Abstract Small helium clusters consisting of two and three helium atoms are unique quantum systems in several aspects. The helium dimer has a single weakly bound state and is of huge spatial extent, such that most of its probability distribution resides outside the potential well in the classically forbidden tunnelling region. The helium trimer possesses only two vibrational states, one of which is of Efimov nature. In this chapter, we discuss application of the Coulomb explosion imaging technique for studying geometries and binding energies of these peculiar two- and three-body quantum systems. Irradiation of a helium cluster by a strong laser field allows tuning interactions between helium atoms. Such ultrashort interaction modification induces response dynamics in a cluster that is observed by combination of the imaging technique with the pump-probe approach.
Abstract Small helium clusters consisting of two and three helium atoms are unique quantum systems in several aspects. The helium dimer has a single weakly bound state and is of huge spatial extent, such that most of its probability distribution resides outside the potential well in the classically forbidden tunnelling region. The helium trimer possesses only two vibrational states, one of which is of Efimov nature. In this chapter, we discuss application of the Coulomb explosion imaging technique for studying geometries and binding energies of these peculiar two- and three-body quantum systems. Irradiation of a helium cluster by a strong laser field allows tuning interactions between helium atoms. Such ultrashort interaction modification induces response dynamics in a cluster that is observed by combination of the imaging technique with the pump-probe approach.
Quantum theory dictates that upon weakening the two-body interaction in a three-body system, an infinite number of three-body bound states of a huge spatial extent emerge just before these three-body states become unbound. Three helium (He) atoms have been predicted to form a molecular system that manifests this peculiarity under natural conditions without artificial tuning of the attraction between particles by an external field. Here we report experimental observation of this long-predicted but experimentally elusive Efimov state of (4)He3 by means of Coulomb explosion imaging. We show spatial images of an Efimov state, confirming the predicted size and a typical structure where two atoms are close to each other while the third is far away.
A combination of the pump-probe technique and Coulomb explosion imaging is used to image the time resolved response of the 4He trimer to the perturbation by a femtosecond laser pulse. In the experiment, the interaction of the helium trimer with a non-ionizing pump-pulse is imaged by an ionizing probe pulse. The momenta, which the charged trimer fragments gain in the Coulomb explosion triggered by the probe pulse, are measured by a COLTRIMS reaction microscope. The response of the helium trimer is first analysed in momentum space. Subsequently, a reconstruction algorithm is used, in order to obtain the structural information about detected trimers from the momenta of the trimer fragments. This allows to analyse the response of the helium trimer in position space. The experiment is primarily motivated by the question, whether a laser pulse can excite the trimer ground state to the Efimov state, which is a huge quantum halo. Although a population of the Efimov state is not observed, in the experiment, the recorded data show the population of an unknown state, which could not yet be identified. Further, the response of the helium trimer shows an alignment wave, which might arise from the interference of two quantum states.
In this paper, we investigate small clusters of helium atoms using the hyperspherical harmonic basis. We consider systems with A=2,3,4,5,6 atoms with an interparticle potential which does not present a strong repulsion at short distances. We use an attractive Gaussian potential that reproduces the values of the dimer binding energy, the atom-atom scattering length, and the effective range obtained with one of the widely used He-He interactions, the Aziz and Slaman potential, called LM2M2. In systems with more than two atoms, we consider a repulsive three-body force that, by construction, reproduces the trimer binding energy of the LM2M2 potential. With this model, consisting of the sum of a two- and three-body potential, we have calculated the spectrum of clusters formed by four, five, and six helium atoms. We have found that these systems present two bound states, one deep and one shallow, close to the threshold fixed by the energy of the $(A\ensuremath{-}1)$-atom system. Universal relations between the energies of the excited state of the A-atom system and the ground-state energy of the $(A\ensuremath{-}1)$-atom system are extracted, as well as the ratio between the ground state of the A-atom system and the ground-state energy of the trimer.
In this work we investigate the structure and dynamics of small clusters of Helium atoms. We consider bound states of clusters having A = 2, 3, 4, 5, 6 atoms and continuum states in the three-atom system. Motivated by the fact that the He-He system has a very large scattering length a compared to the range r 0 of the He-He potential (r 0/a < 1/10), we propose the use of a soft-core interparticle potential. We use an attractive gaussian potential that reproduces the values of the dimer binding energy and the atomatom scattering length obtained with one of the widely used He-He interactions, the LM2M2 potential. In addition, we include a repulsive three-body force to reproduce the trimer binding energy. With this model, consisting in the sum of a two- and a three-body potential, we show the spectrum of the four, five, and sixparticle systems and phase-shifts and inelasticities in the three-atom system. Comparisons to calculations using realistic He-He potentials are given. In addition some universal relations are explored.
Abstract Small helium clusters Hen (n = 2, 3, ... , 10) in molecular beams produced by supersonic expansion of gaseous helium have been observed in several different experiments. Among these clusters the dimer, which has a single very slightly bound state, and the trimer, which could have many bound states, have especially unusual properties which QMC calculations can explain in detail. In this paper, diffusion QMC calculations were used to determine ground state properties for clusters (n = 2, ... , 10) using two accurate, but slightly different pairwise-additive potential energy expressions, a perturbation-based potential by Tang et al.a and an empirical potential (HFD-B) proposed by Aziz et al.b Trial functions for importance sampling were based on those determined earlier by Rick et alc. Expectation values and probability distributions were determined by the descendent-weighting technique to give results independent of the trial functions. As expected, a single bound state of the dimer was found, and its average internuclear distance was predicted to be 51.5 A. Energies for clusters with n = 2, 7 with the HFD-B potential were in good agreement with those of earlier calculations. Comparisons of the results for the two different potential energy expressions showed energies differing by a few percent. Tests of possible nonadditive interactions showed these to be far less important in their effects on predicted energies.