Imaging the structure of the trimer systems 4He3 and 3He4He2

Abstract

Helium shows fascinating quantum phenomena unseen in any other element. In its liquid phase, it is the only known superfluid. The smallest aggregates of helium, the dimer (He 2 ) and the trimer (He 3 ) are, in their predicted structure, unique natural quantum objects. While one might intuitively expect the structure of 4 He 3 to be an equilateral triangle, a manifold of predictions on its shape have yielded an ongoing dispute for more than 20 years. These predictions range from 4 He 3 being mainly linear to being mainly an equilateral triangle. Here we show experimental images of the wave functions of 4 He 3 and 3 He 4 He 2 obtained by Coulomb explosion imaging of mass-selected clusters. We propose that 4 He 3 is a structureless random cloud and that 3 He 4 He 2 exists as a quantum halo state.

Efimov Physics and the Three-Body Parameter for Shallow van der Waals Potentials

“…5 Our result for the n = 1 state shown in Fig. 4a, plotted as a function of θ as opposed to cos θ , agree with the distribution determined experimentally [36]. Comparison with Fig.…”

“…Our study is motivated by a large body of cold atom related work [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and recent experimental measurements of the structural properties of the helium trimer ground and excited states [36,37]. The ground state of the helium trimer is, generally, considered not to be an Efimov state while the helium trimer excited state is considered to be an Efimov state [38][39][40].…”

Energy and structural properties ofN-boson clusters attached to three-body Efimov states: Two-body zero-range interactions and the role of the three-body regulator

“…Although the structural properties of the ground state trimers for the Hamiltonian with two-body van der Waals interactions differ notably from those for the pure Efimov trimer [30,31], these systems exhibit universal features [27,[32][33][34][35][36][37][38][39]. Specifically, the trimer ground state binding momentum κ at unitarity is, to a good approximation, determined by the van der Waals length L vdW [27,39] and independent of the short-range details.…”

“…The structural properties provide additional insights. Indeed, the structures of weaklybound three-body systems with positive a s have recently been measured [30,31]. We first look at the distribution of the angles θ jkl between each pair of position vectors, θ jkl = arccos(r jk ·r kl ).…”

Quantum Halo States in Helium Tetramers

“…7 Existence of the smallest clusters, dimer 4 He 2 , trimers 4 He 3 and 4 He 2 3 He, and tetramers 4 He 4 , 4 He 3 3 He and 4 He 2 3 He 2 , was predicted theoretically [8][9][10][11] and confirmed experimentally. [12][13][14][15][16][17][18] Their stability is affected by the different mass and quantum statistics of helium isotopes, 4 He and 3 He. Both helium dimers and trimers played a significant role in the research 7 of universal scaling laws of energy and size of two-and three-body halos.…”