The $n$-state exponential model refers to coupled Schrödinger equations with potential $V_{ij}\left(x\right)=U_i{\delta }_{ij}+V_{ij}{e}^{-\alpha x}$. Exact solutions in terms of Meijer’s $G$ functions are obtained, provided the $V_{ij}$ factorize according to $V_{ij}=\pm V_i{V}_j$. The nonadiabatic transition matrix $N$ is determined.

$3p$ shakedown spectra of laser excited potassium atoms as well as direct $3p$ photoemission of ground state potassium have been studied. These two excitation schemes lead to the same final states and thereby provide a good basis for a detailed study of the $3p^5(4s3d{)}^1$ configurations of singly ionized potassium and the photoemission processes leading to these configurations. The comparison of direct photoemission from the ground state and conjugate shakedown spectra from $4p_{1∕2}$ laser excited potassium made it possible to experimentally determine the character of final states that are only weakly excited in the direct photoemission but have a much higher relative intensity in the shakedown spectrum. Based on considerations of angular momentum and parity conservation the excitation scheme of the final states can be understood.

Emission of x-rays by large clusters with ${10}^8$ to ${10}^{10}$ constituents irradiated by an intense laser pulse (${10}^{16}$ to ${10}^{18}{\mathrm{Wcm}}^{-2}$) is analyzed. A self-consistent model for the cluster evolution during and after the irradiation is developed. The model takes into account absorption of radiation, formation of multicharged ions, and cluster expansion. The model is applied to relate the parameters of the cluster beam and the laser pulse to those of the forming plasma. It predicts that the plasma stays quasineutral and Maxwellian. We find that the expansion of large clusters goes through different stages after the end of the laser pulse and is not appropriately described by the Coulomb expansion model, which underestimates the cluster lifetime. For a more realistic description, the nonuniformity of the plasma must be considered. X-rays are generated in the interaction of the trapped electrons with the cluster ions. Two such radiative processes are considered in detail: dielectronic recombination and excitation of ions by electron impact followed by photon emission. Under the above conditions, the contributions of both processes to x-ray emission are comparable. To evaluate the x-ray spectrum a statistical description of the spectral lines is justified and applied. Knowing the rates that characterize the processes in the plasma, the main processes proceeding in the system can be identified. A simple calculation including several types of transitions is carried out.

We experimentally investigate a double-pass parametric down-conversion scheme for producing pulsed, polarization-entangled photon pairs with high visibility. The amplitudes for creating photon pairs on each pass interfere to compensate for distinguishing characteristics that normally degrade two-photon visibility. The result is a high-flux source of polarization-entangled photon pulses that does not require spectral filtering. We observe quantum interference visibility of over 95% without the use of spectral filters for $200\mathrm{fs}$ pulses, and up to 98.1% with $5\mathrm{nm}$ bandwidth filters.

We studied energy spectrum for the hydrogen atom with deformed Heisenberg algebra leading to the minimal length. We developed the correct perturbation theory free of divergences. It gives a possibility to calculate analytically in the three-dimensional case the corrections to $s$ levels of the hydrogen atom caused by the minimal length. Comparing our results with the experimental data from precision hydrogen spectroscopy an upper bound for the minimal length is obtained.

Quantum phase transitions are explored with reduced-density-matrix (RDM) mechanics. While in wave mechanics the quantum phase transition is identified by a crossing or avoided crossing between ground- and excited-state energies, in RDM mechanics the transition is characterized by movement of the ground-state two-electron RDM (2-RDM) along the boundary of the convex set of 2-RDMs between regions with dramatically different expectation values (order parameters) of one or more operators. With recent advances the ground-state 2-RDM can be directly computed without the many-particle wave function by variational optimization of the energy with the 2-RDM [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)]. Because the variational calculation of the 2-RDM does not depend on a reference wave function, it can accurately predict the energies and properties of a system both near and far from the quantum phase transition.

