arXiv subjects

Barry I. Schneider

Publications and source records attributed to Barry I. Schneider.

16 recordsLinked to original sources

arXiv2023

Two-electron interference in two-photon attosecond double ionization of neon

The pump-probe experiments enabled by X-ray free-electron lasers (XFEL) will allow us to directly observe correlated electronic motion with attosecond time resolution by detecting photoelectron pairs in coincidence. In helium, the transition between the non-sequential and sequential regime in two-photon double ionization (TPDI) is well explained by a virtual-sequential model. Much less is known, however, about the TPDI process in more complex atoms. Recently, we extended the virtual-sequential model to arbitrary light pulses [Chattopadhyay {\it et al.,} Phys. Rev. A~{\bf 108}, 013114 (2023)]. This extension employs multi-channel scattering states for the single ionization of both the neutral and the ionized target, which we initally applied to helium. In the present study, we show that our extended virtual-sequential model reproduces the qualitative features of the angularly integrated observables with available experimental results for neon, a considerably more complex target. We observe an intriguing feature of inverted two-particle interference in the joint energy distribution of $\mathrm{Ne}$ compared to $\mathrm{He}$. This phenomenon, attributable to the presence of a final doubly ionized state with triplet symmetry coupled to the two photoelectrons, should be observable with current experimental technologies.

physics.atom-ph↗

arXiv2023

ITVOLT: An Iterative Solver for the Time-Dependent Schrödinger Equation

We present a novel approach for solving the time-dependent Schrödinger equation (TDSE). The method we propose converts the TDSE to an equivalent Volterra integral equation; introducing a global Lagrange interpolation of the integrand transforms the equation to a linear system, which is then solved iteratively. In this paper, we derive the method, explore its performance on several examples, and discuss the corresponding numerical details.

math.NA↗

arXiv2021

A Multi-Center Quadrature Scheme for the Molecular Continuum

A common way to evaluate electronic integrals for polyatomic molecules is to use Becke's partitioning scheme [J. Chem. Phys.88, 2547 (1988)] in conjunction with overlapping grids centered at each atomic site. The Becke scheme was designed for integrands that fall off rapidly at large distances, such as those approximating bound electronic states. When applied to states in the electronic continuum, however, Becke scheme exhibits slow convergence and it is highly redundant. Here, we present a modified version of Becke scheme that is applicable to functions of the electronic continuum, such as those involved in molecular photoionization and electron-molecule scattering, and which ensures convergence and efficiency comparable to those realized in the calculation of bound states. In this modified scheme, the atomic weights already present in Becke's partition are smoothly switched off within a range of few bond lengths from their respective nuclei, and complemented by an asymptotically unitary weight. The atomic integrals are evaluated on small spherical grids, centered on each atom, with size commensurate to the support of the corresponding atomic weight. The residual integral of the interstitial and long-range region is evaluated with a central master grid. The accuracy of the method is demonstrated by evaluating integrals involving integrands containing Gaussian Type Orbitals and Yukawa potentials, on the atomic sites, as well as spherical Bessel functions centered on the master grid. These functions are representative of those encountered in realistic electron-scattering and photoionization calculations in polyatomic molecules.

physics.chem-ph↗

arXiv2020

Predicting Kovats Retention Indices Using Graph Neural Networks

The \kovats retention index is a dimensionless quantity that characterizes the rate at which a compound is processed through a gas chromatography column. This quantity is independent of many experimental variables and, as such, is considered a near-universal descriptor of retention time on a chromatography column. The \kovats retention indices of a large number of molecules have been determined experimentally. The "NIST 20: GC Method\slash Retention Index Library" database has collected and, more importantly, curated retention indices of a subset of these compounds resulting in a highly valued reference database. The experimental data in the library form an ideal data set for training machine learning models for the prediction of retention indices of unknown compounds. In this article, we describe the training of a graph neural network model to predict the \kovats retention index for compounds in the NIST library and compare this approach with previous work \cite{2019Matyushin}. We predict the \kovats retention index with a mean unsigned error of 28 index units as compared to 44, the putative best result using a convolutional neural network \cite{2019Matyushin}. The NIST library also incorporates an estimation scheme based on a group contribution approach that achieves a mean unsigned error of 114 compared to the experimental data. Our method uses the same input data source as the group contribution approach, making its application straightforward and convenient to apply to existing libraries. Our results convincingly demonstrate the predictive powers of systematic, data-driven approaches leveraging deep learning methodologies applied to chemical data and for the data in the NIST 20 library outperform previous models.

