonlinear ultrafast optical spectroscopy techniques. Phenomena arising from the coherent control of nonlinear interactions are of importance in fields as diverse as optoelectronics and materials research, in high harmonic generation, in photoionization or molecular dissociation, and in biological applications such as spectroscopy and imaging, among others [1, 2, 3, 4, 5, 6, 7]. Optical quantum coherent control is based on the fact that the phases of interfering transition amplitudes in light-matter interactions can be controlled through the optical phase of coherent light sources that drive the interaction, in such a way that the transition rates to final states and the dynamics at various stages of the process can be modified [1]. In a recent paper [8], a theoretical investigation on the quantum coherent control of the optical transient four-wave mixing of two intense phase-locked femtosecond laser pulses of central angular frequencies ω and 3ω propagating in a two-level atom (TLA) was reported. It was shown how the nonlinear (χ (3) ) coupling to the antiStokes Raman field at frequency 5ω depends critically on the initial relative phase φ of the propagating pulses. In Ref. [8], the study was centered to intense pulses in the visible and ultraviolet spectral regions, with frequencies at resonance or lower than the atomic transition. The phenomena observed in [8], however, can be scaled to various laser and material parameters. In the infrared spectral range, for instance, experiments on ultrafast molecular dynamics are frequently performed by help of twocolor pump probe nonlinear spectroscopy techniques. In this type of studies, due to the high intensities inherent to ultrashort (subpicosecond) pulses, nonlinear effects such as stimulated Raman processes may become important and are often utilized as a complementary tool to gain information [9]. In this Letter, we address the conditions for quantum coherent control of transient four-wave mixing interactions with two phase-locked ω-3ω femtosecond laser pulses in the mid-IR spectral region. Our purpose is to reveal the basic physics for a strict two-level medium and to this end the Maxwell-Bloch TLA will be considered. We will study pulses with a duration of 300 fs (with a w 5w