Helium Dimer Research Articles

Dynamics of molecular rotors in bulk superfluid helium.

Molecules immersed in liquid helium are excellent probes of superfluidity. Their electronic, vibrational, and rotational dynamics provide valuable clues about the superfluid at the nanoscale. Here we report on the experimental study of the laser-induced rotation of helium dimers inside the superfluid 4He bath at variable temperature. The coherent rotational dynamics of [Formula: see text] is initiated in a controlled way by ultrashort laser pulses and tracked by means of time-resolved laser-induced fluorescence. We detect the decay of rotational coherence on the nanosecond time scale and investigate the effects of temperature on the decoherence rate. The observed temperature dependence suggests a nonequilibrium evolution of the quantum bath, accompanied by the emission of the wave of second sound. The method offers ways of studying superfluidity with molecular nanoprobes under variable thermodynamic conditions.

Fragmentation of the 4He2 dimer with the emission of three or four electrons by fast highly charged projectiles

We investigate the fragmentation of the helium dimer, 4He2, into He2+ + He+ and He2+ + He2+ ions in collisions with fast highly charged projectiles. We discuss the main physical mechanisms driving these processes. We explore the energy and angular distributions of the ionic fragments produced during collisions of the dimer with 1 GeV/u U92+ and 11.37 MeV/u S14+ projectiles and also present the total fragmentation cross-sections. According to our results, the fragmentation in these collisions is fully dominated by the direct removal of three or four electrons from the dimer by the projectile in a single collision. Our results also suggest that the total fragmentation cross-sections depend on the binding energy IHe2 of the dimer, being roughly proportional to IHe2.

A simple quantum model for solving two-electron diatomics approximately

Analytical expressions are obtained for the total energy of two-electron heteronuclear diatomics using a minimal basis set consisting of a 1S-Gaussian orbital centered on each atom and a Heitler-London trial wavefunction. The equations are applied to the recently discovered helium hydride cation (2019, Nature 568, 357–9) to understand its stability. Special attention was given to the fulfillment of the virial theorem and the different limiting cases (homonuclear diatomics, short and long internuclear distances). The correctness of equations and numerical results was confirmed via a brute-force Metropolis Monte Carlo integration. Expressions for the moments of the electron density (including the dipole moments) were obtained. The effect of the spin state on the dipole moment is discussed and the model agrees qualitatively with results from more advanced ab initio calculations. I also applied the model to study the metastable helium dimer dication () and the predicted bond length (0.7359 Å) is in good agreement with the experimental value (0.75 ± 0.02 Å). The advantages and limitations of this simple quantum model are discussed.

Topologically-imposed vacancies and mobile solid 3He on carbon nanotube

Low dimensional fermionic quantum systems are exceptionally interesting because they reveal distinctive physical phenomena, including among others, topologically protected excitations, edge states, frustration, and fractionalization. Our aim was to confine 3He on a suspended carbon nanotube to form 2-dimensional Fermi-system. Here we report our measurements of the mechanical resonance of the nanotube with adsorbed sub-monolayer down to 10 mK. At intermediate coverages we have observed the famous 1/3 commensurate solid. However, at larger monolayer densities we have observed a quantum phase transition from 1/3 solid to an unknown, soft, and mobile solid phase. We interpret this mobile solid phase as a bosonic commensurate crystal consisting of helium dimers with topologically-induced zero-point vacancies which are delocalized at low temperatures. We thus demonstrate that 3He on a nanotube merges both fermionic and bosonic phenomena, with a quantum phase transition between fermionic solid 1/3 phase and the observed bosonic dimer solid.

Reduced density matrix functional theory from an ab initio seniority-zero wave function: Exact and approximate formulations along adiabatic connection paths

Currently, there is a growing interest in the development of a new hierarchy of methods based on the concept of seniority, which has been introduced quite recently in quantum chemistry. Despite the enormous potential of these methods, the accurate description of both dynamical and static correlation effects within a single and in-principle-exact approach remains a challenge. In this work, we propose an alternative formulation of reduced density-matrix functional theory (RDMFT) where the (one-electron reduced) density matrix is mapped onto an ab initio seniority-zero wave function. In this theory, the exact natural orbitals and their occupancies are determined self-consistently from an effective seniority-zero calculation. The latter involves a universal higher-seniority density matrix functional for which an adiabatic connection (AC) formula is derived and implemented under specific constraints that are related to the density matrix. The pronounced curvature of the (constrained) AC integrand, which is numerically observed in prototypical hydrogen chains and the Helium dimer, indicates that a description of higher-seniority correlations within second-order perturbation theory is inadequate in this context. Applying multiple linear interpolations along the AC or connecting second-order perturbation theory to a full-seniority treatment via Pad\'{e} approximants are better strategies. Such information is expected to serve as a guide in the future design of higher-seniority density-matrix functional approximations.

