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The Journal of Chemical Physics

Equivalence of the Kobrak–Rice photoselective adiabatic passage and the Brumer–Shapiro strong field methods for control of product formation in a reaction

Mark N. Kobrak, Stuart A. Rice

Published Jul 1, 1998• 63 citations
Publisher

Abstract

It is shown that the photoselective adiabatic passage approach to control of product formation in a chemical reaction proposed by Kobrak and Rice may be viewed as a high-field limit of the strong field Brumer–Shapiro scheme. It is further shown that the adiabatic passage representation provides new insight into the nature of control over chemical reactions in strong fields, and that it correctly predicts the results of physically realistic simulations of the sodium dimer.

DOI
10.1063/1.476550

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It is shown that the photoselective adiabatic passage approach to control of product formation in a chemical reaction proposed by Kobrak and Rice may be viewed as a high-field limit of the strong field Brumer–Shapiro scheme. It is further shown that the adiabatic passage representation provides new insight into the nature of control over chemical reactions in strong fields, and that it correctly predicts the results of physically realistic simulations of the sodium dimer.
Two-pulse selective photochemistry that exploits population transfer via adiabatic passage is considered for the case that there are degenerate product states with different lifetimes. As an example, a four-level model system with a complex symmetric Hamiltonian is constructed. Analytical and numerical studies of this model system demonstrate that extensive control over the product branching ratio can be achieved by detuning either the pump pulse or the Stokes pulse while maintaining negligible population in the intermediate state. This control approach represents a significant simplification of both the Kobrak-Rice extended stimulated Raman adiabatic passage scheme and the Chen-Shapiro-Brumer strong-field control scheme.
In this paper we extend the existing theory of stimulated Raman adiabatic passage (StiRAP) in three-level systems to examine the nature of selective photoexcitation using counterintuitively ordered pulses. Our goal is to develop a version of StiRAP that permits control of product selectivity in a chemical reaction. We analyze the case of selective excitation to one state in a pair of degenerate target states in a four-level system, and find that one cannot control the ratio of the populations in the two states in a resonant two-photon process. However, the extension of the system to include a fifth state and a third laser field makes selective excitation to one of the degenerate states possible. It is found that, subject to reasonable restrictions, one may accomplish complete population transfer to a single target state of a degenerate pair of states in a five-level system.
We describe the exploitation of adiabatic transfer of population between selected states of a molecule as a means for the control of product selectivity in a branching unimolecular reaction. The particular procedures employed to achieve that adiabatic transfer of population depend on the character of the spectrum of states of the molecule; the ones we consider are either extensions of, or are illuminated by, the STIRAP method. The results of studies of efficient selective population of one of a pair of nearly degenerate states in the thiophosgene molecule, and of efficient promotion of the HCN → CNH isomerization reaction, are reported. In the former case the adiabatic population transfer is achieved by use of the Kobrak-Rice extended STIRAP method, while in the latter case it is achieved by use of consecutive STIRAP processes. In both cases the efficiency of selective population transfer is shown to be insensitive to radiative
We present the ability to coherently control triatomic chemical reactions with pulsed-laser techniques. We show that one can control the final state probability distribution of triatomic chemical reactions with nearly 100% selectivity. We develop the population transfer by adiabatic passage theory to coherently control the chemical reaction with the ability of choosing the translational energies of the final reaction products. We also show a new way to achieve the creation of both homonuclear and heteronuclear diatomic molecules at an ultracold temperature using laser catalysis.
Debbie Jin and Jun Ye, in “Polar molecules in the quantum regime” (PHYSICS TODAY, May 2011, page 27), provide an enlightening overview of their recent work on cold molecular gases; they note a significant opportunity to study and manipulate chemical reactions in a regime in which quantum effects are important. In the case of their potassium–rubidium system, they regard the observed reaction KRb + KRb → K2 + Rb2 as being of great interest but also as being a significant impediment to the goal of preparing a quantum gas of oriented KRb molecules.The cold gas that Jin and Ye have created does indeed offer a unique environment to study chemical reactions that are strongly affected by quantum mechanics. One such opportunity, not noted in their article, is the ability to manipulate reaction cross sections by “coherent control.”11. M. Shapiro, P. Brumer, Principles of the Quantum Control of Molecular Processes, Wiley, New York (2003); Quantum Control of Molecular Processes, Wiley-VCH, Weinheim, Germany, in press. In that approach one creates an initial superposition of scattering states that allows control over reaction cross sections through quantum interference.Two coherent control scenarios are worth examining toward the goal of controlling or reducing the KRb + KRb reactive cross section. The first was designed to control cross sections in the scattering of identical diatomic molecules, and the second is a method capable of suppressing reactive scattering by suitable preparation of the initial scattering state. Both are discussed in reference 11. M. Shapiro, P. Brumer, Principles of the Quantum Control of Molecular Processes, Wiley, New York (2003); Quantum Control of Molecular Processes, Wiley-VCH, Weinheim, Germany, in press. .Demonstrating coherent control of collisional processes in the cold KRb gas would contribute greatly to understanding and manipulating chemical reactions on a fundamental quantum level. The use of such control to suppress the KRb + KRb reaction, if successful, would be an added technological benefit on the way to producing the desired quantum gas of oriented molecules.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. M. Shapiro, P. Brumer, Principles of the Quantum Control of Molecular Processes, Wiley, New York (2003); Google ScholarQuantum Control of Molecular Processes, Wiley-VCH, Weinheim, Germany, in press. Google Scholar© 2011 American Institute of Physics.
A previously reported method for shaping electromagnetic field pulses to achieve chemical selectivity is extended and applied to a simple multiple level model system. The pulse shaping approach is based on optimal control theory, where both the time-dependent Schrödinger equation and the constant pulse energy are used as constraints on the variational scheme. A conjugate gradient direction method is used to direct the convergence of the iterative process used to calculate the optimum pulse shape. The method is applied to a five-level system interacting with an optical (laser) field. Results demonstrating selectivity and stability are compared to those of other recent related investigations.