Quantum Halo States in Helium Tetramers

Abstract

Universality of quantum halo states enables comparison of systems from different fields of physics, as demonstrated in two-and three-body clusters. In the present work, we studied weakly-bound helium tetramers in order to test whether some of these four-body realistic systems qualify as halos. Their ground-state binding energies and structural properties were thoroughly estimated using the diffusion Monte Carlo method with pure estimators. Helium tetramer properties proved to be less sensitive on the potential model than previously evaluated trimer properties. We predict the existence of the realistic four-body halo 4 He 2 3 He 2 , while 4 He 4 and 4 He 3 3 He are close to the border and thus can be used as prototypes of quasi-halo systems. Our results could be tested by experimental determination of tetramers' structural properties, using a similar setup to the one developed for the study of helium trimers.

Universality of size-energy ratio in four-body systems

“…Constituents and tetramer types are distinguished with different symbols (see the legends). Available published data were taken from helium 20 , helium-alkali 21 , and helium-tritium tetramers 31 . Necessary additional features, like the structure properties 〈 r 2 〉, and new data for all other clusters included in the Figure were calculated.…”

“…A stochastic approach was applied by means of the second-order diffusion Monte Carlo method 33 in which pure estimators 34 were implemented. Masses and trial wave-functions were taken from our previous works 15,20,21,31 , while the same bias removal approach was applied.…”

“…Extensions of the imaging approach applied in the case of helium trimers was qualified as feasible for the four-body sector 8 . Recently, four-body halo and quasi-halo states were predicted to exist in helium tetramers 20 and in tetramers obtained by swapping one He atom by an alkali one 21 . Moreover, a thorough analysis for a large set of pure and mixed weakly-bound atomic dimers and trimers showed that universal size-energy scaling extends even below the halo area 15 , in the so called quasi-halo region.…”

Few-body bound states of two-dimensional bosons

“…While most of the theoretical and experimental studies of halos have been carried out in three dimensions [135][136][137][138][139], there is an increasing interest in halos in two dimensions (2D) [108,109,122]. In fact, two dimensions are especially interesting as halos in 2D have different properties [122] of the 3D ones.…”

“…In particular, we study the ground state of up to six particles occupying the A and B layers, with A and B denoting particles in different planes. To find the exact system properties we rely on the diffusion Monte Carlo (DMC) method (see Chapter 2) with pure estimators ( see Subsection 2.5.4), which has been used previously to get an accurate description of quantum halo states in Helium dimers [137], trimers and tetramers [138,139]. Also, we report relevant structure properties of the clusters, such as the spatial density distributions and the pair distribution functions for characteristic interlayer separations.…”