We introduce the so-called "Classical Optimal Control Optimization" (COCO) method for global energy minimization based on the implementation of the diffeomorphic modulation under observable-response-preserving homotopy (DMORPH) gradient algorithm. A probe particle with time-dependent mass m(t;β) and dipole μ(r,t;β) is evolved classically on the potential energy surface V(r) coupled to an electric field E(t;β), as described by the time-dependent density of states represented on a grid, or otherwise as a linear combination of Gaussians generated by the k-means clustering algorithm. Control parameters β defining m(t;β), μ(r,t;β), and E(t;β) are optimized by following the gradients of the energy with respect to β, adapting them to steer the particle toward the global minimum energy configuration. We find that the resulting COCO algorithm is capable of resolving near-degenerate states separated by large energy barriers and successfully locates the global minima of golf potentials on flat and rugged surfaces, previously explored for testing quantum annealing methodologies and the quantum optimal control optimization (QuOCO) method. Preliminary results show successful energy minimization of multidimensional Lennard-Jones clusters. Beyond the analysis of energy minimization in the specific model systems investigated, we anticipate COCO should be valuable for solving minimization problems in general, including optimization of parameters in applications to machine learning and molecular structure determination.

Understanding how to control reaction dynamics of polyatomic systems by using ultrafast laser technology is a fundamental challenge of great technological interest. Here, we report a Floquet theoretical study of the effect of light-induced potentials on the ultrafast cis-trans photoisomerization dynamics of rhodopsin. The Floquet Hamiltonian involves an empirical 3-state 25-mode model with frequencies and excited-state gradients parametrized to reproduce the rhodopsin electronic vertical excitation energy, the resonance Raman spectrum, and the photoisomerization time and efficiency as probed by ultrafast spectroscopy. We simulate the excited state relaxation dynamics using the time-dependent self-consistent field method, as described by a 3-state 2-mode nuclear wavepacket coupled to a Gaussian ansatz of 23 vibronic modes. We analyze the reaction time and product yield obtained with pulses of various widths and intensity profiles, defining 'dressed states' where the perturbational effect of the pulses is naturally decoupled along the different reaction channels. We find pulses that delay the excited-state photoisomerization for hundreds of femtoseconds, and we gain insights on the underlying control mechanisms. The reported findings provide understanding of quantum control, particularly valuable for the development of ultrafast optical switches based on visual pigments.

A rigorous method for simulations of quantum dynamics is introduced on the basis of concatenation of semiclassical thawed Gaussian propagation steps. The time-evolving state is represented as a linear superposition of closely overlapping Gaussians that evolve in time according to their characteristic equations of motion, integrated by fourth-order Runge-Kutta or velocity Verlet. The expansion coefficients of the initial superposition are updated after each semiclassical propagation period by implementing the Husimi Transform analytically in the basis of closely overlapping Gaussians. An advantage of the resulting time-sliced thawed Gaussian (TSTG) method is that it allows for full-quantum dynamics propagation without any kind of multidimensional integral calculation, or inversion of overlap matrices. The accuracy of the TSTG method is demonstrated as applied to simulations of quantum tunneling, showing quantitative agreement with benchmark calculations based on the split-operator Fourier transform method.

We introduce a quantum optimal control algorithm for energy minimization that combines the diffeomorphic modulation under observable response preserving homotopy (D-MORPH) gradient and the Broyden Fletcher Goldfarb Shanno (BFGS) iterative scheme for nonlinear optimization. An extended set of controls defining the time-dependent mass, dipole moment, and external perturbational field are optimized to find an effective Hamiltonian that steers the dynamics of the system into the global minimum without getting trapped into local minima. The algorithm is illustrated as applied to energy minimization on rugged surfaces and golf potentials comparable to those previously explored for testing quantum annealing methodologies.

The wave packet molecular dynamics (WPMD) method provides a variational approximation to the solution of the time-dependent Schrödinger equation. Its application in the field of high-temperature dense plasmas has yielded diverging electron width (spreading), which results in diminishing electron-nuclear interactions. Electron spreading has previously been ascribed to a shortcoming of the WPMD method and has been counteracted by various heuristic additions to the models used. We employ more accurate methods to determine if spreading continues to be predicted by them and how WPMD can be improved. A scattering process involving a single dynamic electron interacting with a periodic array of statically screened protons is used as a model problem for comparison. We compare the numerically exact split operator Fourier transform method, the Wigner trajectory method, and the time-dependent variational principle (TDVP). Within the framework of the TDVP, we use the standard variational form of WPMD, the single Gaussian wave packet (WP), as well as a sum of Gaussian WPs, as in the split WP method. Wave packet spreading is predicted by all methods, so it is not the source of the unphysical diminishing of electron-nuclear interactions in WPMD at high temperatures. Instead, the Gaussian WP's inability to correctly reproduce breakup of the electron's probability density into localized density near the protons is responsible for the deviation from more accurate predictions. Extensions of WPMD must include a mechanism for breakup to occur in order to yield dynamics that lead to accurate electron densities.

A general coherent control scheme for speeding up quantum tunneling of proton transfer through Coulombic barriers is analysed. The quantum control scenario is based on repetitive electron impact ionization pulses that affect the ensuing interference phenomena responsible for quantum dynamics and force the proton to tunnel into classically forbidden regions of configuration space. The scheme is demonstrated for the simplest model of nuclear fusion, hinting at the possible enhancement of reactive scattering based on low energy collisions.