Electron capture and direct elastic scattering in collisions of ${\mathrm{H}}^{+}$ ions with $\mathrm{N}{\mathrm{H}}_2$ molecules between 0.5 and $1.5\mathrm{keV}$ are theoretically investigated. A molecular representation is adopted within a fully quantum-mechanical approach. We consider the following four different molecular configurations for collision dynamics: (I) the proton approaches the N atom along the bisector of the $\mathrm{H}\mathrm{N}\mathrm{H}$ bond angle, passing the midpoint of the $\mathrm{H}\mathrm{H}$ line, (II) it comes along the same line as in (I), but in the opposite direction, (III) the proton approaches the N atom in the $\mathrm{H}\mathrm{N}\mathrm{H}$ plane and perpendicularly to the bisector of the $\mathrm{H}\mathrm{N}\mathrm{H}$ bond angle, and (IV) the proton approaches the N atom perpendicularly to the $\mathrm{H}\mathrm{N}\mathrm{H}$ plane. Differential cross sections for elastic scattering and electron capture are calculated at 1.5 and $0.5\mathrm{keV}$ for these different molecular orientations. Total cross sections for these four orientations as well as orientation-averaged total cross sections are also calculated. Our results indicate that electron-capture dynamics and corresponding electron-capture cross sections depend substantially on the molecular configuration, thus revealing a strong steric effect.

We studied the resonant Raman scattering of x rays in the vicinity of the $K$ absorption edge of silicon. The investigation was carried out at the plane grating monochromator beamline for undulator radiation of the PTB laboratory at BESSY II in Berlin. Cross sections were determined absolutely for a wide energy range of incident photons with small relative uncertainties employing calibrated instrumentation avoiding any reference samples. The experimentally determined values differ clearly from the theoretical ones found in the literature.

We present one- and two-photon diffraction and interference experiments involving parametric down-converted photon pairs. By controlling the divergence of the pump beam in parametric down-conversion, the diffraction-interference pattern produced by an object changes from a quantum (perfectly correlated) case to a classical (uncorrelated) one. The observed diffraction and interference patterns are accurately reproduced by Fourier-optical analysis taking into account the quantum spatial correlation. We show that the relation between the spatial correlation and the object size plays a crucial role in the formation of both one- and two-photon diffraction-interference patterns.

An orbital-dependent nonlocal correlation energy functional has been derived from an energy formula defined in the transcorrelated method. The obtained functional explicitly depends on a Jastrow function, which has been successfully used for the electron gas and solids. We found that our correlation energy functional is successfully used with the exact exchange energy functional and gives relatively good estimates for the total energy and the ionization potential for atoms and ions.

We consider vacuum fluctuations of the quantum electromagnetic field in the presence of an infinite and perfectly conducting plate. We evaluate how the change of vacuum fluctuations due to the plate modifies the Casimir-Polder potential between two atoms placed near the plate. We use two different methods to evaluate the Casimir-Polder potential in the presence of the plate. They also give insights on the role of boundary conditions in the Casimir-Polder interatomic potential, as well as indications for possible generalizations to more complicated boundary conditions.

We make a geometric study of the phases acquired by a general, pure bipartite two-level system after a cyclic unitary evolution. The geometric representation of the two particle Hilbert space makes use of Hopf fibrations. It allows for a simple description of the dynamics of the entangled state’s phase during the whole evolution. The global phase after a cyclic evolution is always an entire multiple of $\pi$ for all bipartite states, a result that does not depend on the degree of entanglement. There are three different types of phases combining themselves so as to result in the $n\pi$ global phase. They can be identified as dynamical, geometrical, and topological. Each one of them can be easily identified using the presented geometric description. The interplay between them depends on the initial state and on its trajectory, and the results obtained are shown to be in connection to those on mixed state phases.

We present an asymptotic bipartite entanglement-distillation protocol that outperforms all existing asymptotic schemes. This protocol is based on the breeding protocol with the incorporation of two-way classical communication. Like breeding, the protocol starts with an infinite number of copies of a Bell-diagonal mixed state. Breeding can be carried out as successive stages of partial information extraction, yielding the same result: one bit of information is gained at the cost (measurement) of one pure Bell state pair (ebit). The basic principle of our protocol is at every stage to replace measurements on ebits by measurements on a finite number of copies, whenever there are two equiprobable outcomes. In that case, the entropy of the global state is reduced by more than one bit. Therefore, every such replacement results in an improvement of the protocol. We explain how our protocol is organized as to have as many replacements as possible. The yield is then calculated for Werner states.

