Long-range Atomic Interactions Research Articles

A simple and efficient graph Transformer architecture for molecular properties prediction

Graph Transformer architecture started to catch fire in molecular properties prediction due to its ability to represent complex interactions between all nodes. However, the self-attention mechanism in Transformer encoder part transforms the graph data into a fully-connected graph for graph representation learning, causing the loss of the original structural information of the graph. In this work, Local Transformer is proposed to keep the original graph structure and aggregate local information of nodes. In the model, a simple graph convolution is designed to replace the self-attention module, which reaches the state-of-the-art performance on ZINC dataset. Further, in order to rectify the problem that graph neural networks(GNNs) cannot capture long-range interactions of atoms, a novel end-to-end framework combined the GNN with Local and Global Transformer is proposed, which achieves good results on QM9 dataset.

Improved Singum Model Based on Finite Deformation of Crystals with the Thermodynamic Equation of State

The recently published simplified singum model has been improved by using the thermodynamics-based equation of state (EOS) of solids to derive a new interatomic potential based on elastic constants. The finite deformation formulation under hydrostatic load has been used to evaluate the pressure-volume (p-v) relationship for the EOS of a solid. Using the bulk modulus and its derivatives at the free-stress state, one can construct the EOS, from which a new form of interatomic potential is derived for the singum, which exhibits much higher accuracy than the previous one obtained from the Fermi energy and provides a general approach to construct the interatomic potential. The long-range atomic interactions are approximated to be proportional to the pressure. This improved singum model is demonstrated for the face-centered cubic (FCC) lattice of single-crystalline aluminum. The elastic properties at different pressures are subsequently predicted through the bond length change and compared with the available experimental data. The model can be straightforwardly extended to higher-order terms of EOS with better accuracy and other types of lattices.

Observation of a superradiant quantum phase transition in an intracavity degenerate Fermi gas.

Coupling Bose-Einstein condensates to optical cavities has enabled the study of many-body states with long-range interactions. However, equivalent experiments with ultracold Fermi gases have remained largely unexplored. Here, we report an experimental realization of a superradiant quantum phase transition of a degenerate Fermi gas in a transversely pumped optical cavity. The self-ordering checkerboard density pattern of Fermi gases and superradiant transitions of the cavity field spontaneously emerge by increasing the pumping intensity above a threshold value. The effects of Fermi statistics are manifested by an inverse square root scaling of the threshold with atom number and the slow dynamics of low–atomic momentum states. Our work provides an ideal platform for studying nonequilibirium dynamics of many-body states for long-range interacting Fermi gases.

Self-bound droplet clusters in laser-driven Bose-Einstein condensates

We investigate a two-dimensional Bose-Einstein condensate that is optically driven via a retro-reflecting mirror, forming a single optical feedback loop. This induces a peculiar type of long-range atomic interaction with highly oscillatory behavior, and we show here how the sign of the underlying interaction potential can be controlled by additional optical elements and external fields. This additional tunability enriches the behavior of the system substantially, and gives rise to a surprising range of new ground states of the condensate. In particular, we find the emergence of self-bound crystals of quantum droplets with various lattice structures, from simple and familiar triangular arrays to complex superlattice structures and crystals with entirely broken rotational symmetry. This includes mesoscopic clusters composed of small numbers of quantum droplets as well as extended crystalline structures. Importantly, such ordered states are entirely self-bound and stable without any external in-plane confinement, having no counterpart to other quantum-gas settings with long-range atomic interactions.

Vibration of nonlocal perforated nanobeams with general boundary conditions

This article presents a comprehensive model to investigate a free vibration and resonance frequencies of nanostructure perforated beam element as nano-resonator. Nano-scale size dependency of regular square perforated beam is considered by using nonlocal differential form of Eringen constitutive equation. Equivalent mass, inertia, bending and shear rigidities of perforated beam structure are developed. Kinematic displacement assumptions of both Timoshenko and Euler-Bernoulli are assumed to consider thick and thin beams, respectively. So, this model considers the effect of shear on natural frequencies of perforated nanobeams. Equations of motion for local and nonlocal elastic beam are derived. After that, analytical solutions of frequency equations are deduced as function of nonlocal and perforation parameters. The proposed model is validated and verified with previous works. Parametric studies are performed to illustrate the influence of a long-range atomic interaction, hole perforation size, number of rows of holes and boundary conditions on fundamental frequencies of perforated nanobeams. The proposed model is supportive in designing and production of nanobeam resonator used in nanoelectromechanical systems NEMS.

