Few-atom Systems Research Articles

Theoretical Investigation of Spectroscopic Properties of the Alkaline-Earth-Metal Monohydrides toward Laser Cooling and Magneto-Optical Trapping.

Alkaline-earth-metal monohydrides MH (M = Be, Mg, Ca, Sr, Ba) have long been regarded as promising candidates toward laser cooling and trapping; however, their rich internal level structures that are amenable to magneto-optical trapping have not been completely explored. Here, we first systematically evaluated Franck-Condon factors of these alkaline-earth-metal monohydrides in the A2Π1/2 ← X2Σ+ transition, exploiting three respective methods (the Morse potential, the closed-form approximation, and the Rydberg-Klein-Rees method). The effective Hamiltonian matrix was introduced for MgH, CaH, SrH, and BaH individually in order to figure out their molecular hyperfine structures of X2Σ+, the transition wavelengths in the vacuum, and hyperfine branching ratios of A2Π1/2(J' = 1/2,+) ← X2Σ+(N = 1,-), followed by possible sideband modulation proposals to address all hyperfine manifolds. Lastly, the Zeeman energy level structures and associated magnetic g factors of the ground state X2Σ+(N = 1,-) were also presented. Our theoretical results here not only shed more light on the molecular spectroscopy of alkaline-earth-metal monohydrides toward laser cooling and magneto-optical trapping but also can contribute to research in molecular collisions involving few-atom molecular systems, spectral analysis in astrophysics and astrochemistry, and even precision measurement of fundamental constants such as the quest for nonzero detection of electron's electric dipole moment.

Variational quantum algorithm for molecular geometry optimization

Classical algorithms for predicting the equilibrium geometry of strongly correlated molecules require expensive wave function methods that become impractical already for few-atom systems. In this work, we introduce a variational quantum algorithm for finding the most stable structure of a molecule by explicitly considering the parametric dependence of the electronic Hamiltonian on the nuclear coordinates. The equilibrium geometry of the molecule is obtained by minimizing a more general cost function that depends on both the quantum circuit and the Hamiltonian parameters, which are simultaneously optimized at each step. The algorithm is applied to find the equilibrium geometries of the ${\mathrm{H}}_{2},$ ${\mathrm{H}}_{3}{}^{+},$ ${\mathrm{BeH}}_{2},$ and ${\mathrm{H}}_{2}\mathrm{O}$ molecules. The quantum circuits used to prepare the electronic ground state for each molecule were designed using an adaptive algorithm where excitation gates in the form of Givens rotations are selected according to the norm of their gradient. All quantum simulations are performed using the PennyLane library for quantum differentiable programming. The optimized geometrical parameters for the simulated molecules show an excellent agreement with their counterparts computed using classical quantum chemistry methods.

Probing the edge between integrability and quantum chaos in interacting few-atom systems

Interacting quantum systems in the chaotic domain are at the core of various ongoing studies of many-body physics, ranging from the scrambling of quantum information to the onset of thermalization. We propose a minimum model for chaos that can be experimentally realized with cold atoms trapped in one-dimensional multi-well potentials. We explore the emergence of chaos as the number of particles is increased, starting with as few as two, and as the number of wells is increased, ranging from a double well to a multi-well Kronig-Penney-like system. In this way, we illuminate the narrow boundary between integrability and chaos in a highly tunable few-body system. We show that the competition between the particle interactions and the periodic structure of the confining potential reveals subtle indications of quantum chaos for 3 particles, while for 4 particles stronger signatures are seen. The analysis is performed for bosonic particles and could also be extended to distinguishable fermions.

Pair Correlations and Photoassociation Dynamics of Two Atoms in an Optical Tweezer.