The angular dependence of dissociative electron attachment (DEA) to polyatomic targets is formulated in the local complex potential model, under the assumption that the axial recoil approximation describes the dissociation dynamics. An additional approximation, which is found to be valid in the case of ${\mathrm{H}}_2\mathrm{O}$ but not in the case of ${\mathrm{H}}_2\mathrm{S}$, makes it possible to describe the angular dependence of DEA solely from an analysis of the fixed-nuclei entrance amplitude, without carrying out nuclear dynamics calculations. For ${\mathrm{H}}_2\mathrm{S}$, the final-vibrational-state-specific angular dependence of DEA is obtained by incorporating the variation of the angular dependence of the entrance amplitude with nuclear geometry into the nuclear dynamics. Scattering calculations using the complex Kohn method and, for ${\mathrm{H}}_2\mathrm{S}$, full quantum calculations of the nuclear dynamics using the multiconfiguration time-dependent Hartree method, are performed.

It is demonstrated that the fullerene shell dramatically affects the radiative and Auger vacancy decay of an endohedral atom $A@{\mathrm{C}}_{60}$. The collectivized electrons of the ${\mathrm{C}}_{60}$ shell add new possibilities for radiative and nonradiative decays similar to that in ordinary atoms where the vacancies in the initial and final state almost always belong to different subshells. It is shown that the smallness of the atomic shell radii as compared to that of the fullerene shell provides an opportunity to derive the simple formulas for the probabilities of the electron transitions. It is shown that the radiative and Auger (or Koster-Kronig) widths of the vacancy decay due to electron transition in the atom $A$ in $A@{\mathrm{C}}_{60}$ acquire an additional factor that can be expressed via the polarizability of the ${\mathrm{C}}_{60}$ at transition energy. It is demonstrated that due to an opening of the nonradiative decay channel for vacancies in subvalent subshells the decay probability increases by five to six orders of magnitude.

A robust scheme for trapping and cooling atoms is described. It combines a deep dipole-trap which localizes the atom in the center of a cavity with a laser directly exciting the atom. In that way one obtains three-dimensional cooling while the atom is dipole-trapped. In particular, we identify a cooling force along the large spatial modulations of the trap. A feature of this setup, with respect to a dipole trap alone, is that all cooling forces keep a constant amplitude if the trap depth is increased simultaneously with the intensity of the probe laser. No strong coupling is required, which makes such a technique experimentally attractive. Several analytical expressions for the cooling forces and heating rates are derived and interpreted by analogy to ordinary laser cooling.

We study the photon creation inside a perfectly conducting, spherical oscillating cavity. The electromagnetic field inside the cavity is described by means of two scalar fields which satisfy Dirichlet and (generalized) Neumann boundary conditions. As a preliminary step, we analyze the dynamical Casimir effect for both scalar fields. We then consider the full electromagnetic case. The conservation of angular momentum of the electromagnetic field is also discussed, showing that photons inside the cavity are created in singlet states.

We report the creation of a confined slow beam of heavy-water $\left({\mathrm{D}}_2\mathrm{O}\right)$ molecules with a translational temperature around $1\mathrm{K}$. This is achieved by filtering slow ${\mathrm{D}}_2\mathrm{O}$ from a thermal ensemble with inhomogeneous static electric fields exploiting the quadratic Stark shift of ${\mathrm{D}}_2\mathrm{O}$. All previous demonstrations of electric-field manipulation of cold dipolar molecules rely on a predominantly linear Stark shift. Further, on the basis of elementary molecular properties and our filtering technique we argue that our ${\mathrm{D}}_2\mathrm{O}$ beam contains molecules in only a few rovibrational states.