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arXiv:quant-ph/0002054 · Physical Review Letters

How to Study the Elusive Efimov State of the H4e3 Molecule through a New Atom-Optical State-Selection Technique

Gerhard C. Hegerfeldt, Thorsten Köhler

Published Apr 10, 2000• 17 citations
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Abstract

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.

DOI
10.1103/physrevlett.84.3215

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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.
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.
Helium trimer bound states are calculated with a variational method described in terms of pair atom coordinates and distributed Gaussian functions by assuming zero total angular momentum. With the two-body interaction potential used, a weakly bound state for the dimer and only two bound states for the trimer are found. Although strictly speaking the first excited trimer state is not an Efimov state, we show that this state presents several characteristics of the Efimov behavior which are extensively discussed in the present work. Special emphasis is placed on the main geometrical configurations contributing to the two bound trimer states, and suggestions are made on the possible ways of experimentally detecting the Efimov-type state.
The Efimov effect, with its ladder of weakly bound three-atomic molecules, poses intriguing questions in the theoretically controversial and experimentally demanding regime of merging of the first excited Efimov energy level with the atom-dimer continuum. Using an original experimental technique, where a coherent superposition state of diatomic and triatomic molecules is utilized, we investigate this regime and reveal a striking behavior: Instead of merging with the atom-dimer continuum the trimer energy level rebounds from it and becomes a deeper bound state again. In addition, instead of a tangential approach between the two levels we observe a rather narrow resonance, providing a new challenge and guide for few-body theories to incorporate realistic interatomic potentials.
Few-Body Problem Seemingly simple, quantum mechanical few-body systems are notoriously difficult to describe. Efimov trimers, three-body bound states with interactions tuned to be in close vicinity of the formation of two-body bound states, are the most tractable of these systems, with relevance, for example, in nuclear physics. Observed recently in ultracold atomic gases through their signatures in the rate of inelastic three-body collisions, Efimov trimers are predicted to appear at interaction strengths whose ratios are universally specified. By measuring binding energy as a function of interaction strength, Lompe et al. (p. 940 ) directly observed the association of three distinguishable atoms into a bound state. This technique may enable more precise studies of the trimer state, potentially revealing the nature of nonuniversal corrections suggested by prior experiments.