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arXiv:quant-ph/0405010 · Physical Review Letters

Coherent Control of Resonance-Mediated Reactions: F+HD

Vlado Zeman, Moshe Shapiro, Paul W. Brumer

Published Apr 2, 2004• 39 citations
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Abstract

Cross sections resulting from scattering that proceeds via an intermediate resonance are shown to be exceptionally controllable using a coherent superposition of only two initial states. Full quantum computations on F+HD(v=0;j=0,1)-->H+DF, D+HF, which exhibits a resonance in one of the reactive channels, support the formal arguments, showing that control is indeed vast. In this case the ratio of reactive integral cross sections can be altered by a factor of 62 (compared to a noncoherent factor of only 3.3), while the ratio of reactive differential cross sections can be altered by a factor of over 6000 (compared to a noncoherent factor of less than 7). These results constitute the first prediction of extensive quantum control in a collisional process.

DOI
10.1103/physrevlett.92.133204

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Cross sections resulting from scattering that proceeds via an intermediate resonance are shown to be exceptionally controllable using a coherent superposition of only two initial states. Full quantum computations on F+HD(v=0;j=0,1)-->H+DF, D+HF, which exhibits a resonance in one of the reactive channels, support the formal arguments, showing that control is indeed vast. In this case the ratio of reactive integral cross sections can be altered by a factor of 62 (compared to a noncoherent factor of only 3.3), while the ratio of reactive differential cross sections can be altered by a factor of over 6000 (compared to a noncoherent factor of less than 7). These results constitute the first prediction of extensive quantum control in a collisional process.
Fundamental entanglement related challenges have prevented quantum-interference-based control (i.e., coherent control) of collisional cross sections from being implemented in the laboratory. Here, differential cross sections for reactive scattering at low temperatures are shown to provide a unique opportunity to display such interference-based control by forming coherent superpositions of degenerate rotational states of reactant molecules $|jm\ensuremath{\rangle}$ with different mmm. In particular, we identify and quantify a unique signature of coherent control in reactive scattering with applications to $\mathrm{F}+ {\mathrm{H}}_{2}\ensuremath{\rightarrow}$ H +HF+\mathrm{HF}+HF and HF +++ D $\ensuremath{\leftarrow}$ F $+\mathrm{HD} \ensuremath{\rightarrow}\mathrm{HD} +$ F at 11K11\phantom{\rule{4pt}{0ex}}\mathrm{K}11K. Control is shown to be extensive.
We show that quantum interference-based coherent control is a highly efficient tool for tuning ultracold molecular collision dynamics that is free from the limitations of commonly used methods that rely on external electromagnetic fields. By varying the relative populations and phases of initial coherent superpositions of degenerate molecular states, we demonstrate complete coherent control over integral scattering cross sections in the ultracold s-wave regime of both the initial and final collision channels. The proposed control methodology is applied to ultracold O_{2}+O_{2} collisions, showing extensive control over s-wave spin-exchange cross sections and product branching ratios over many orders of magnitude.
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.
We explore coherent control of Penning and associative ionization in cold collisions of metastable He∗(23S){\mathrm{He}}^{*}(2{\phantom{\rule{4pt}{0ex}}}^{3}S)He∗(23S) atoms via the quantum interference between different states of the He2∗{\mathrm{He}}_{2}^{*}He2∗​ collision complex. By tuning the preparation coefficients of the initial atomic spin states, we can benefit from the quantum interference between molecular channels to maximize or minimize the cross sections for Penning and associative ionization. In particular, we find that we can enhance the ionization ratio by 30% in the cold regime. This work is significant for the coherent control of chemical reactions in the cold and ultracold regimes.
The optical theorem is a fundamental aspect of quantum scattering theory. Here, we generalize this theorem to the case where the incident scattering state is a superposition of internal states of the collision partners, introducing additional interference contributions and, e.g., providing a route to control the total integral cross section. As in its standard form, forward scattering plays an essential role in the generalized optical theorem, but with interference terms being related to the inelastic forward scattering amplitudes between states in the initial superposition. Using the resultant control index, we show that extensive control is possible over ultracold collisions of oxygen molecules in their rovibrational ground states, and of 85Rb-85Rb collisions, promising systems for the first experimental demonstration of the quantum interference control of the total scattering cross section.
The optical theorem is a fundamental aspect of quantum scattering theory. Here, we generalize this theorem to the case where the incident scattering state is a superposition of internal states of the collision partners, introducing additional interference contributions and, e.g., providing a route to control the total integral cross section. As in its standard form, forward scattering plays an essential role in the multichannel optical theorem, but with interference terms being related to the inelastic forward scattering amplitudes between states in the initial superposition. Using the resultant control index, we show that extensive control is possible over ultracold collisions of oxygen molecules in their rovibrational ground states, and of $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{85}\mathrm{Rb}$ collisions, promising systems for the experimental demonstration of the quantum interference control of the total scattering cross section.