We investigate the photoassociation dynamics of exactly two laser-cooled ^{85}Rb atoms in an optical tweezer and reveal fundamentally different behavior to photoassociation in many-atom ensembles. We observe nonexponential decay in our two-atom experiment that cannot be described by a single rate coefficient and find its origin in our system's pair correlation. This is in stark contrast to many-atom photoassociation dynamics, which are governed by decay with a single rate coefficient. We also investigate photoassociation in a three-atom system, thereby probing the transition from two-atom dynamics to many-atom dynamics. Our experiments reveal additional reaction dynamics that are only accessible through the control of single atoms and suggest photoassociation could measure pair correlations in few-atom systems. It further showcases our complete control over the quantum state of individual atoms and molecules, which provides information unobtainable from many-atom experiments.

Covariance-Map Imaging: A Powerful Tool for Chemical Dynamics Studies.

Over the past decade or so, the state-of-the-art in the field of chemical reaction dynamics has progressed from studies of few-atom systems to wide-ranging investigations into a variety of photoinduced and collision-induced processes in much larger molecules. Many of these studies are of direct relevance to a wide audience of chemists, spanning fields such as atmospheric chemistry, astrochemistry, synthetic chemistry, and chemical biology. Key to this work has been the technique of velocity-map imaging, which allows complete product scattering distributions to be recorded for the process of interest. Recent advances in camera technology have enabled the development of multimass velocity-map imaging, in which the scattering distributions of all reaction products can be recorded in a single measurement. In addition to the scattering distributions of individual reaction products, the data set now contains information on correlations between the scattering distributions of two or more fragments. These correlations can be revealed using the technique of statistical covariance, yielding an approach known as covariance-map imaging. This review will introduce the reader to covariance mapping and will describe various applications of the technique within the field of chemical dynamics. The underlying concepts will be illustrated through a series of simple simulations, before moving on to describe a number of recent experimental studies in which covariance mapping has been used to obtain mechanistic insight and information on molecular structure on the femtosecond time scale.

Large-Scale Quantum Dynamics with Matrix Product States.

Dynamical electronic- and vibrational-structure theories have received a growing interest in the past few years due to their ability to simulate spectra recorded with ultrafast experimental techniques. The exact time evolution of a molecular system can, in principle, be obtained from the time-dependent version of full configuration interaction. Such an approach is, however, limited to few-atom systems due to the exponential increase of its cost with the system dimension. In the present work, we overcome this unfavorable scaling by employing the time-dependent density matrix renormalization group (TD-DMRG) which parametrizes the time-dependent wave function as a matrix product state. The time-dependent Schrödinger equation is then integrated with a sweep-based algorithm, as in standard time-independent DMRG. Unlike other TD-DMRG approaches, the one presented here leads to a set of coupled equations that can be integrated exactly. The resulting theory enables us to study real- and imaginary-time evolutions of Hamiltonians comprising more than 20 degrees of freedom that are challenging for current state-of-the-art quantum dynamics algorithms. We apply our algorithm to the simulation of quantum dynamics of models of increasing complexity, ranging from simple excitonic Hamiltonians to more complex ab initio vibronic ones.

Competition between finite-size effects and dipole–dipole interactions in few-atom systems

In this paper, we study the competition between finite-size effects (i.e. discernibility of particles) and dipole–dipole interactions in few-atom systems coupled to the electromagnetic field in vacuum. We consider two hallmarks of cooperative effects, superradiance and subradiance, and compute for each the rate of energy radiated by the atoms and the coherence of the atomic state during the time evolution. We adopt a statistical approach in order to extract the typical behaviour of the atomic dynamics and average over random atomic distributions in spherical containers with prescribed with k0 the radiation wavenumber and R the average interatomic distance. Our approach allows us to highlight the tradeoff between finite-size effects and dipole–dipole interactions in superradiance/subradiance. In particular, we show the existence of an optimal value of for which the superradiant intensity and coherence pulses are the less affected by dephasing effects induced by dipole–dipole interactions and finite-size effects.

Comparing models for the ground state energy of a trapped one-dimensional Fermi gas with a single impurity

We discuss the local density approximation approach to calculating the ground state energy of a one-dimensional Fermi gas containing a single impurity, and compare the results with exact numerical values that we have for up to 11 particles for general interaction strengths and up to 30 particles in the strongly interacting case. We also calculate the contact coefficient in the strongly interacting regime. The different theoretical predictions are compared to recent experimental results with few-atom systems. Firstly, we find that the local density approximation suffers from great ambiguity in the few-atom regime, yet it works surprisingly well for some models. Secondly, we find that the strong interaction theories quickly break down when the number of particles increase or the interaction strength decreases.