Building machine learning assisted phase diagrams: Three chemically relevant examples

In this work, we present a systematic procedure to build phase diagrams for chemically relevant properties by the use of a semi-supervised machine learning technique called uncertainty sampling. Concretely, we focus on ground state spin multiplicity and chemical bonding properties. As a first step, we have obtained single-eutectic-point-containing solid–liquid systems that have been suitable for contrasting the validity of this approach. Once this was settled, on the one hand, we built magnetic phase diagrams for several Hooke atoms containing a few electrons (4 and 6) trapped in spheroidal harmonic potentials. Changing the parameters of the confinement potential, such as curvature and anisotropy, and interelectronic interaction strength, we have been able to obtain and rationalize magnetic phase transitions flipping the ground state spin multiplicity from singlet (nonmagnetic) to triplet (magnetic) states. On the other hand, Bader’s analysis is performed upon helium dimers confined by spherical harmonic potentials. Covalency is studied using descriptors as the sign for Δρ(rC) and H(rC), and the dependency on the degrees of freedom of the system is studied, i.e., potential curvature ω2 and interatomic distance R. As a result, we have observed that there may exist a covalent bond between He atoms for short enough distances and strong enough confinement. This machine learning procedure could, in principle, be applied to the study of other chemically relevant properties involving phase diagrams, saving a lot of computational resources.

Fragmentation of the He24 dimer by relativistic highly charged projectiles in collisions with small kinetic energy release

We study theoretically the fragmentation of the helium dimer, $^4$He$_2$, into singly charged ions in collisions with relativistic highly-charged projectiles. We discuss the main mechanisms driving this process with the focus on the fragmentation caused by direct ionization of both atomic sites of the dimer in a single collision with the projectile. This direct mechanism dominates the He$_2$ $\to $ He$^+$ + He$^+$ breakup events with the kinetic energies of the emerging ionic fragments below $4$--$5$ eV. We explore the energy and angular distributions of the He$^+$ ions produced in collisions with $1$ and $7$ GeV/u U$^{92+}$ projectiles and show that their shape is significantly affected by relativistic and higher-order effects in the interaction between the projectile and the dimer. We also show that the shape of the energy spectrum is quite sensitive to the binding energy of the He$_2$ dimer which can be exploited for its precise determination. The contribution of the direct mechanism to the total cross section for the He$_2$ fragmentation by $1$ and $7$ GeV/u U$^{92+}$ was calculated to be $3.65$ Mb and $2.4$ Mb, respectively, representing roughly half of this cross section.

Generation of Basis Sets for Accurate Molecular Calculations: Application to Helium Atom and Dimer

A new approach for basis set generation is reported and tested in helium atom and dimer. The basis sets thus computed, named sigma, range from DZ to 5Z and consist of the same composition as Dunning basis sets but with a different treatment of contractions. The performance of the sigma sets is analyzed for energy and other properties of He atom and He dimer, and the results are compared with those obtained with Dunning and ANO basis sets. The sigma basis sets and their extended versions up to triple augmented provide better energy values than Dunning basis sets of the same composition, and similar values to those attained with the currently available ANO. Extrapolation to complete basis set of correlation energy is compared between the sigma basis sets and those of Dunning, showing the better performance of the former in this respect.

Probing the Helium Dimer by Relativistic Highly Charged Projectiles.

We study the fragmentation of He_{2} dimers into He^{+} ions by relativistic highly charged projectiles. We demonstrate that the interaction between an ultrafast projectile with an extremely extended object-the helium dimer-possesses interesting features that are absent in collisions with "normal" molecules. We also show that such projectiles, due to their enormous interaction range, can accurately probe the ground state of the dimer and even be used for a determination of its binding energy.

