Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The Journal of Chemical Physics

Effect of the Gouy phase on the coherent phase control of chemical reactions

Robert J. Gordon, Vishal J. Barge

Published Nov 26, 2007• 13 citations
Publisher

Abstract

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.

DOI
10.1063/1.2787011

Related papers

Coherent control in bulk and nanostructure semiconductors

John E. Sipe, Henry M. van Driel

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.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 23, 1998•0 citations

Coherent radiative control of product yields and quantum state populations in photodissociation

Paul W. Brumer

A method for controlling branching unimolecular reactions, developed in collaboration with M. Shapiro of the Weizmann Institute, which uses the coherence of weak lasers, is presented. It is shown that preselected chemical products may be obtained, in preference to others, by utilizing the interference between naturally occurring processes. Our specific application then entails the dissociation of a bound superposition state with control attained by manipulating the relative intensities and phases of coherent laser beams. Enhanced yields of chemical products of interest are shown to result. Similar control is attainable for the populations of individual product quantum states. Computational results on the I*II branching ratios in the photodissociation of CH3, I and FI are presented as examples. Proposals for experiments which demonstrate coherent control present a challenge to the laser community which is well worth accepting.

International Laser Science Conference•Jan 1, 1986•0 citations

COHERENT CONTROL OF DIRECT AND RESONANT UNIMOLECULAR

Moshe Shapiroa, Paul Brumerb

A General method of controlling branching (direct and resonant) unimolecular reactions, using the coherence of lasers is presented. It is shown that pre-selected products may be obtained, in preference to others, as a result of interference be­ tween decay channels of a superposition of degenerate continuum states. It is shown that such states can be prepared by exciting a superposition of bound states using two coherent light sources with a well defined relative phase. Theoretical limits of coherent control, in direct and compound (statistical like) processes are derived. En­ hanced (often 100%) yields of ~he (chemical) products of interest are obtained. Computational results on the I /1 branching ratios in the photodissociation of FI and CH31, including the effects of initial conditions are presented. In addition, complete blocking-off of a single pre-selected quantum state of a given reaction product, resulting in population inversion with respect to all higher energetic levels, is shown to be attainable.

•Jan 1, 1986•0 citations

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

Robert J. Gordon, Jeanette A. Fiss, Ani Khachatrian +3 more

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.

Advances in multi-photon processes and spectroscopy•Dec 1, 2000•0 citations

Phase lag near the resonances in (ω1,ω3) coherent control

Sungyul Lee

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.

The Journal of Chemical Physics•Mar 8, 1998•15 citations

Multiproduct coherent control of photodissociation via two-photon versus two-photon interference

Zhidang Chen, Paul W. Brumer, Moshe Shapiro

We show that the branching ratios into two or three channel photodissociation products can be controlled by a novel resonant two-photon vs two-photon coherent control scenario. The method allows for control even when the initial molecular system is in a mixed state, e.g., in thermal equilibrium, a significant advance for controlling reactions. Essential to the technique is the phase locking between different frequencies which results in cancellation of incoherences due to laser phase jumps. Reduction of uncontrolled background contributions also obtains. The scenario is demonstrated computationally on Na2 photodissociation, where a wide range of control is achieved over branching into two product channels [Na(3s)+Na(4s) vs Na(3s)+Na(3p)] at lower energies and over three product channels at energies above the Na(3s)+Na(3d) threshold.

The Journal of Chemical Physics•May 1, 1993•47 citations
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.
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.
A method for controlling branching unimolecular reactions, developed in collaboration with M. Shapiro of the Weizmann Institute, which uses the coherence of weak lasers, is presented. It is shown that preselected chemical products may be obtained, in preference to others, by utilizing the interference between naturally occurring processes. Our specific application then entails the dissociation of a bound superposition state with control attained by manipulating the relative intensities and phases of coherent laser beams. Enhanced yields of chemical products of interest are shown to result. Similar control is attainable for the populations of individual product quantum states. Computational results on the I*II branching ratios in the photodissociation of CH3, I and FI are presented as examples. Proposals for experiments which demonstrate coherent control present a challenge to the laser community which is well worth accepting.
A General method of controlling branching (direct and resonant) unimolecular reactions, using the coherence of lasers is presented. It is shown that pre-selected products may be obtained, in preference to others, as a result of interference be­ tween decay channels of a superposition of degenerate continuum states. It is shown that such states can be prepared by exciting a superposition of bound states using two coherent light sources with a well defined relative phase. Theoretical limits of coherent control, in direct and compound (statistical like) processes are derived. En­ hanced (often 100%) yields of ~he (chemical) products of interest are obtained. Computational results on the I /1 branching ratios in the photodissociation of FI and CH31, including the effects of initial conditions are presented. In addition, complete blocking-off of a single pre-selected quantum state of a given reaction product, resulting in population inversion with respect to all higher energetic levels, is shown to be attainable.
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.
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.
We show that the branching ratios into two or three channel photodissociation products can be controlled by a novel resonant two-photon vs two-photon coherent control scenario. The method allows for control even when the initial molecular system is in a mixed state, e.g., in thermal equilibrium, a significant advance for controlling reactions. Essential to the technique is the phase locking between different frequencies which results in cancellation of incoherences due to laser phase jumps. Reduction of uncontrolled background contributions also obtains. The scenario is demonstrated computationally on Na2 photodissociation, where a wide range of control is achieved over branching into two product channels [Na(3s)+Na(4s) vs Na(3s)+Na(3p)] at lower energies and over three product channels at energies above the Na(3s)+Na(3d) threshold.