Configuration-Space Sampling in Potential Energy Surface Fitting: A Space-Reduced Bond-Order Grid Approach.

Potential energy surfaces (PESs) for use in dynamics calculations of few-atom reactive systems are commonly modeled as functional forms fitting or interpolating a set of ab initio energies computed at many nuclear configurations. An automated procedure is here proposed for optimal configuration-space sampling in generating this set of energies as part of the grid-empowered molecular simulator GEMS (Laganà et al., J. Grid Comput. 2010, 8, 571-586). The scheme is based on a space-reduced formulation of the so-called bond-order variables allowing for a balanced representation of the attractive and repulsive regions of a diatom configuration space. Uniform grids based on space-reduced bond-order variables are proven to outperform those defined on the more conventional bond-length variables in converging the fitted/interpolated PES to the computed ab initio one with increasing number of grid points. Benchmarks are performed on the one- and three-dimensional prototype systems H2 and H3 using both a local-interpolation (modified Shepard) and a global-fitting (Aguado-Paniagua) scheme.

(Keynote) Nanoscale Memories: What Does Physics Have to Say?

The central question addressed in this paper is: What is the smallest volume of matter needed for memory devices? It will be shown that, at least in principle, 1-nm devices can be envisioned, which are based on the re-arrangement of atoms; examples include atomic/ionic switches and resistive memory (ReRAM). While theoretical feasibility of the 1-nm devices has been justified based on electrical properties of the few-atom systems, it is still an open question whether such small structure could have sufficient thermal stability for reliable operation. For example, Joule heat will be released as the current passes through the structure, which can potentially destroy the few-atom conductive bridge (CB). In this paper, initial studies of thermal properties of atomic contacts and nanoscale interfaces are presented.

(Keynote) Nanoscale Memories: What Does Physics Have to Say?

Device scaling and energy consumption during computation has become a matter of strategic importance for future information technologies. The central question addressed in this talk is: What is the smallest volume of matter needed for a memory element? A generic physics-based abstraction for memory devices will be introduced and applied to several baseline memory technologies. The scaling limit of electron-based devices is~5-7 nm due to quantum-mechanical tunneling. Smaller devices can be made, if information-bearing particles are used whose mass is greater than the mass of an electron. Therefore the new principles for devices, scalable to ~1 nm, could be ‘moving atoms’ instead of ‘moving electrons’. Theoretical feasibility of the 1-nm devices will be justified based on electrical properties of the few-atom systems. Next, thermal properties of atomic contacts and devices such as nanoionic switch/ReRAM memory cell will be discussed to provide an insight whether such small structure could have sufficient thermal stability for reliable operation. An important task for sub-10 nm nanodevices is recognition of the fundamental role of ‘defects’ that should not be treated as imperfections but instead as controllable entities. The materials nonstoichiometry due to point defects plays a key role in the electronic properties of many materials, for example in metal oxides. Due to these nonstoichiometric defects, the materials often behave as doped semiconductors. In fact, these materials form a special class, sometimes called ‘chemiconductors’. In addition to solid-state nanoionic devices such as ReRAM) concepts of ‘fluid nanoelectronics’ are proposed that utilize liquid media, which may offer a new promising path to replace the foundation of today’s computing technologies. Examples include nanoionic devices based on electrolyte-filled nanochannels. In principle, such structures might be used to make devices scalable to ~1 nm or below. Recently there have been suggestions from research that the physical limits of semiconductor technology may in fact be overcome by borrowing from synthetic biology principles. For example, it has recently been shown that DNA can be used to achieve storage densities that cannot be approached by any known solid-state technology. This lecture will examine how one might develop a technology in the semiconductor context that would open up DNA memory to widespread applications.