physics.chem-ph↗

arXiv2020

A Science Gateway for Atomic and Molecular Physics

We describe the creation of a new Atomic and Molecular Physics science gateway (AMPGateway). The gateway is designed to bring together a subset of the AMP community to work collectively to make their codes available and easier to use by the partners as well as others. By necessity, a project such as this requires the developers to work on issues of portability, documentation, ease of input, as well as making sure the codes can run on a variety of architectures. Here we outline our efforts to build this AMP gateway and future directions.

physics.comp-ph↗

arXiv2019

Comparison of Numerical Approaches to the Time-Dependent Schrödinger Solutions in One Dimension

We examine the performance of various time propagation schemes using a one-dimensional model of the hydrogen atom. In this model the exact Coulomb potential is replaced by a soft-core interaction. The model has been shown to be a reasonable representation of what occurs in the fully three-dimensional hydrogen atom. Our results show that while many numerically simple (low order) propagation schemes work, they often require quite small time-steps. Comparing them against more accurate methods, which may require more work per time-step but allow much larger time-steps, can be illuminating. We show that at least in this problem, the compute time for a number of the more accurate methods is actually less than lower order schemes. Finally, we make some remarks on what to expect in generalizing our findings to more than one dimension.

physics.comp-ph↗

arXiv2018

Application of the Complex Kohn Variational Method to Attosecond Spectroscopy

The complex Kohn variational method is extended to compute light-driven electronic transitions between continuum wavefunctions in atomic and molecular systems. This development enables the study of multiphoton processes in the perturbative regime for arbitrary light polarization. As a proof of principle, we apply the method to compute the photoelectron spectrum arising from the pump-probe two-photon ionization of helium induced by a sequence of extreme ultraviolet and infrared-light pulses. We compare several two-photon ionization pump-probe spectra, resonant with the (2s2p)1P1o Feshbach resonance, with independent simulations based on the atomic B-spline close- coupling STOCK code, and find good agreement between the two approaches. This new finite-pulse perturbative approach is a step towards the ab initio study of weak-field attosecond processes in poly-electronic molecules.

physics.atom-ph↗

arXiv2014

Time delays for attosecond streaking in photoionization of neon

We revisit the time-resolved photoemission in neon atoms as probed by attosecond streaking. We calculate streaking time shifts for the emission of 2p and 2s electrons and compare the relative delay as measured in a recent experiment by Schultze et al. [Science 328, 1658 (2010)]. The B-spline R-matrix method is employed to calculate accurate Eisenbud-Wigner-Smith time delays from multi- electron dipole transition matrix elements for photoionization. The additional laser field-induced time shifts in the exit channel are obtained from separate, time-dependent simulations of a full streaking process by solving the time-dependent Schrödinger equation on the single-active-electron level. The resulting accurate total relative streaking time shifts between 2s and 2p emission lie well below the experimental data. We identify the presence of unresolved shake-up satellites in the experiment as a potential source of error in the determination of streaking time shifts.

physics.atom-ph↗

arXiv2013

Elastic scattering of a Bose-Einstein condensate at a potential landscape

We investigate the elastic scattering of Bose-Einstein condensates at shallow periodic and disorder potentials. We show that the collective scattering of the macroscopic quantum object couples to internal degrees of freedom of the Bose-Einstein condensate such that the Bose-Einstein condensate gets depleted. As a precursor for the excitation of the Bose-Einstein condensate we observe wave chaos within a mean-field theory.

cond-mat.quant-gas↗

arXiv2011

Breakup of the aligned H$_2$ molecule by xuv laser pulses: A time-dependent treatment in prolate spheroidal coordinates

We have carried out calculations of the triple-differential cross section for one-photon double ionization of molecular hydrogen for a central photon energy of $75$~eV, using a fully {\it ab initio}, nonperturbative approach to solve the time-dependent \Schro equation in prolate spheroidal coordinates. The spatial coordinates $ξ$ and $η$ are discretized in a finite-element discrete-variable representation. The wave packet of the laser-driven two-electron system is propagated in time through an effective short iterative Lanczos method to simulate the double ionization of the hydrogen molecule. For both symmetric and asymmetric energy sharing, the present results agree to a satisfactory level with most earlier predictions for the absolute magnitude and the shape of the angular distributions. A notable exception, however, concerns the predictions of the recent time-independent calculations based on the exterior complex scaling method in prolate spheroidal coordinates [Phys.~Rev.~A~{\bf 82}, 023423 (2010)]. Extensive tests of the numerical implementation were performed, including the effect of truncating the Neumann expansion for the dielectronic interaction on the description of the initial bound state and the predicted cross sections. We observe that the dominant escape mode of the two photoelectrons dramatically depends upon the energy sharing. In the parallel geometry, when the ejected electrons are collected along the direction of the laser polarization axis, back-to-back escape is the dominant channel for strongly asymmetric energy sharing, while it is completely forbidden if the two electrons share the excess energy equally.

