Quantum reflection from an oscillating surface

We describe an experimentally realistic situation of the quantum reflection of helium atoms from an oscillating surface. The temporal modulation of the potential induces clear sidebands in the reflection probability as a function of momentum. Theses sidebands could be exploited to slow down atoms and molecules in the experiment.Comment: 9 pages, 4 figure

Spectral properties of planar helium under periodic driving

We present an original method for the accurate quantum treatment of the planar three body Coulomb problem under electromagnetic driving. Our ab initio approach combines Floquet theory, complex dilation, and the representation of the Hamiltonian in suitably chosen coordinates without adjustable parameters. The resulting complex-symmetric, sparse banded generalized eigenvalue problem of rather high dimension is solved using advanced techniques of parallel programming. In the present thesis, this theoretical/numerical machinery is employed to provide a complete description of the bound and of the doubly excited spectrum of the field-free 2D helium atom. In particular, we report on frozen planet quantum states in planar helium. For the driven atom, we focus on the near resonantly driven frozen planet configuration, and give evidence for the existence of nondispersive two-electron wave packets which propagate along the associated periodic orbit. This represents a highly nontrivial qualitative confirmation of earlier calculations on a 1D model atom, though with important enhancements of the decay rate of these atomic eigenstates in the field, due to the transverse decay channel. The latter is already found to enhance the decay rates of the unperturbed frozen planet as compared to the 1D model, in surprisingly good quantitative agreement with 3D results.Wir stellen eine originelle Methode zur akkuraten quantenmechanischen Behandlung des planaren Drei-Koerper-Coulombproblems in Gegenwart eines elektromagnetischen Feldes vor. Unser ab initio Zugang vereint Floquet-Theorie, komplexe Dilatation und die Darstellung des Hamilton-Operators in geeignet gewaehlten Koordinaten -- ohne freie Parameter. Das resultierende, durch eine komplex-symmetrische, duenn besetzte Bandmatrix dargestellte verallgemeinerte Eigenwertproblem vergleichsweise grosser Dimension wird mittels fortgeschrittener Methoden paralleler Programmierung geloest. In der vorliegenden Dissertation wird dieser theoretisch/numerische Apparat zur vollstaendigen Charakterisierung des gebundenen sowie des doppelt angeregten Spektrums des feldfreien zweidimensionalen Heliumatoms genutzt. Insbesondere untersuchen wir die frozen planet-Konfiguration in planarem Helium. Bei dem durch ein aeusseres Feld gestoerten Atom konzentrieren wir uns auf die nahresonant getriebene frozen planet-Konfiguration und stellen erste Ergebnisse vor, welche die Existenz nichtdispergierender Wellenpakete nahelegen, die entlang des korrespondierenden klassischen Orbits propagieren. Hierbei handelt es sich um eine hoch nichttriviale Bestaetigung frueherer Ergebnisse fuer ein eindimensionales Modellatom, bei freilich merklicher Ueberhoehung der Zerfallsrate der atomaren Eigenzustaende im Feld -- aufgrund des zusaetzlich verfuegbaren, transversalen Zerfallskanals. Letzterer macht sich bereits durch eine Ueberhoehung der Zerfallsraten des ungestoerten frozen planet im Vergleich zum eindimensionalen Modell bemerkbar, in ueberraschend quantitativer Uebereinstimmung mit den Ergebnissen dreidimensionaler Rechnungen

Ab initio quantum approach to planar helium under periodic driving

We present a method for the accurate quantum treatment of the planar three-body Coulomb problem under electromagnetic driving. Our ab initio approach combines Floquet theory, complex dilation, and the representation of the Hamiltonian in suitably chosen coordinates, without adjustable parameters. The resulting complex-symmetric sparse banded generalized eigenvalue problem of rather high dimension is solved using advanced techniques of parallel programming. This theoretical and numerical machinery is employed to provide a complete description of the bound and of the doubly excited spectrum of the field-free two-dimensional (2D) helium atom. For the driven atom, we focus on the near resonantly driven frozen planet configuration, and give evidence for the existence of nondispersive two-electron wave packets