Nonlinear spectroscopy of trapped ions

Nonlinear spectroscopy employs a series of laser pulses to interrogate dynamics in large interacting many-body systems, and it has become a highly successful method for experiments in chemical physics. Current quantum optical experiments approach system sizes and levels of complexity that require the development of efficient techniques to assess spectral and dynamical features with scalable experimental overhead. However, established methods from optical spectroscopy of macroscopic ensembles cannot be applied straightforwardly to few-atom systems. Based on the ideas proposed in M. Gessner et al., (arXiv:1312.3365), we develop a diagrammatic approach to construct nonlinear measurement protocols for controlled quantum systems, and we discuss experimental implementations with trapped ion technology in detail. These methods, in combination with distinct features of ultracold-matter systems, allow us to monitor and analyze excitation dynamics in both the electronic and vibrational degrees of freedom. They are independent of system size, and they can therefore reliably probe systems in which, e.g., quantum state tomography becomes prohibitively expensive. We propose signals that can probe steady-state currents, detect the influence of anharmonicities on phonon transport, and identify signatures of chaotic dynamics near a quantum phase transition in an Ising-type spin chain.

Temperature dependence of small harmonically trapped atom systems with Bose, Fermi, and Boltzmann statistics

While the zero-temperature properties of harmonically trapped cold few-atom systems have been discussed fairly extensively over the past decade, much less is known about the finite-temperature properties. Working in the canonical ensemble, we characterize small harmonically trapped atomic systems as a function of the temperature using analytical and numerical techniques. We present results for the energetics, structural properties, condensate fraction, superfluid fraction, and superfluid density. Our calculations for the two-body system underline that the condensate and superfluid fractions are distinctly different quantities. Our work demonstrates that the path integral Monte Carlo method yields reliable results for bosonic and fermionic systems over a wide temperature range, including the regime where the de Broglie wave length is large, i.e., where the statistics plays an important role. The regime where the Fermi sign problem leads to reasonably large signal to noise ratios is mapped out for selected parameter combinations. Our calculations for bosons focus on the unitary regime, where the physics is expected to be governed by the three-body parameter. If the three-body parameter is large compared to the inverse of the harmonic oscillator length, we find that the bosons form a droplet at low temperature and behave approximately like a non-interacting Bose and eventually Boltzmann gas at high temperature. The change of the behavior occurs over a fairly narrow temperature range. A simple model that reproduces the key aspects of the phase transition like feature, which can potentially be observed in cold atom Bose gas experiments, is presented.

Anisotropic deformation of the Rydberg-blockade sphere in few-atom systems

Rydberg blockade sphere persists an intriguing picture by which a number of collective many-body effects caused by the strong Rydberg-Rydberg interactions can be clearly understood and profoundly investigated. In the present work, we develop a new definition for the effective two-atom blockade radius and show that the original spherically shaped blockade surface would be deformed when the real number of atoms increases from two to three. This deformation of blockade sphere reveals spatially anisotropic and shrunken properties which strongly depend on the interatomic distance. In addition, we also study the optimal conditions for the Rydberg antiblockade effect and make predictions for improving the antiblockade efficiency in few-atom systems.

Derivative Couplings with Built-In Electron-Translation Factors: Application to Benzene

Derivative couplings are the essential quantities at the interface between electronic-structure calculations and nonadiabatic dynamics. Unfortunately, standard approaches for calculating these couplings usually neglect electronic motion, which can lead to spurious electronic transitions. Here we provide a general framework for correcting these anomalies by incorporating perturbative electron-translation factors (ETFs) into the atomic-orbital basis. For a range of representative organic molecules, we find that our ETF correction is often small but can be qualitatively important, especially for few-atom systems or highly symmetric molecules. Our method entails no additional computational cost, such that ETFs are “built-in,” and it is equivalent to a simple rule of thumb: We should set the antisymmetrized version of the nuclear overlap-matrix derivative to zero wherever it appears. Thus, we expect that built-in ETFs will be regularly incorporated into future studies of nonadiabatic dynamics.

