The sensitivity of atomic transition frequencies to variation of the fine structure constant $\alpha =e^2∕\hslash c$ increases proportional to $Z^2$ where $Z$ is the nuclear charge. Recently several lines of heavy ions $\mathrm{Ge}\mathrm{II}$, $\mathrm{Sn}\mathrm{II}$, and $\mathrm{Pb}\mathrm{II}$ have been detected in quasar absorption spectra. We have performed accurate many-body calculations of the ${\alpha }^2$ dependence of transition frequencies ($q$ coefficients) for these atoms and found an order-of-magnitude increase in sensitivity in comparison with atomic transitions which were previously used to search for temporal and spatial variation of $\alpha$ in quasar absorption systems. An interesting feature in $\mathrm{Pb}\mathrm{II}$ is a highly nonlinear dependence on ${\alpha }^2$ due to the level pseudocrossings.

The vibrationally resolved C $1s$ single-hole ionization cross sections of ${\mathrm{H}}_2\mathrm{CO}$ are measured in the region of the ${\sigma }^{*}$ shape resonance. The energy of the shape resonance is pushed down by the excitation of the C-O stretching vibration $v_2^{\prime }$. Our calculations, which take account of elastic multiple scattering within the C-O potential box, show that the downward shift of the shape resonance energy is originated from the elongation of the characteristic internuclear C-O distance in the core-ionized molecule with an increase in $v_2^{\prime }$. The characteristic internuclear distance varies from $R^{+}(0,0,0)=1.198\mathrm{\AA }$ up to $R^{+}(0,2,0)=1.415\mathrm{\AA }$. In addition to the elastic multiple-scattering mechanism, the internal inelastic scattering of the C $1s$ photoelectron by valence electrons is suggested as a possible mechanism responsible for the enhancement of vibrational excitations through the shape resonance and near threshold.

We have carried out relativistic distorted-wave calculations for inelastic electron scattering from the $6s5d{}^{1,3}D_2$ and $6s6p{}^{1}P_1$ excited states of barium in the energy range from 20 to 40 eV. Results are presented for the differential cross sections and electron-impact coherence parameters and compared with experimental measurements and other theoretical calculations for these quantities.

The close-coupling approach to electron-helium single ionization is analyzed and several ways of defining the scattering amplitudes are determined, for both equal- and unequal-energy outgoing electrons. Nevertheless, the various definitions all lead to the same cross section. The convergent close-coupling (CCC) method with Laguerre (CCC-L) and box-based (CCC-B) target functions is applied to calculate electron-impact ionization of helium for the cases where the two outgoing electrons have equal energy. Excellent absolute agreement with experiment is obtained for all available cases of comparison.

Expressions for momentum distributions of electrons in antiproton–hydrogen-atom collisions are derived in the framework of the advanced adiabatic approach for the time- independent Schrödinger equation. Protonium formation cross sections for states with different $n$ and $l$ spherical quantum numbers are also obtained. Total ionization and protonium formation cross sections are compared with other calculations in the interval of impact energies from $0.5\mathrm{eV}$ to $10\mathrm{keV}$. We show that diabatic states promoted into the continuum can be rigorously defined within the advanced adiabatic framework.

The interaction experienced by a fast electric dipole moving parallel and close to a flat solid surface is studied using the dielectric formalism. Analytical expressions for the force acting on the dipole, for random and for particular orientations, are obtained. Several features related to the dynamical effects on the induced forces are discussed, and numerical values are obtained for the different cases. The calculated energy loss of the electric dipole provides useful estimations which could be of interest for small-angle scattering experiments using polar molecules.

Electron emission by 130–430-eV ${\mathrm{Ar}}^{+}$ ion impact on polycrystalline Al surfaces is studied extending the theory of Auger neutralization to include the singular response of the metal conduction band to the sudden change of charge in the incoming hole state, following its neutralization. The effect is manifested in the high-energy tail of the electron energy distributions, where the theory accounts very well with experiments.

