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arXiv:quant-ph/0412064 · Physical Review Letters

Matter Wave Diffraction from an Inclined Transmission Grating: Searching for the Elusive H4e Trimer Efimov State

Rüdiger Brühl, Anton Kalinin, Oleg Kornilov, Jan Peter Toennies, Gerhard C. Hegerfeldt, M. Stoll

Published Aug 2, 2005• 78 citations
arXivHTMLPDF

Abstract

The size of the helium trimer is determined by diffracting a beam of 4He clusters from a 100 nm period grating inclined by 21 degrees. Because of the bar thickness the projected slit width is roughly halved to 27 nm, increasing the sensitivity to the trimer size. The peak intensities measured out to the eighth order are evaluated via a few-body scattering theory. The trimer pair distance is found to be (r) = 1.1(+0.4)(-0.5) nm in agreement with predictions for the ground state. No evidence for a significant amount of Efimov trimers is found. Their concentration is estimated to be under 6%, less than expected.

DOI
10.1103/physrevlett.95.063002

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The size of the helium trimer is determined by diffracting a beam of 4He clusters from a 100 nm period grating inclined by 21 degrees. Because of the bar thickness the projected slit width is roughly halved to 27 nm, increasing the sensitivity to the trimer size. The peak intensities measured out to the eighth order are evaluated via a few-body scattering theory. The trimer pair distance is found to be (r) = 1.1(+0.4)(-0.5) nm in agreement with predictions for the ground state. No evidence for a significant amount of Efimov trimers is found. Their concentration is estimated to be under 6%, less than expected.
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.
Excited states and excitation energies of weakly bound systems, e.g., atomic few-body systems and clusters, are difficult to study experimentally. For this purpose we propose a new and very general atom-optical method which is based on inelastic diffraction from transmission gratings. The technique is applicable to the recently found helium trimer molecule 4He3, allowing for the first time an investigation of the possible existence of an excited trimer state and determination of its excitation energy. This would be of fundamental importance for the famous Efimov effect.
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.
The size distributions of neutral 4He clusters in cryogenic jet beams, analyzed by diffraction from a 100 nm period transmission grating, reveal magic numbers at N=10-11, 14, 22, 26-27, and 44 atoms. Whereas magic numbers in nuclei and clusters are attributed to enhanced stabilities, this is not expected for quantum fluid He clusters on the basis of numerous calculations. These magic numbers occur at threshold sizes for which the quantized excitations calculated with the diffusion Monte Carlo method are stabilized, thereby providing the first experimental confirmation for the energy levels of 4He clusters.
We have measured the diffraction of metastable helium atoms by a transmission grating with a period of 500 nm. The atomic beam is derived from a supersonic nozzle by adiabatic gas expansion with a velocity ratio v/Δv 20; with the nozzle cooled to liquid nitrogen temperature, the corresponding de Broglie wave length of the helium atoms is 1.08 Å. We have observed diffraction peaks up to the third order with a good signal-to-noise ratio. The position and the height of the different orders are in satisfactory agreement with the measured grating shape and the mean velocity in the atomic beam. As was pointed out previously, such transmission gratings offer one way to realize an atom-wave interferometer.1 In this context, our results demonstrate that an efficient diffraction can also be obtained with excited-state atoms: Here the use of metastable rare-gas atoms is of special interest because they are easy to handle and can be detected on almost zero background. As an alternative to the use of transmission gratings in matter-wave interferometry, we also discuss a simple double-slit arrangement that may provide another approach to the study of atomic interference phenomena.
Molecular beams of rare gas atoms and D2{\mathrm{D}}_{2}D2​ have been diffracted from 100-nm-period SiNx{\mathrm{SiN}}_{x}SiNx​ transmission gratings. The relative intensities of the diffraction peaks out to the eighth order depend on the diffracting particle and are interpreted in terms of effective slit widths. These differences have been analyzed by a new theory which accounts for the long-range van der Waals ${\ensuremath{-}C}_{3}/{l}^{3}$ interaction of the particles with the walls of the grating bars. The values of the C3{C}_{3}C3​ constant for two different gratings are in good agreement and the results exhibit the expected linear dependence on the dipole polarizability.