An accurate and efficient algorithm for dynamics simulations of particles with attractive 1/r singular potentials is introduced. The method is applied to semiclassical dynamics simulations of electron proton scattering processes in the Wigner-transform time-dependent picture, showing excellent agreement with full quantum dynamics calculations. Rather than avoiding the singularity problem by using a pseudopotential, the algorithm predicts the outcome of close-encounter two-body collisions for the true 1/r potential by solving the Kepler problem analytically and corrects the trajectory for multiscattering with other particles in the system by using standard numerical techniques (e.g., velocity Verlet, or Gear Predictor corrector algorithms). The resulting integration is time-reversal symmetric and can be applied to the general multibody dynamics problem featuring close encounters as occur in electron ion scattering events, in particle antiparticle dynamics, as well as in classical simulations of charged interstellar gas dynamics and gravitational celestial mechanics.

Submitted for the DPP11 Meeting of The American Physical Society A Different Time-Dependent Variational Principle Approach: Going Beyond Wave Packet Molecular Dynamics PAUL GRABOWSKI, Los Alamos National Laboratory, ANDREAS MARKMANN, Yale University, MICHAEL MURILLO, Los Alamos National Laboratory, FRANK GRAZIANI, Lawrence Livermore National Laboratory, CIMARRON COLLABORATION — During inertial confinement fusion, matter evolves from a solid condensed matter phase through the warm dense matter (WDM) regime to a hot dense matter. In WDM, quantum mechanical effects are important because of both Fermi-Dirac statistics and the rate of electrons transitioning in and out of bound states is large. The time-dependent temperature and quickly changing local environment require a time-dependent quantum method. A converged dynamical quantum simulation is intractable for more than a few particles. Instead, we take as a feasible goal to match the statistical properties of a warm dense plasma. The time-dependent variational principle gives a framework for producing equations of motion. A commonly used ansatz is a Hartree product of isotropic Gaussian wave packets (wave packet molecular dynamics). The resulting dynamics do not produce the right statistics. We therefore introduce a plane wave basis and discuss its advantages and test its ability to reproduce radial distribution functions produced by hyper-netted chain calculations. Paul Grabowski Los Alamos National Laboratory Date submitted: 15 Jul 2011 Electronic form version 1.4

We describe the status of a new time-dependent simulation capability for dense plasmas. The backbone of this multi-institutional effort – the Cimarron Project – is the massively parallel molecular dynamics (MD) code “ddcMD,” developed at Lawrence Livermore National Laboratory. The project’s focus is material conditions such as exist in inertial confinement fusion experiments, and in many stellar interiors: high temperatures, high densities, significant electromagnetic fields, mixtures of high- and low-Z elements, and non-Maxwellian particle distributions. Of particular importance is our ability to incorporate into this classical MD code key atomic, radiative, and nuclear processes, so that their interacting effects under non-ideal plasma conditions can be investigated. This paper summarizes progress in computational methodology, discusses strengths and weaknesses of quantum statistical potentials as effective interactions for MD, explains the model used for quantum events possibly occurring in a collision, describes two new experimental efforts that play a central role in our validation work, highlights some significant results obtained to date, outlines concepts now being explored to deal more efficiently with the very disparate dynamical timescales that arise in fusion plasmas, and provides a careful comparison of quantum effects on electron trajectories predicted by more elaborate dynamical methods.

Submitted for the DPP11 Meeting of The American Physical Society Semiclassical Simulation of Electron Scattering in Warm Dense Plasma Conditions ANDREAS MARKMANN, Yale University, PAUL GRABOWSKI, MICHAEL MURILLO, LANL, FRANK GRAZIANI, LLNL, VICTOR BATISTA, Yale University, CIMARRON COLLABORATION — We introduce an efficient algorithm for dynamics simulation of particles with attractive potentials developed within the Cimarron Project, where electron-proton scattering is to be treated explicitly. Such simulations provide valuable insights and guidance for current experimental efforts at the National Ignition Facility. Electrons rapidly transition between bound and free states, while their environment changes rapidly, requiring simulations to account for quantum effects. Large scale simulations modeling quantum effects need to be tuned by comparison to high accuracy quantum or semiclassical simulations. Our algorithm is applied to semiclassical simulations of electron-proton scattering processes in the Wigner-transform time-dependent picture. Heisenberg uncertainty and interference are compared to exact quantum dynamics. Protons are modeled through full Coulomb potentials and screened Coulomb (Yukawa) potentials, respectively. The relative importance of quantum effects such as uncertainty and interference is inferred from the results. Andreas Markmann Yale University Date submitted: 25 Jul 2011 Electronic form version 1.4

This work explores the feasibility of using shaped electrostatic potentials to achieve specified final scattering distributions of an electron wave packet in a two dimensional subsurface plane of a semiconductor. When electron transport takes place in the ballistic regime, and features of the scattering potentials are smaller than the wavelength of the incident electron then coherent quantum effects can arise. Simulations employing potential forms based on analogous optical principles demonstrate the ability to manipulate quantum interferences in two dimensions. Simulations are presented showing that suitably shaped electrostatic potentials may be used to separate an initially localized Gaussian wave packet into disjoint components or concomitantly to combine a highly dispersed packet into a compact form. The results also indicate that highly complex scattering objectives may be achieved by utilizing adaptive closed-loop optimal control in the laboratory to determine the potential forms needed to manipulate the scattering of an incoming wave packet. An adaptive feedback algorithm can be used to vary individual voltages of multipixel gates on the surface of a solid state structure to thereby find the potential features in the transport plane needed to produce a desired scattering objective. A proposed experimental design is described for testing the concept of adaptive control of coherent electron transport in semiconductors.