Explicit time-propagation method to treat the dynamics of driven complex systems

We describe the efficient implementation of an explicit method to solve systems of stiff differential equations either on a grid or within a spectral approach. This method is based on an ansatz that approximates the solution. This ansatz depends on stiffness parameters that are shown to be related to the eigenfrequencies of the system. The accuracy and the performance of the method are tested in three different cases. First, we treat a highly stiff single differential equation, where explicit schemes converge rather slowly. Then, we solve the stationary Schrodinger equation associated to the quantum reflection of an ultracold atom by a surface. Finally, we consider the interaction of atomic hydrogen with a strong low-frequency laser pulse whose duration is of the order of 25 fs. We focus on the calculation of the above-threshold ionization electron spectrum, a problem which, under such realistic physical conditions, is computationally very demanding

Highly doubly excited states of planar helium: Fluctuations in photoionization cross sections

Photoionization cross sections calculated up to the 20th single ionization threshold of triplet P states of planar helium exhibit fluctuations. These are mainly due to a dominant series of resonances which can be associated with an approximate quantum number F=N-K in accordance with three-dimensional full calculations and experimental observations. As the energy increases the dominant role of a single series as sole contributor is apparently lost as new series start to contribute significantly to the cross sections. This would result in an earlier onset of Ericson fluctuations as in the picture of a single dominant series, where the onset is expected around I-34

The dynamics of the ionization of atoms exposed to strong low-frequency fields

We present a theoretical study of strong-low-frequency-field ionization of atoms in the intermediate regime where the Keldysh parameter is close to one. For that purpose we have developed a novel method based on an explicit algorithm for the propagation of the time-dependent Schrödinger equation which is known to be very stiff. This method overcomes the stiffness by taking into account the eigenfrequencies of the interacting system. With the help of this approach we are able in particular to investigate the ionization of the hydrogen atom by ultra-short (25 fs) 790 nm laser pulses at intensities 0.5−6 × 1014 W/cm2

Spectral representation of the three-body Coulomb problem. II. Autoionizing doubly excited states of unnatural parity in helium

A spectral approach of configuration interaction type is used to evaluate energies and widths for a wide range of singlet and triplet P-e resonance states of helium up to the eighth single ionization threshold. While the present data are in excellent agreement with existing theoretical results (below the N = 3-5 ionization threshold) obtained within an explicitly correlated approach, there are substantial differences with the energies, the widths, and the number of resonances obtained with the stabilization method

Spectral representation of the three-body Coulomb problem. I. Nonautoionizing doubly excited states of high angular momentum in helium

We investigate high-lying doubly excited nonautoionizing states of helium with total angular momentum L = 1,2, ...,9 with the help of a configuration interaction approach. We provide highly precise nonrelativistic energies of these states and discuss the properties of the wave functions with respect to the particle exchange operator

Spectral representation of the three-body Coulomb problem: Perspectives for highly doubly excited states of helium

We present a spectral method of configuration-interaction type for three-dimensional helium which combines the complex rotation method with an appropriate expansion of the atom wave function in a basis of products of Coulomb-Sturmian functions of the electron radial coordinates with independent dilation parameters for the two electrons and bipolar spherical harmonics of the angular coordinates. The matrix elements of the kinetic energy and of the electron-nucleus interaction term are calculated using Gauss-Laguerre integration techniques. A combination of Gauss-Laguerre integration techniques with the generalized Wigner-Eckart theorem and recurrence relations allows an efficient and stable calculation of the matrix elements of the electron-electron interaction. The freedom of the choice of the dilation parameters permits us to access highly excited states with rather small sizes of the basis. Highly doubly excited states up to the tenth ionization threshold of singlet and triplet S states of helium are presented

Smoothness properties of the quantum-mechanical and WKB phase shifts for two-dimensional scattering

As a contribution to a current controversial discussion we show that the smoothness properties of the quantum-mechanical and the WKB phase shifts for elastic scattering by a smooth repulsive radially symmetric potential in two spatial dimensions are different