Stability buckling and bending of nanobeams including cutouts

This manuscript developed a comprehensive model and numerical studies to illustrate the effect of perforation parameters on critical buckling loads and static bending of thin and thick nanobeams for all boundary conditions, for the first time. Analytical closed-form solutions are presented for buckling loads and static deflections, respectively. Euler–Bernoulli beam theory is exploited for thin beam analysis, and Timoshenko beam theory is proposed to consider a shear effect in case of thick beam analysis. Nonlocal differential form of elasticity theory is included to consider a size scale effect that is missing in case of classical theory and macro-analysis. Geometrical adaptations for perforated beam structures are illustrated in simplest form. Equilibrium equations for local and nonlocal beam are derived in detail. Numerical studies are illustrated to demonstrate influences of long-range atomic interaction, hole perforation size, number of rows of holes and boundary conditions on buckling loads and deflection of perforated nanobeams. The recommended model is helpful in designing nanoresonators and nanoactuators used in NEMS structures and nanotechnology.

Photon transport mediated by an atomic chain trapped along a photonic crystal waveguide

We theoretically investigate the transport properties of a weak coherent input field scattered by an ensemble of $\Lambda$-type atoms coupled to a one-dimensional photonic crystal waveguide. In our model, the atoms are randomly located in the lattice along the crystal axis. We analyze the transmission spectrum mediated by the tunable long-range atomic interactions, and observe the highest-energy dip. The results show that the highest-energy dip location is associated with the number of the atoms, which provides an accurate measuring tool for the emitter-waveguide system. We also quantify the influence of a Gaussian inhomogeneous broadening and the dephasing on the transmission spectrum, concluding that the highest-energy dip is immune to both the inhomogeneous broadening and the dephasing. Furthermore, we study photon-photon correlations of the reflected field and observe quantum beats. With tremendous progress in coupling atoms to photonic crystal waveguides, our results may be experimentally realizable in the near future.

Generation of single- and two-mode multiphoton states in waveguide QED

Single and two-mode multiphoton states are the cornerstone of many quantum technologies, e.g., metrology. In the optical regime these states are generally obtained combining heralded single-photons with linear optics tools and post-selection, leading to inherent low success probabilities. In a recent paper, we design several protocols that harness the long-range atomic interactions induced in waveguide QED to improve fidelities and protocols of single-mode multiphoton emission. Here, we give full details of these protocols, revisit them to simplify some of their requirements and also extend them to generate two-mode multiphoton states, such as Yurke or NOON states.

Resonance frequencies of size dependent perforated nonlocal nanobeam

Perforation is a common procedure in fabrication process of micro/nano-electromechanical systems (M/NEMS). Therefore, this paper presents an effort to study the resonance frequencies of size dependent regular square perforated nonlocal nanobeam, which not be discussed before. Equivalent characteristic parameters of perforated beam such as, bending stiffness, shear stiffness, mass, and rotary inertia are presented. The size-scale effect of long-range atomic interaction of nanobeam is described by using nonlocal differential form of Eringen model. Constitutive and governing equations of local and nonlocal perforated Timoshenko and Euler–Bernoulli nanobeam are derived. Analytical solution are exploited to solve the proposed model and derived closed form frequency equations as function of nanoscale and perforation parameters. The verification of current model is presented and compared with published works. Numerical results are illustrated to present the influences of length scale parameter, number of perforated holes, perforation size, and shear effects on the natural frequencies of both nanobeams theories. The obtained results are supportive in mechanical design of high-precision measurement nanobeams sensor and actuators.

