We study Bragg spectroscopy of ultracold atoms in one-dimensional optical lattices as a method for probing the excitation spectrum in the Mott-insulator phase, in particular the one-particle-hole excitation band. Within the framework of perturbation theory we obtain an analytical expression for the dynamic structure factor and use it to calculate the imparted energy which was shown to be a relevant observable in recent experiments. We test the accuracy of our approximations by comparing them with numerically exact solutions of the Bose-Hubbard model in restricted cases and establish the limits of validity of our linear-response analysis. Finally we show that when the system is deep in the Mott-insulator regime, its response to the Bragg perturbation is temperature dependent. We suggest that this dependence might be used as a tool to probe temperatures of order of the Mott gap.

Single and double ionization processes are calculated for a 1D model of ${\mathrm{H}}_2$ from numerical solution of the time-dependent Schrödinger equation in the presence of an intense $I⩽5\times {10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$, ultrashort $\left(10\text{cycles}\right)$ $800\mathrm{nm}$ laser pulse. Laser-induced electron recollision, LIERC, is identified from a systematic analysis of bound and continuum populations in the two-electron wave function. Recollision is shown to be responsible for double ionization at lower intensities, $I<{10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$ and persists also in the first two excited states of ${\mathrm{H}}_2$, the $A{}^3\Sigma _u^{+}$ and $B{}^1\Sigma _u^{+}$ states. The effects of the symmetry (antisymmetry) of the two-electrons wave function is found to be dominant at large internuclear distances where enhanced ionization is operative, especially in the $A{}^3\Sigma _u^{+}$, where the exclusion principle suppresses double ionization from LIERC. Furthermore, at large distances, double ionization is shown to occur with equal excitation of the highest occupied and lowest unoccupied molecular orbitals of the ${\mathrm{H}}_2^{+}$ core ion. Negligible core excitation occurs at equilibrium.

Coherent x-ray generation is investigated for a thin solid layer or any other periodic atomic structure with limited dimensions exposed to a short, superintense laser pulse. We single out a selective range of parameters at which the impact of nonlinear collective processes on ion dynamics is reduced. This allows us to consider an ionic structure that is quasiregular during the brief interaction, which we prove also by particle-in-cell simulations. In the relativistic regimes of the interaction, when the transversal oscillation amplitude of the electron in the laser field exceeds the layer transversal width, the multiphoton scattering of electrons dominates over recombination to bound states. Electrons accelerated by the laser field penetrate through the periodic ionic structure, emitting coherent bremsstrahlung. Hard x rays are shown to amplify along the interaction length due to stimulated coherent bremsstrahlung. The high gain of the scheme compensates for the short interaction length, yielding a gain-length product competitive with other coherent x-ray sources. Limitations on the gain due to the energy spread of the electrons and the short time of the interaction are estimated.

We study phase-conjugate degenerate four-wave mixing (DFWM) in an optically pumped, two-level atomic system (the $3s{}^{2}S_{1∕2}$, $F=2$, $m_F=2\to 3p{}^{2}P_{3∕2}$, $F=3$, $m_F=3$ transition in a diffuse, collision-free, thermal beam of sodium) using phase-modulated laser beams. In this investigation, we study the detailed line shape of the four-wave mixing signal as a function of the temporal delay between the probe field and the pump fields at different intensities of the cw pump waves and modulation frequencies. We show that phase modulation of the pump and probe beams leads to strong amplitude modulation of the phase-conjugate beam and report excellent agreement between our experimental observations of the DFWM spectra and the results of numerical calculations. Our numerical results suggest an enhancement of the “local” DFWM signal when the sidebands of the phase-modulated laser are resonant with dressed-state transitions, but that this resonance is less obvious in the total signal generated. We also show that the complex line shapes depend sensitively upon the delay of the probe beam, with the peak DFWM signal occurring when the probe beam is advanced compared to the pump beam.

A simple relationship to transform spectroscopic signals obtained with laser beams of Gaussian spatial profiles into their component along the laser propagation axis is demonstrated. The transform uses the derivative of the signals with respect to laser intensity and leads to the removal of spatial effects due to the uneven laser profile. The usefulness of such a transform is explained with the help of experimental applications.

When an optimal measurement of $(S_x,S_y,S_z)$ is made on a qubit and what we call a mutually unbiased mixture of the resulting ensembles is taken, then the post-measurement density matrix is shown to be related to the premeasurement density matrix through a simple linear relation. It is also shown that the form of this relation is the same for all quantum systems. It is shown that for a general quantum system such a relation holds only when the measurements are made in mutually unbiased bases. The post-measurement density matrix is shown to be a normalized incoherent superposition of the identity map and the pin map of Gorini and Sudarshan. A pin map is one which maps all density matrices to a fixed density matrix which in our case turns out to be the unit matrix. The result is shown to be true irrespective of whether the initial state is pure or mixed. For spin-$1∕2$ systems it is also shown explicitly that nonorthogonal measurements fail to give such a linear relation no matter how the ensembles are mixed.

We define an entanglement measure, called the partial tangle, which represents the residual two-qubit entanglement of a three-qubit pure state. By its explicit calculations for three-qubit pure states, we show that the partial tangle is closely related to the faithfulness of a teleportation scheme over a three-qubit pure state.

Propagation of nanosecond light pulses in a resonantly absorbing medium is studied. Deviation from the conventional group velocity and superluminal-to-subluminal transition were observed for the natural atomic transitions of Rb. The observed frequency and atomic density dependences of the propagation delay in the anomalous dispersion region, where the conventional concept of the group velocity breaks down, are reproduced well by the theory of the net group delay.