In this paper, we demonstrate a detailed derivation of general analytical expressions of photoionization rates of spatially aligned large polyatomic molecules in the tunneling photoionization region. First, the molecular Coulomb-corrected Volkov function is derived for determining the continuum state, and the position dependence of the atoms forming the molecule is explicitly included in it. Second, using the molecular Coulomb-corrected Volkov function, a Keldysh-type photoionization rate formula is derived. For this, a linear combination of atomic orbitals will be used for the initial state. The obtained photoionization rate formula shows that the molecular photoionization rate is the sum of the photoionization rates of the individual occupied orbitals of the atoms forming the molecule, which are modified by the position dependence of the atoms, and the quantum interference terms arising from the corresponding occupied orbitals of the constituent identical and different atoms. The formula explicitly indicates that the photoionization rate sensitively depends on the angle between the molecular axis and the polarization vector of the linearly polarized laser field, the internuclear distance, and the atomic ionization potential $I$ by the expression $\exp (2\sqrt{2mI}\vec{F}\bullet {\vec{R}}_j∕\hslash F)$. This is a clear indication of the appropriateness of the formulas derived in this work since it is consistent with the experimental and numerical results obtained so far. Using the formula, we show numerical results of photoionization rates of all-trans polyacetylene radicals. In addition, from the formula is directly drawn the conclusion that the photoionization rate corresponding to the quantum interference terms is smaller when the distance between the atoms is longer in the case of laser polarization parallel to the molecular backbone.

We address spin dephasing induced by stochastic transitions between different precession frequencies. A very famous analytical approximation is the Gaussian approximation presented by [Anderson and Weiss, Rev. Mod. Phys. 25, 269 (1953)]. It states that independent from the transition dynamics, a Gaussian frequency distribution implies a Gaussian distribution of the phase angles, which provides a simple analytical result for the transverse magnetization decay. In contrast we find that (i) the assumption of Gaussian dephasing restricts the stochastic dynamics to a very limited class, (ii) the Anderson-Weiss model is applicable only in a special case of fluctuations, i.e., if and only if the Green’s function $G({\omega }_2,{\omega }_1,\Delta t)$ describing the transition probability between two frequencies ${\omega }_1\to {\omega }_2$ is Gaussian, and (iii) the exact time course of magnetization decay is dependent on the relaxation time in the motional narrowing limit and the correlation time describing the correlation function of the local frequencies. In contrast to previous publications, we conclude that a Gaussian equilibrium distribution of local frequencies does not imply a Gaussian-distributed phase angle. The general theory is illustrated by calculating the Green’s function of the transition dynamics for a stochastic process in the strong collision approximation. The result is highly relevant for describing relaxation processes in the presence of local field inhomogeneities.

We study quantum dynamical properties of a spin-1 atomic Bose-Einstein condensate in a double-well potential. Adopting a mean field theory and single spatial mode approximation, we characterize our model system as two coupled spins. For certain initial states, we find full magnetization oscillations between wells not accompanied by mass (or atom numbers) exchange. We identify dynamic regimes of collective spin variables arising from nonlinear self-interactions that are different from the usual Josephson oscillations. We also discuss magnetization beats and incomplete oscillations of collective spin variables other than the magnetization. Our study points to an alternative approach to observe coherent tunnelling of a condensate through a (spatial) potential barrier.

It is shown by means of quantum trajectory simulations that two different types of collective behavior are possible in the overdamped many-atom micromaser. Depending on the parameters, the micromaser can either superradiate or subradiate. This alternative corresponds to positive or negative correlations between the dipole moments of individual intracavity atoms. We perform simulations with realistic parameters to show that superradiance and subradiance should be observable with available experimental setups.

The THz spectrum of the spontaneous emission of an interacting electron-ion gas, recently observed in laser pulse ionized air, is theoretically analyzed. Using the correlation expansion of the involved many particle system, the contribution of electron-molecule and electron-ion collisions to the transitions in the free electron continuum are treated. Depending on the particle density and the ion distribution, electromagnetic emission is found from the terahertz range up to optical frequencies.