Changing optical band structure with single photons

Achieving strong interactions between individual photons enables a wide variety of exciting possibilities in quantum information science and many-body physics. Cold atoms interfaced with nanophotonic structures have emerged as a platform to realize novel forms of nonlinear interactions. In particular, when atoms are coupled to a photonic crystal waveguide, long-range atomic interactions can arise that are mediated by localized atom-photon bound states. We theoretically show that in such a system, the absorption of a single photon can change the band structure for a subsequent photon. This occurs because the first photon affects the atoms in the chain in an alternating fashion, thus leading to an effective period doubling of the system and a new optical band structure for the composite atom-nanophotonic system. We demonstrate how this mechanism can be engineered to realize a single-photon switch, where the first incoming photon switches the system from being highly transmissive to highly reflective, and analyze how signatures can be observed via non-classical correlations of the outgoing photon field.

Adjacency graphs and long-range interactions of atoms in quasi-degenerate states: applied graph theory

We analyze, in general terms, the evolution of energy levels in quantum mechanics, as a function of a coupling parameter, and demonstrate the possibility of level crossings in systems described by irreducible matrices. In long-range interactions, the coupling parameter is the interatomic distance. We demonstrate the utility of adjacency matrices and adjacency graphs in the analysis of "hidden" symmetries of a problem; these allow us to break reducible matrices into irreducible subcomponents. A possible breakdown of the no-crossing theorem for higher-dimensional irreducible matrices is indicated, and an application to the 2S-2S interaction in hydrogen is briefly described. The analysis of interatomic interactions in this system is important for further progress on optical measurements of the 2S hyperfine splitting.

Stability diagram of the collective atomic recoil laser with thermal atoms

We experimentally investigate cold thermal atoms in a single sidedly pumped optical ring resonator for temperatures between 0.4 and $9\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$. The threshold for collective atomic recoil lasing (CARL) is recorded for various pump-cavity detunings. The resulting stability diagram is interpreted by simulating the classical CARL equations. We find that the stability diagram for thermal atoms shows the same asymmetry as observed for Bose-Einstein condensates in previous experiments. Whereas for condensates the asymmetry is well explained by a Dicke-type quantum model we here discuss a simplified classical model. It complements the quantum model and provides an intuitive explanation based on the change in the long-range atomic interaction with pump-cavity detuning.

On Atomistic-to-Continuum Couplings without Ghost Forces in Three Dimensions

In this paper, we construct energy-based numerical methods free of ghost forces in three-dimensional lattices arising in crystalline materials modeled by pair interaction potentials. The analysis hinges on establishing a connection of the coupled system to conforming finite elements. Key ingredients are: (i) a new representation of discrete derivatives related to long range interactions of atoms as volume integrals of gradients of piecewise linear functions over bond volumes, and (ii) the construction of an underlying globally continuous function representing the coupled modeling method.

Corrections to the Optical Transition Energies in Single-Wall Carbon Nanotubes of Smaller Diameters

ABSTRACTOptical spectroscopy characterization of carbon nanotube samples requires accurate determination of their band structure and exciton binding energies. In this paper, we present a non-orthogonal density-functional based tight-binding calculation for the electronic transition energies in single-wall carbon nanotubes. We show that the curvature-induced rehybridization of the electronic orbitals, long-range atomic interactions, and geometrical structure relaxation all have a significant impact on the electronic transition energies in the small diameter limit. After including quasiparticle corrections and exciton binding energies, the calculated electronic transition energies show good agreement with the experimental transition energies observed by photoluminescence and resonance Raman spectroscopy.

Pixel mapping analysis to characterize long-range order interactions in crystals under ion irradiation

High-dose irradiation can cause agglomeration of projectile particles if the impurity concentration exceeds a certain level. In previous classical molecular-dynamics calculations we have investigated the importance of ionimpacts for agglomeration. This has also shown that some long-range network forces exist in a crystal, which may relate phase transition and ion bombardment. In order to investigate the long-range order interactions, we propose a method to describe the lattice interactions macroscopically. We call it pixel mapping (PM). With the help of PM, we can clearly describe details of the intermediate processes and estimate the degree of crystallinity during ion irradiation. B implantation into a B doped Si crystal at different bombarding energies was analyzed by PM. Sudden changes from a crystalline to an amorphous state after a certain number of ion impacts were observed and analyzed by PM. PM described clearly these change as cooperative lattice reactions and revealed the long-range order interactions between target atoms in a crystal. Therefore, we can conclude that impurity agglomeration is cooperatively triggered by long-range interactions of atoms in a mesoscopic regime, and PM is a powerful method to elicit the long-range interactions of atoms in a crystal.