Photofragmentation of large dimers into singly charged ions via the knockout mechanism

We study the fragmentation of very large dimers into two singly charged ions caused by absorption of a photon. In this process a photo electron emitted from one atom of the dimer has certain chances to hit the other atom knocking out one of its electrons. This results in the production of two singly charged ions and the consequent Coulomb explosion of the residual doubly charged system. We develop a theory of this process and apply it to calculate the fragmentation of $^4$He$_2$, $^7$Li - $^4$He and $^6$Li - $^4$He dimers. Our results for the helium dimer are in good agreement with available experimental data. For the Li-He dimers (where experimental data are still absent) our results predict that this fragmentation mechanism becomes much more efficient than in the case of He$_2$. We also show that, provided the recoil effects are of minor importance, the so called reflection approximation is very accurate also for large dimers.

Vortex beams of atoms and molecules.

Angular momentum plays a central role in quantum mechanics, recurring in every length scale from the microscopic interactions of light and matter to the macroscopic behavior of superfluids. Vortex beams, carrying intrinsic orbital angular momentum (OAM), are now regularly generated with elementary particles such as photons and electrons. Thus far, the creation of a vortex beam of a nonelementary particle has never been demonstrated experimentally. We present vortex beams of atoms and molecules, formed by diffracting supersonic beams of helium atoms and dimers off transmission gratings. This method is general and could be applied to most atomic and molecular gases. Our results may open new frontiers in atomic physics, using the additional degree of freedom of OAM to probe collisions and alter fundamental interactions.

Potential curve for a Helium dimer confined by prolate spheroidal boxes

Potential curve for a Helium dimer confined by prolate spheroidal boxes

A basis set superposition error‐free second‐order perturbation theory from Hermitian chemical Hamiltonian approach self‐consistent field canonic orbitals

AbstractWe present an alternative perturbational approach free of basis set superposition error (BSSE) within the framework of the chemical Hamiltonian approach (CHA). The new formulation (CHA‐S‐MP2) is based on canonic (and orthogonal) CHA orbitals obtained from a hermitized CHA Fock operator. The final expression shows a considerable simplification of the method as compared to the previous CHA‐MP2 formalism. Numerical full geometry optimizations of water and hydrogen fluoride dimers and potential energy surfaces for helium and argon dimers for several basis sets are presented. The present method is compared to both the counterpoise and previous CHA‐MP2 BSSE correction schemes, showing a remarkable agreement between all three methods. However, the wrong behavior using the aug‐cc‐pVDZ basis set indicates that the present method is not as robust as the original non‐hermitian CHA‐MP2 formulation.

Vortex beams of atoms and molecules

Angular momentum plays a central role in a multitude of phenomena in quantum mechanics, recurring in every length scale from the microscopic interactions of light and matter to the macroscopic behavior of superfluids. Vortex beams, carrying intrinsic orbital angular momentum (OAM), are now regularly generated with elementary particles such as photons and electrons, and harnessed for numerous applications including microscopy and communication. Untapped possibilities remain hidden in vortices of non-elementary particles, as their composite structure can lead to coupling of OAM with internal degrees of freedom. However, thus far, the creation of a vortex beam of a non-elementary particle has never been demonstrated experimentally. We present the first vortex beams of atoms and molecules, formed by diffracting supersonic beams of helium atoms and dimers, respectively, off binary masks made from transmission gratings. By achieving large particle coherence lengths and nanometric grating features, we observe a series of vortex rings corresponding to different OAM states in the accumulated images of particles impacting a detector. This method is general and can be applied to most atomic and molecular gases. Our results may open new frontiers in atomic physics, utilizing the additional degree of freedom of OAM to probe collisions and alter fundamental interactions.

Interatomic Coulombic decay in Neon–Helium cluster: a complex absorbing potential based equation-of-motion coupled cluster investigation

ABSTRACT The interatomic Coulombic decay (ICD) of the and states in neon–helium dimer is studied using highly accurate complex absorbing potential based equation-of-motion coupled cluster (CAP-EOMCC) method. The ICD decay process for the state in neon–helium dimer is closed at its equilibrium bond distance. However, the decay channel is open at large bond distance of 6.2 Å. The decay channel for the double ionised state is open at 3.46 Å. From our calculations, we have noticed that the decay rate of state in neon–helium dimer is four times faster compared to the state. We have also investigated how the decay rate of state in neon–helium cluster varies in the presence of different helium environment.

