Esa Räsänen

Optimal control of high-harmonic generation by intense few-cycle pulses

This work was supported by the Academy of Finland; COST Action CM1204 (XLIC); the European Community’s FP7 through the CRONOS project, Grant No. 280879; nthe European Research Council Advanced Grant DYNamo (Grant No. ERC-2010-AdG-267374); Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT578-13); Spanish Grant No. FIS2010-21282-C02-01; and the University of Zaragoza (Project No. UZ2012-CIE-06).

Bill2d — A software package for classical two-dimensional Hamiltonian systems☆

Abstract We present Bill2d , a modern and efficient C++ package for classical simulations of two-dimensional Hamiltonian systems. Bill2d can be used for various billiard and diffusion problems with one or more charged particles with interactions, different external potentials, an external magnetic field, periodic and open boundaries, etc. The software package can also calculate many key quantities in complex systems such as Poincare sections, survival probabilities, and diffusion coefficients. While aiming at a large class of applicable systems, the code also strives for ease-of-use, efficiency, and modularity for the implementation of additional features. The package comes along with a user guide, a developer’s manual, and a documentation of the application program interface (API). Program summary Program title: Bill2d Catalogue identifier: AEYL_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEYL_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 37098 No. of bytes in distributed program, including test data, etc.: 1155037 Distribution format: tar.gz Programming language: C++(14). Computer: Tested on x86 and x86 64 architectures. Operating systems: Tested on Linux, and OS X versions 10.9–10.11. Has the code been vectorized or parallelized?: Shared memory parallelization when simulating ensembles of systems. Vectorization of operations with R 2 vectors. RAM: Simulation dependent: kilobytes to gigabytes Classification: 4.3, 7.8, 7.9, 7.10, 16.9. External routines: Boost, CMake, GSL, HDF5; and optionally Google-Mock, GoogleTest, and Doxygen Nature of problem: Numerical propagation of classical two-dimensional single and many-body systems, possibly in a magnetic field, and calculation of relevant quantities such as Poincare sections, survival probabilities, diffusion co-efficients, etc. Solution method: Symplectic numerical integration of Hamilton’s equations of motion in Cartesian coordinates, or solution of Newton’s equations of motion if in a magnetic field. The program implements several well-established algorithms. Restrictions: Pointlike particles with equal masses and charges, although the latter restrictions are easy to lift. Unusual features: Program is efficient, extremely modular and easy to extend, and allows arbitrary particle–particle interactions. Additional comments: The source code is also available at https://bitbucket.org/solanpaa/bill2d . See README for locations of user guide, developer manual, and API docs. Running time: From milliseconds to days, depends on type of simulation.

Coulomb-interacting billiards in circular cavities

We apply a molecular dynamics scheme to analyze classically chaotic properties of a two-dimensional circular billiard system containing two Coulomb-interacting electrons. As such, the system resembles a prototype model for a semiconductor quantum dot. The interaction strength is varied from the noninteracting limit with zero potential energy up to the strongly interacting regime where the relative kinetic energy approaches zero. At weak interactions the bouncing maps show jumps between quasi-regular orbits. In the strong-interaction limit we find an analytic expression for the bouncing map. Its validity in the general case is assessed by comparison with our numerical data. To obtain a more quantitative view on the dynamics as the interaction strength is varied, we compute and analyze the escape rates of the system. Apart from very weak or strong interactions, the escape rates show consistently exponential behavior, thus suggesting strongly chaotic dynamics and a phase space without significant sticky regions within the considered time scales.We apply a molecular dynamics scheme to analyze classically chaotic properties of a two-dimensional circular billiard system containing two Coulombinteracting electrons. As such, the system resembles a prototype model for a semiconductor quantum dot. The interaction strength is varied from the noninteracting limit with zero potential energy up to the strongly interacting regime where the relative kinetic energy approaches zero. At weak interactions the bouncing maps show jumps between quasi-regular orbits. In the strong-interaction limit we find an analytic expression for the bouncing map. Its validity in the general case is assessed by comparison with our numerical data. To obtain a more quantitative view on the dynamics as the interaction strength is varied, we compute and analyze the escape rates of the system. Apart from very weak or strong interactions, the escape rates show consistently exponential behavior, thus suggesting strongly chaotic dynamics and a phase space without significant sticky regions within the considered time scales. PACS numbers: 05.45.Pq, 82.40.Bj, 73.21.La Chaotic properties of Coulomb-interacting circular billiards 2

Controllable quantum scars in semiconductor quantum dots

Quantum scars are enhancements of quantum probability density along classical periodic orbits. We study the recently discovered phenomenon of strong, perturbation-induced quantum scarring in the two-dimensional harmonic oscillator exposed to a homogeneous magnetic field. We demonstrate that both the geometry and the orientation of the scars are fully controllable with a magnetic field and a focused perturbative potential, respectively. These properties may open a path into an experimental scheme to manipulate electric currents in nanostructures fabricated in a two-dimensional electron gas.

Optimal control of photoelectron emission by realistic waveforms

Abstract Recent experimental techniques in multicolor waveform synthesis allow the temporal shaping of strong femtosecond laser pulses with applications in the control of quantum mechanical processes in atoms, molecules, and nanostructures. Prediction of the shapes of the optimal waveforms can be done computationally using quantum optimal control theory. In this work we demonstrate the control of above-threshold photoemission of one-dimensional hydrogen model with pulses feasible for experimental waveform synthesis. By mixing different spectral channels and thus lowering the intensity requirements for individual channels, the resulting optimal pulses can extend the cutoff energies by at least up to 50% and bring up the electron yield by several orders of magnitude. Insights into the electron dynamics for optimized photoelectron emission are obtained with a semiclassical two-step model.

Hermitian one-particle density matrix through a semiclassical gradient expansion

We carry out the semiclassical expansion of the one-particle density matrix up to the second order in We use the method of Grammaticos and Voros based on the Wigner transform of operators. We show that the resulting density matrix is Hermitian and idempotent in contrast with the well-known result of the semiclassical Kirzhnits expansion. Our density matrix leads to the same particle density and kinetic energy density as in the literature, and it satisfies the consistency criterion of the Euler equation. The derived Hermitian density matrix clarifies the ambiguity in the usefulness of gradient expansion approximations and might reignite the development of density functionals with semiclassical methods.