How interference reveals geometric phase

doi:10.1126/science.abb9148

GSTDTAP > 气候变化

DOI	10.1126/science.abb9148
	How interference reveals geometric phase
	F. Javier Aoiz
	2020-05-15
发表期刊	Science
出版年	2020
英文摘要	The paths that particles take underlie many interesting quantum phenomena, including the Berry phase effect or geometric phase (GP) effect ([ 1 ][1]). In chemical reactions, GP manifests near a conical intersection (CI) connecting two potential energy surfaces (PESs). If the nuclei complete a closed path around a CI, the electronic wave function changes sign, forcing a change of sign of the nuclear wave function so that the total wave function remains single-valued, and this fact has nontrivial effects on dynamics ([ 2 ][2]–[ 7 ][3]). On page 767 of this issue, Xie et al. ([ 8 ][4]) provide experimental evidence of the GP effect in the hydrogen exchange reaction, H + HD → H2 + D, at energies well below the CI. Oscillatory structure in the energy dependence of backscattering at specific final states is caused by interference between two distinct topological paths to the same products, one surmounting a single transition state and another that encircles the CI after overcoming two transition states. Interference between different pathways is a fascinating quantum phenomenon that may be best exemplified by the double-slit experiment, first conducted by Young with light more than 200 years ago and later carried out with electrons, neutrons, and even heavy molecules such as fullerenes. As Feynman pointed out, “The double-slit experiment has in it the heart of quantum mechanics. In reality, it contains the only mystery, the basic peculiarities of all quantum mechanics” ([ 9 ][5]). As in those experiments, it can be expected that whenever two different paths (or trajectories) described by different wave functions lead to the same final state, interference between them will manifest as an oscillatory pattern as a function of a measurable quantity ([ 10 ][6]). The hydrogen exchange reaction exhibits a CI between the ground-state and first-excited-state PESs at a total energy of 2.75 eV and has become a benchmark system for studying both theoretically and experimentally the effect of GP on the reaction dynamics. However, GP has been elusive, and the search for experimental evidence has been challenging and even fruitless until recently. In previous work ([ 11 ][7]), the same group demonstrated convincing experimental evidence of GP in the H + HD → H2 + D reaction by measuring the H2 product state–resolved angular distribution at the collision energy of 2.77 eV, which relative to H2 at equilibrium is a total energy 0.24 eV above the CI. The high angular and energy resolution made it possible to discern strong oscillations in the forward-scattering region (0° to 30°)—that is, in the direction of the incoming H atom. ![Figure][8] Interfering paths Two reaction pathways for the H + HD reaction are shown schematically on a sketch of the potential energy surface in hyperspherical coordinates. Although the contribution of path 2 to the total reactivity is almost negligible at the energies investigated by Xie et al. , it gives rise to a strong interference with path 1 at backward-scattering angles and causes a characteristic oscillatory pattern with energy. GRAPHIC: A. KITTERMAN/ SCIENCE Although nongeometric phase (NGP) calculations also predict sharp oscillations, they could not reproduce the observed oscillation patterns, which were clearly out of phase. However, when GP was incorporated into the theoretical treatment, the agreement with the experimental result was excellent. Moreover, the authors carried out rigorous nonadiabatic calculations that coupled the ground-state and first-excited-state PESs that showed an almost perfect agreement with the GP treatment and with the experimental oscillatory structure ([ 11 ][7]). In principle, the higher the energy, the more likely would be the detection of GP effects. Kendrick, Juanes-Marcos, and Althorpe have shown with different theoretical approaches that below 1.6 eV, there are no differences between GP and NGP calculations for the H3 system ([ 3 ][9]–[ 5 ][10]). The question is whether GP can still be observed at energies below the CI, specifically in the collision energy range of 1.92 to 2.21 eV that Xie et al. investigated. Instead of trying to measure angular distributions at fixed collision energies, where the GP effects would be too small to be detected, they looked at the change of the signal at extreme backward-scattering angles (∼180°) by scanning the collision energy. They did so by changing the crossing angle between the H and HD beams and controlling exquisitely all of the other experimental conditions. They found an oscillatory structure that could only be accounted for with GP or nonadiabatic calculations, whereas the NGP results were markedly out of phase with respect to the experimental results. The origin of those oscillations should be some sort of interference. Following Althorpe and co-workers ([ 5 ][10]–[ 7 ][3]), Xie et al. show that there are two different reaction paths around the CI. Path 1 is a clockwise looping and goes over just one transition state (TS1), and path 2 is a counterclockwise looping that surmounts two transition states (TS2 and TS3) (see the figure). The oscillations observed must be caused by interference between the two pathways. Specifically, Xie et al. examined the oscillations in backscattering as a function of energy. The scattering wave functions Ψ for each path can be written as and , respectively, and similarly rewritten for the respective scattering amplitudes. Using the backscattering amplitudes calculated with NGP and GP, they derived the moduli and phases of the scattering amplitudes for path 1 and path 2. The authors found that the relative phases for the two paths are almost the same until the collision energy reaches 1.3 eV. For higher energies, the phases diverge, rapidly decreasing for path 1 and increasing for path 2, which gives rise to fast oscillations in the energy dependence of backscattering. From this analysis, it became apparent that the oscillations, as a function of the energy predicted by the NGP and GP calculations, are caused by the interference between the two pathways. Moreover, the analysis shows that there is a phase difference between NGP and GP oscillations of precisely 180°. Quasi-classical trajectory calculations by Xie et al. and in previous studies ([ 6 ][11], [ 7 ][3]) also predict the existence of the two mechanisms: abstraction through TS1, and insertion through TS2 and then TS3. At a collision energy of 2.0 eV, just 0.23% of trajectories into H2 products react via path 2. Had it not been for the quantum interference, the insertion mechanisms would have passed unnoticed. However, interference can cause negligible contributions to exert large effects, because it sums the probability amplitudes and then squares the result to yield probabilities, rather than just adding the probabilities ([ 9 ][5], [ 10 ][6], [ 12 ][12]). Quantum interference reveals the presence of the CI at energies well below its energy on the PES. The phenomenon observed is analogous to the Aharonov-Bohm effect, and as in that case, it may occur far away from the CI. 1. [↵][13]1. M. V. Berry , Proc. R. Soc. London Ser. A 392, 45 (1984). [OpenUrl][14][CrossRef][15][PubMed][16] 2. 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领域	气候变化 ; 资源环境
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文献类型	期刊论文
条目标识符	http://119.78.100.173/C666/handle/2XK7JSWQ/267705
专题	气候变化资源环境科学
推荐引用方式 GB/T 7714	F. Javier Aoiz. How interference reveals geometric phase[J]. Science,2020.
APA	F. Javier Aoiz.(2020).How interference reveals geometric phase.Science.
MLA	F. Javier Aoiz."How interference reveals geometric phase".Science (2020).