The measurement of the Casimir force between a large gold coated sphere and single crystal silicon plate is performed with an atomic force microscope. A rigorous statistical comparison of data with theory is done, without use of the concept of root-mean-square deviation, and excellent agreement is obtained. The Casimir force between metal and semiconductor is demonstrated to be qualitatively different than between two similar or dissimilar metals, which opens opportunities for applications in nanotechnology.

The development of electronic states in krypton clusters is investigated by high-resolution core-level electron spectroscopy. The energy ordering of bulk versus surface $3d^{-1}np(n>5)$ core-excited states in neutral clusters is demonstrated to be reversed to the $3d^{-1}5p$ level situation. The cluster $3d^{-1}6p,7p$ states are proven to be at a lower energy than the corresponding atomic levels. These findings reveal the ioniclike energy structure of the neutral cluster core-excited levels. The phenomenon is explained by a spatial spread of the excited orbitals over the cluster lattice.

We examine the propagation of solitary waves in elongated clouds of trapped bosonic atoms as the confinement, the strength of the interatomic interaction, and the atom density are varied. We identify three different physical regimes and develop a general formalism that allows us to interpolate between them. Finally we pay special attention to the transition to the Tonks-Girardeau limit of strongly interacting bosons.

We have used a microfabricated atom chip to split a single Bose-Einstein condensate of sodium atoms into two spatially separated condensates. Dynamical splitting was achieved by deforming the trap along the tightly confining direction into a purely magnetic double-well potential. We observed the matter wave interference pattern formed upon releasing the condensates from the microtraps. The intrinsic features of the quartic potential at the merge point, such as zero trap frequency and extremely high field-sensitivity, caused random variations of the relative phase between the two split condensates. Moreover, the perturbation from the abrupt change of the trapping potential during the splitting was observed to induce vortices.

The potential energy surfaces corresponding to the long-lived fixed-nuclei electron scattering resonances of ${\mathrm{H}}_2\mathrm{O}$ relevant to the dissociative electron attachment process are examined using a combination of ab initio scattering and bound-state calculations. These surfaces have a rich topology, characterized by three main features: a conical intersection between the ${}^{2}A_1$ and ${}^{2}B_2$ Feshbach resonance states; charge-transfer behavior in the $\mathrm{OH}\left({}^2\Pi \right)+{\mathrm{H}}^{-}$ asymptote of the ${}^{2}B_1$ and ${}^{2}A_1$ resonances; and an inherent double-valuedness of the surface for the ${}^{2}B_2$ state the $C_{2v}$ geometry, arising from a branch-point degeneracy with a ${}^{2}B_2$ shape resonance. In total, eight individual seams of degeneracy among these resonances are identified.

We study in detail the mechanisms causing dephasing of hyperfine coherences of cesium atoms confined by a far-off-resonant standing-wave optical dipole trap [S. Kuhr et al., Phys. Rev. Lett. 91, 213002 (2003)]. Using Ramsey-spectroscopy and spin-echo techniques, we measure the reversible and irreversible dephasing times of the ground-state coherences. We present an analytical model to interpret the experimental data and identify the homogeneous and inhomogeneous dephasing mechanisms. Our scheme to prepare and detect the atomic hyperfine state is applied at the level of a single atom as well as for ensembles of up to 50 atoms.

We present a split-beam neutron interferometric experiment to test the noncyclic geometric phase tied to the spatial evolution of the system: The subjacent two-dimensional Hilbert space is spanned by the two possible paths in the interferometer, and the evolution of the state is controlled by phase shifters and absorbers. A related experiment was reported previously by Hasegawa et al. [Phys Rev A 53, 2486 (1996)] to verify the cyclic spatial geometric phase. The interpretation of this experiment, namely to ascribe a geometric phase to this particular state evolution, has met with severe criticism from Wagh [Phys. Rev A 59, 1715 (1999)]. The extension to a noncyclic evolution manifests the correctness of the interpretation of the previous experiment by means of an explicit calculation of the noncyclic geometric phase in terms of paths on the Bloch-sphere.

We present a theoretical study of the dissipative component of the force acting on a highly charged ion moving in front of a solid surface at large distances. The friction force (stopping power) of the surface is analyzed employing both the specular-reflection model and time-dependent density functional theory (TDDFT). Contributions from particle-hole and plasmon excitations are discussed. A simple method to include the correction due to the finite width of the plasmon resonance at large wavelength into the TDDFT description of the stopping power is suggested. We present applications to the energy loss of charged particles undergoing distant collisions at grazing incidence angles with the internal surface of the microcapillary. Our results indicate that the correlation between the angular distribution and the energy loss of transmitted ions can be used to probe the dielectric properties of the capillary material at large distances.

We investigate the potential of the so-called cross-correlation frequency-resolved optical gating (XFROG) technique originally developed for ultrashort laser pulses for the recovery of the amplitude and phase of the condensate wave function of a Bose-Einstein condensate. Key features of the XFROG method are its high resolution, versatility, and stability against noise and some sources of systematic errors. After showing how an analog of XFROG can be realized for Bose-Einstein condensates, we illustrate its effectiveness in determining the amplitude and phase of the wave function of a vortex state. The impact of a reduction of the number of measurements and of typical sources of noise on the field reconstruction are also analyzed.

We investigate the dynamics of the system of multiple bright and dark quasisolitons generated in a one-component ultracold Fermi gas via the phase imprinting technique in terms of atomic orbitals approach. In particular, we analyze the collision between two bright quasisolitons and find that quasisolitons are subject to the superposition principle.