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Materie-Optik mit Edelgasmolekülen an Nanostrukturen

W. Stoll

Published Jan 1, 2004• 0 citations
Publisher

Abstract

The advance of matter optics, thus the coherent scattering of an atom or molecule beam from a nanostructured grating, recently gave conclusive evidence for the extremely weakly bound diatomic and triatomic van der Waals clusters of helium in a precision experiment. A quantum mechanical multi-channel many-body scattering theory, as it is presented and extended in this work, is essential for the quantitative description of such an experiment. In order to enhance the resolution of the most recent measurements the grating was tilted with respect to the incident beam. At first, the asymmetry of the diffraction pattern caused by this was theoretically studied for the case of atom diffraction. Subsequently, the ground state of the helium trimer was investigated and its bond length determined to be about 1 nm. Another part of this work considers inelastic diffraction and shows, using small hydrogen dimers as an example, that matter optics allows, in principle, for the spectroscopy of weakly bound clusters.

DOI
10.53846/goediss-2711

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The advance of matter optics, thus the coherent scattering of an atom or molecule beam from a nanostructured grating, recently gave conclusive evidence for the extremely weakly bound diatomic and triatomic van der Waals clusters of helium in a precision experiment. A quantum mechanical multi-channel many-body scattering theory, as it is presented and extended in this work, is essential for the quantitative description of such an experiment. In order to enhance the resolution of the most recent measurements the grating was tilted with respect to the incident beam. At first, the asymmetry of the diffraction pattern caused by this was theoretically studied for the case of atom diffraction. Subsequently, the ground state of the helium trimer was investigated and its bond length determined to be about 1 nm. Another part of this work considers inelastic diffraction and shows, using small hydrogen dimers as an example, that matter optics allows, in principle, for the spectroscopy of weakly bound clusters.
We study the coherent inelastic diffraction of very weakly bound two-body clusters from a material transmission grating. We show that internal transitions of the clusters can lead to new separate peaks in the diffraction pattern, whose angular positions determine the excitation energies. Using a quantum mechanical approach to few-body scattering theory, we determine the relative peak intensities for the diffraction of the van der Waals dimers (D 2 ) 2 and H 2 D 2 . Based on the results for these realistic examples, we discuss the possible applications and experimental challenges of this coherent inelastic diffraction technique.
Exciting experiments in the field of atom and molecule optics have lately drawn much attention to the effects involved in the coherent diffraction of particle beams. We review the influence of the finite size of the particles and of their energy level spectrum on the diffraction pattern. In turn, we demonstrate how experimental diffraction measurements allow to determine these quantities of weakly bound molecules by considering the diffraction of the dimer and trimer of helium, and the deuterium molecule dimer.
A molecular beam consisting of small helium clusters is diffracted from a 100 nm period transmission grating. The relative dimer intensities have been measured out to the 7th order and are used to determine the reduction of the effective slit width resulting from the finite size of the dimer. From a theoretical analysis of the data which also takes into account the van der Waals interaction with the grating bars, the bond length (mean internuclear distance) and the binding energy are found to be $〈r〉\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}52\ifmmode\pm\else\textpm\fi{}4\AA{}$ and $|{E}_{b}|\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.1+0.3/\ensuremath{-}0.2$ mK.
We study the diffraction of atoms and weakly bound three-atomic molecules from a transmission grating at non-normal incidence. Due to the thickness of the grating bars, the slits are partially shadowed. Therefore, the projected slit width decreases more strongly with the angle of incidence than the projected period, increasing, in principle, the experimental resolution. The shadowing, however, requires a revision of the theory of atom diffraction. We derive an expression in the style of the Kirchhoff integral of optics and show that the diffraction pattern exhibits a characteristic asymmetry which must be accounted for when comparing with experimental data. We then analyze the diffraction of weakly bound trimers and show that their finite size manifests itself in a further reduction of the slit width by (3∕4)⟨r⟩(3∕4)⟨r⟩(3∕4)⟨r⟩ where ⟨r⟩⟨r⟩⟨r⟩ is the average bond length. The improved resolution at non-normal incidence may in particular allow us to discern, by means of their bond lengths, between the small ground state of the helium trimer [$⟨r⟩\ensuremath{\approx}1\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, Barletta and Kievsky, Phys. Rev. A 64, 042514 (2001)] and its predicted Efimov-type excited state ($⟨r⟩\ensuremath{\approx}8\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, ibid.), and in this way to experimentally prove the existence of this long-sought Efimov state.
A few years ago, diffraction of atoms by double slits and gratings was achieved for the first time, and standard optical wave-theory provided an excellent description of the experiments. More recently, diffraction of weakly bound molecules and even clusters has been observed. Due to their size and to possible breakup processes optical wave-theory is no longer adequate and a more sophisticated approach is needed. Moreover, surface effects, which can modify the diffraction pattern of atoms and molecules, give rise to further complications. In this article a fully quantum mechanical approach to these questions is discussed.
In atom optics, optical wave theory has been very successful in describing the diffraction of atoms by microfabricated structures. For a molecule, however, with a binding energy smaller than the kinetic energy and with a non-negligible diameter, wave optics may no longer be adequate due to the effects of finite size and breakups. To study the role of the two effects we consider the diffraction of weakly bound diatomic systems such as the helium dimer. We find striking deviations from classical optics, in particular from Babinet's principle, and use the results to clarify the role of finite size and breakups, respectively, in the diffraction from strips, slits, and transmission gratings. As an application the determination of the He2{\mathrm{He}}_{2}He2​ size by transmission through holes and by diffraction experiments is investigated.