Ultrafast manipulation of the weakly bound helium dimer

Controlling the interactions between atoms with external fields opened up new branches in physics ranging from strongly correlated atomic systems to ideal Bose and Fermi gases and Efimov physics. Such control usually prepares samples that are stationary or evolve adiabatically in time. On the other hand, in molecular physics external ultrashort laser fields are employed to create anisotropic potentials that launch ultrafast rotational wave packets and align molecules in free space. Here we combine these two regimes of ultrafast times and low energies. We apply a short laser pulse to the helium dimer, a weakly bound and highly delocalized single bound state quantum system. The laser field locally tunes the interaction between two helium atoms, imparting an angular momentum of $2\hbar$ and evoking an initially confined dissociative wave packet. We record a movie of the density and phase of this wave packet as it evolves from the inside out. At large internuclear distances, where the interaction between the two helium atoms is negligible, the wave packet is essentially free. This work paves the way for future tomography of wave packet dynamics and provides the technique for studying exotic and otherwise hardly accessible quantum systems such as halo and Efimov states.

Gently stirred not shaken

Manipulating weakly bound helium dimers with ultrafast laser pulses reveals their quantum behaviour. This method opens a route towards studying the low-energy dynamics of other exotic and fragile quantum states.

Legendre-spectral Dyson equation solver with super-exponential convergence.

Quantum many-body systems in thermal equilibrium can be described by the imaginary time Green's function formalism. However, the treatment of large molecular or solid ab initio problems with a fully realistic Hamiltonian in large basis sets is hampered by the storage of the Green's function and the precision of the solution of the Dyson equation. We present a Legendre-spectral algorithm for solving the Dyson equation that addresses both of these issues. By formulating the algorithm in Legendre coefficient space, our method inherits the known faster-than-exponential convergence of the Green's function's Legendre series expansion. In this basis, the fast recursive method for Legendre polynomial convolution enables us to develop a Dyson equation solver with quadratic scaling. We present benchmarks of the algorithm by computing the dissociation energy of the helium dimer He2 within dressed second-order perturbation theory. For this system, the application of the Legendre spectral algorithm allows us to achieve an energy accuracy of 10-9Eh with only a few hundred expansion coefficients.

Optical and spectroscopic study of a supersonic flowing helium plasma: energy transport in the afterglow

Flowing plasma jets are increasingly investigated and used for surface treatments, including biological matter, and as soft ionization sources for mass spectrometry. They have the characteristic capability to transport energy from the plasma excitation region to the flowing afterglow, and therefore to a distant application surface, in a controlled manner. The ability to transport and deposit energy into a specimen is related to the actual energy transport mechanism. In case of a flowing helium plasma, the energy in the flowing afterglow may be carried by metastable helium atoms and long-lived helium dimer ions. In this work a systematic investigation of the optical and spectroscopic characteristics of a supersonic flowing helium plasma in vacuum and its afterglow as function of the helium gas density is presented. The experimental data are compared with numerical modeling of the plasma excitation and helium dimer ion formation supported by a Computational Fluid Dynamic simulation of the helium jet. The results indicate that the plasma afterglow is effectively due to helium dimer ions recombination via a three-body reaction.

Theoretical study of molecular-frame angular emission distributions of electrons emitted by interatomic Coulombic decay from helium dimers

Molecular frame angular distributions of electrons released by interatomic Coulombic decay of ${\mathrm{He}}^{+*}(2\ensuremath{\ell})\text{\ensuremath{-}}\mathrm{He}$ states are studied theoretically by means of electronic structure and nonadiabatic nuclear dynamics calculations. In previous experimental work [Phys. Rev. A 82, 063405 (2010)], distinct variations of the angular emission patterns have been observed for different ranges of kinetic-energy release of the fragment ions. Good agreement between the presently computed and these measured angular distributions can be achieved by assuming nonequal populations of ${}^{2}{\mathrm{\ensuremath{\Sigma}}}_{g/u}^{+}$ and ${}^{2}{\mathrm{\ensuremath{\Pi}}}_{g/u}$ decaying electronic states via initial shake-up ionization of the dimers.