We analyze a lifetime-broadened four-state, ladder-type four-wave mixing (FWM) scheme in the context of optical soliton formation. We show that a pulsed probe field and a pulsed FWM field of considerably different frequency can evolve into a pair of matched solitons with the same temporal shape and ultraslow group velocity $(V_g∕c\sim {10}^{-3})$, i.e., two-color ultraslow optical solitons. In addition, we show regimes where two-color superluminal $(V_g∕c<0)$ optical soliton propagation may occur.

An exact analytic solution is presented for coherent resonant excitation of a two-state quantum system driven by a time-dependent pulsed external field with a hyperbolic-secant shape in the presence of dephasing. Analytic results are derived for the amplitude and phase shift of the damped Rabi oscillations.

The model of the quantum protocols sealing a classical bit is studied. It is shown that there exist upper bounds on its security. For any protocol where the bit can be read correctly with the probability $\alpha$, and reading the bit can be detected with the probability $\beta$, the upper bounds are $\beta ⩽1∕2$ and $\alpha +\beta ⩽9∕8$.

Beam propagation in a helically twisted optical waveguide is theoretically studied and shown to provide an optical analog to the electron wave packet dynamics of a two-dimensional atom subject to a high-frequency and high-intensity circularly polarized laser field.

Using the Bloch-Messiah reduction we show that squeezing is an “irreducible” resource which remains invariant under transformations by linear optical elements. In particular, this gives a decomposition of any optical circuit with linear input-output relations into a linear multiport interferometer followed by a unique set of single-mode squeezers and then another multiport interferometer. Using this decomposition we derive a no-go theorem for creating superpositions of macroscopically distinct states from single-photon detection. Further, we demonstrate the equivalence between several schemes for randomly creating polarization-entangled states. Finally, we derive minimal quantum optical circuits for ideal quantum nondemolition coupling of quadrature-phase amplitudes.

The motion of neutral particles with magnetic moments in an inhomogeneous magnetic field is described in a quantum mechanical framework. The validity of the semiclassical approximations which are generally used to describe these phenomena is discussed. Approximate expressions for the evolution operator are derived and compared to the exact calculations. Focusing and spin-flip phenomena are predicted. The reliability of Stern-Gerlach experiments to measure spin projections is assessed in this framework.

Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any $n$-qubit gate of this type using at most $2^{n-1}-1$ controlled-NOT gates, $2^{n-1}$ one-qubit gates, and a single diagonal $n$-qubit gate. To illustrate the versatility of these gates we then apply them to the decomposition of a general $n$-qubit gate and a state preparation procedure. Moreover, we study their implementation using only nearest-neighbor gates. We give upper bounds for the one-qubit and controlled-NOT gate counts for all the aforementioned applications. In all four cases, the proposed circuit topologies either improve on or achieve the previously reported upper bounds for the gate counts. Thus, they provide the most efficient method for general gate decompositions currently known.

Energies of $6s^{2}n{p}_j$ $(n=6–9)$, $6s^{2}n{s}_{1∕2}$ $(n=7–9)$, $6s^{2}n{d}_j$ $(n=6–8)$, and $6s^{2}n{f}_{5∕2}$ $(n=5–6)$ states in $\mathrm{Tl}\mathrm{I}$ and $\mathrm{Pb}\mathrm{II}$ are obtained using relativistic many-body perturbation theory. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the 72 possible $6s^{2}n{l}_j\text{−}6s^2{n}^{\prime }{l}_{j^{\prime }}^{\prime }$ electric-dipole transitions. Electric-quadrupole and magnetic-dipole matrix elements are evaluated to obtain $6s^{2}n{p}_{3∕2}\text{−}6s^{2}m{p}_{1∕2}$ $(n,m=6,7)$ transition rates. Hyperfine constants $A$ are evaluated for $6s^{2}n{p}_j$ $(n=6–9)$, $6s^{2}n{s}_{1∕2}$ $(n=7–9)$, and $6s^{2}n{d}_j$ $(n=6–8)$ states in ${}^{205}\mathrm{Tl}$. First-, second-, third-, and all-order corrections to the energies and matrix elements and first- and second-order Breit corrections to energies are calculated. In our implementation of the all-order method, single and double excitations of Dirac-Fock wave functions are included to all orders in perturbation theory. These calculations provide a theoretical benchmark for comparison with experiment and theory.