physics.atom-ph↗

arXiv2010

Two-photon Double Ionization of H$_2$ in Intense Femtosecond Laser Pulses

Triple-differential cross sections for two-photon double ionization of molecular hydrogen are presented for a central photon energy of 30 eV. The calculations are based on a fully {\it ab initio}, nonperturbative, approach to the time-dependent Schroedinger equation in prolate spheroidal coordinates, discretized by a finite-element discrete-variable-representation. The wave function is propagated in time for a few femtoseconds using the short, iterative Lanczos method to study the correlated response of the two photoelectrons to short, intense laser radiation. The current results often lie in between those of Colgan {\it et al} [J. Phys. B {\bf 41} (2008) 121002] and Morales {\it et al} [J. Phys. B {\bf 41} (2009) 134013]. However, we argue that these individual predictions should not be compared directly to each other, but preferably to experimental data generated under well-defined conditions.

physics.atom-ph↗

arXiv2009

Electron correlation in two-photon double ionization of helium from attosecond to FEL pulses

We investigate the role of electron correlation in the two-photon double ionization of helium for ultrashort XUV pulses with durations ranging from a hundred attoseconds to a few femtoseconds. We perform time-dependent ab initio calculations for pulses with mean frequencies in the so-called "sequential" regime (photon energy above 54.4 eV). Electron correlation induced by the time correlation between emission events manifests itself in the angular distribution of the ejected electrons, which strongly depends on the energy sharing between them. We show that for ultrashort pulses two-photon double ionization probabilities scale non-uniformly with pulse duration depending on the energy sharing between the electrons. Most interestingly we find evidence for an interference between direct ("nonsequential") and indirect ("sequential") double photo-ionization with intermediate shake-up states, the strength of which is controlled by the pulse duration. This observation may provide a route toward measuring the pulse duration of FEL pulses.

physics.atom-ph↗

arXiv2006

A two-channel R-matrix analysis of magnetic field induced Feshbach resonances

A Feshbach resonance arises in cold atom scattering due to the complex interplay between several coupled channels. However, the essential physics of the resonance may be encapsulated in a simplified model consisting of just two coupled channels. In this paper we describe in detail how such an effective Feshbach model can be constructed from knowledge of a few key parameters, characterizing the atomic Born-Oppenheimer potentials and the low energy scattering near the resonance. These parameters may be obtained either from experiment or full coupled channels calculations. Using R-matrix theory we analyze the bound state spectrum and the scattering properties of the two-channel model, and find it to be in good agreement with exact calculations.

cond-mat.other↗

arXiv2004

Comments on the Discrete Variable Representation

We discuss the application of the Discrete Variable Representation to Schrödinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well-behaved, the boundary conditions are satisfied and the calculation is rapidly convergent. The accuracy of the method is demonstrated by applying it to the hydrogen atom. We emphasize that the method is equally capable of describing bound states and continuum solutions.

physics.chem-ph↗

arXiv1999

Nucleation of vortex arrays in rotating anisotropic Bose-Einstein condensates

The nucleation of vortices and the resulting structures of vortex arrays in dilute, trapped, zero-temperature Bose-Einstein condensates are investigated numerically. Vortices are generated by rotating a three-dimensional, anisotropic harmonic atom trap. The condensate ground state is obtained by propagating the Gross-Pitaevskii equation in imaginary time. Vortices first appear at a rotation frequency significantly larger than the critical frequency for vortex stabilization. This is consistent with a critical velocity mechanism for vortex nucleation. At higher frequencies, the structures of the vortex arrays are strongly influenced by trap geometry.

cond-mat.stat-mech↗

arXiv1999

Vortex stability of interacting Bose-Einstein condensates confined in anisotropic harmonic traps

Vortex states of weakly-interacting Bose-Einstein condensates confined in three-dimensional rotating harmonic traps are investigated numerically at zero temperature. The ground state in the rotating frame is obtained by propagating the Gross-Pitaevskii equation for the condensate in imaginary time. The total energies between states with and without a vortex are compared, yielding critical rotation frequencies that depend on the anisotropy of the trap and the number of atoms. Vortices displaced from the center of nonrotating traps are found to have long lifetimes for sufficiently large numbers of atoms. The relationship between vortex stability and bound core states is explored.

cond-mat.stat-mech↗