Dilute Bose gases interacting via power-law potentials

Neutral atoms interact through a van der Waals potential which asymptotically falls off as ${r}^{\ensuremath{-}6}$. In ultracold gases, this interaction can be described to a good approximation by the atom-atom scattering length. However, corrections arise that depend on the characteristic length of the van der Waals potential. We parametrize these corrections by analyzing the energies of two- and few-atom systems under external harmonic confinement, obtained by numerically and analytically solving the Schr\"odinger equation. We generalize our results to particles interacting through a longer-ranged potential which asymptotically falls off as ${r}^{\ensuremath{-}4}$.

Treatment of geometric singularities in implicit solvent models

Geometric singularities, such as cusps and self-intersecting surfaces, are major obstacles to the accuracy, convergence, and stability of the numerical solution of the Poisson-Boltzmann (PB) equation. In earlier work, an interface technique based PB solver was developed using the matched interface and boundary (MIB) method, which explicitly enforces the flux jump condition at the solvent-solute interfaces and leads to highly accurate biomolecular electrostatics in continuum electric environments. However, such a PB solver, denoted as MIBPB-I, cannot maintain the designed second order convergence whenever there are geometric singularities, such as cusps and self-intersecting surfaces. Moreover, the matrix of the MIBPB-I is not optimally symmetrical, resulting in the convergence difficulty. The present work presents a new interface method based PB solver, denoted as MIBPB-II, to address the aforementioned problems. The present MIBPB-II solver is systematical and robust in treating geometric singularities and delivers second order convergence for arbitrarily complex molecular surfaces of proteins. A new procedure is introduced to make the MIBPB-II matrix optimally symmetrical and diagonally dominant. The MIBPB-II solver is extensively validated by the molecular surfaces of few-atom systems and a set of 24 proteins. Converged electrostatic potentials and solvation free energies are obtained at a coarse grid spacing of 0.5 A and are considerably more accurate than those obtained by the PBEQ and the APBS at finer grid spacings.

Zn−Se−Temultilayers with submonolayer quantities of Te: Type-II quantum structures and isoelectronic centers

Detailed studies with spectral and time-resolved photoluminescence, photoluminescence excitation, and absorption spectroscopies show the formation of type-II quantum structures (quantum dots) in a $\mathrm{Zn}\ensuremath{-}\mathrm{Se}\ensuremath{-}\mathrm{Te}$ multilayer system with submonolayer quantities of Te. Moreover, it is shown that in addition to these quantum dots, Te isoelectronic centers are also present in the same material system and contribute to the photoluminescence emissions. This could be siginificant for the better understanding of the scaling laws between many-atom systems (e.g., quantum dots) and few-atom systems (e.g., isoelectronic centers).

Theoretical study of finite-temperature spectroscopy in van der Waals clusters. I. Probing phase changes in CaArn

The photoabsorption spectra of calcium-doped argon clusters CaArn are investigated at thermal equilibrium using a variety of theoretical and numerical tools. The influence of temperature on the absorption spectra is estimated using the quantum superposition method for a variety of cluster sizes in the range 6⩽n⩽146. At the harmonic level of approximation, the absorption intensity is calculated through an extension of the Gaussian theory by Wadi and Pollak [J. Chem. Phys. 110, 11890 (1999)]. This theory is tested on simple, few-atom systems in both the classical and quantum regimes for which highly accurate Monte Carlo data can be obtained. By incorporating quantum anharmonic corrections to the partition functions and respective weights of the isomers, we show that the superposition method can correctly describe the finite-temperature spectroscopic properties of CaArn systems. The use of the absorption spectrum as a possible probe of isomerization or phase changes in the argon cluster is discussed at the light of finite-size effects.

Why ice floats on water

Why ice floats on water is an unresolved question that underlines the special properties of water. We argue that it is resolved by taking a different approach to structure than is usual, the “exponential scale” description. The exponential scale is placed on a firm foundation based on underlying quantum mechanics. The approach includes and is more general than conventional approaches to molecular and chemical interactions, based on separate and different kinds of “bonds”. These are based on perturbation theories applied to few-atom systems. The present approach to the many-body problem is in the same spirit as, but more general than Lifshitz theory of intermolecular interactions.