Dynamics of solitary waves in diatomic chains with long-range Kac-Baker interactions

An analytical study of the influence of the long-range atomic interactions on the properties of soliton-like excitations in a one-dimensional (1D) anharmonic chain is presented. The model chosen is a nonlinear diatomic chain in which atoms are assumed to interact via a cubic and/or quartic nonlinear short-range potential and a linear long-range Kac-Baker type pair potential. In the continuum approximation, using scaling arguments, it is shown that the coupled nonlinear difference-differential equations for the motion of the two different masses can be decoupled and reduced to a generalized Boussinesq equation which admits supersonic and subsonic acoustic kink (pulse) solitons, long-wavelength acoustic oscillating solutions of breather type and optical envelope type solitons of a nonlinear Schrodinger equation. A possible alternation of envelope and dark is found that can exist not only for acoustic mode but also for optical mode.

Discreteness effects in a Phi 4 chain with long-range interactions

The authors study the influence of discreteness on kink motion in a one-dimensional Phi 4 chain with long-range atomic interactions of Kac-Baker type. They use a discretized Hamiltonian formalism in which the kink appears as a canonical degree of freedom. It is shown that the kink oscillatory motion and lattice trapping processes depend strongly on the range of interaction.

Role of long-range interactions in the melting of a metallic surface.

Ion-shadowing and -blocking studies of melted layers on the (110) surface of Pb reveal an increasing melt thickness with temperature, which follows first a logarithmic growth law \ensuremath{\Vert}ln(${T}_{m}$-T)\ensuremath{\Vert}, then asymptotically a power law (${T}_{m}$-T${)}^{\mathrm{\ensuremath{-}}r}$, with r=0.315\ifmmode\pm\else\textpm\fi{}0.015. The logarithmic and power-law growth result from short-range and long-range atomic interactions, respectively. The correlation length within the melted phase is determined to be ${\ensuremath{\xi}}_{l}$=0.63 nm and for the Hamaker constant we find W=(0.40\ifmmode\pm\else\textpm\fi{}0.05)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}21}$ J.

The vibrational motions in vitreous silica at high temperatures

Vitreous silica was studied at the temperatures 293 K, 673 K and 1073 K using inelastic neutron scattering. The zeroeth moment of the dynamic scattering function S( Q, E) agrees well with neutron diffraction results. It was found that the structure factors for elastic and inelastic scattering change with temperature in a Q region which reveals mostly long-range atomic interactions rather than those from nearest and next-nearest neighbours. The temperature variation was interpreted as if the structural and dynamical correlations between neighbouring SiO 4 polyhedra decrease when the temperature increases. Effective Debye-Waller factors were derived and found to increase linearly with temperature. It was also found that the vibrational amplitudes of the atoms in silica, within the experimental errors, are the same as those in high cristobalite. Through extrapolation to zero wave vector transfer of the spectrum of the longitudinal current-current correlation function, effective frequency distribution functions were obtained as well as generalized structure factors for inelastic scattering.

Solitons in anharmonic chains with long-range interactions

The authors study the influence of long-range atomic interactions on the properties of soliton-like excitations in a one-dimensional anharmonic chain. In the continuum approximation supersonic and subsonic kink pulse soliton solutions are found that can coexist in the lattice. The corresponding velocity domains are separated by a gap that depends on the range of the interaction. The modulated-wave solutions are investigated in the weakly non-linear case and the small-wavevector limit. A possible alternation of envelope and dark solitons is found that can exist for both cooperative and competitive short- and long-range interactions.