We construct wave packets for the hydrogen atom labeled by the classical action-angle variables with the following properties. (i) The time evolution is exactly given by classical evolution of the angle variables. (The angle variable corresponding to the position on the orbit is now noncompact and we do not get exactly the same state after one period; however, the gross features do not change. In particular, the wave packet remains peaked around the labels.) (ii) The resolution of the identity using this overcomplete set involves exactly the classical phase-space measure. (iii) The semiclassical limit is related to Bohr-Sommerfeld quantization. (iv) They are almost minimum uncertainty wave packets in position and momentum.

We report results of ab initio calculation of the spin-rotational Hamiltonian parameters including $P$- and $P,T$-odd terms for the BaF molecule. The ground-state wave function of BaF molecule is found with the help of the relativistic effective core potential method followed by the restoration of molecular four-component spinors in the core region of barium in the framework of a nonvariational procedure. Core polarization effects are included with the help of the atomic many-body perturbation theory for the Barium atom. For the hyperfine constants the accuracy of this method is about 5–10 %.

A saddle-point complex-rotation method is used to calculate the resonance energy, width, and photoionization cross section (PICS) of lithium below the ${\mathrm{Li}}^{+}$ $1s2s$${}^{3}S$ threshold. Fourteen ${}^2{P}^o$ resonances are studied. These results are compared with the most precise experimental data in the literature. Most of the Auger widths of these resonances are extremely narrow, which makes a direct theory-experiment PICS comparison difficult. However, if we convolute the predicted cross section with a Gaussian profile using the experimental resolution for full width at half maximum, the resulting profile agrees closely with the high-resolution photoion measurement.

We study the spectra of light emitted during slow ion-atom collisions due to repeated electron transfer during the interactions, using the power radiated per unit solid angle by the diatomic time-dependent dipole. We present results relevant to experiments where the emitted light would be collected from all collisions, irrespective of their deflection angle or impact parameter. We calculate the spectra of polarized light emitted in $p+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collisions, at a projectile energy of 100 eV, integrated over impact parameters, versus the light detector angle. Emitted light frequencies are distributed over the uv and near uv ranges. We also estimate the rate of photon emission for typical experimental ion and atom densities.

A conspicuous fluorination effect, prominent structures in elastic differential cross sections below 100 eV, in electron-methane and fluoromethanes (${\mathrm{CH}}_4,$ ${\mathrm{CH}}_3{\mathrm{F}}_1,$ ${\mathrm{CH}}_2{\mathrm{F}}_2,$ ${\mathrm{CH}}_1{\mathrm{F}}_3,$ and ${\mathrm{CF}}_4$) collisions has been found in a systematic manner. The effect becomes more prominent when the number of fluorine atoms increases. Further, a systematic undulation due to F atoms at small-angle scatterings has also been observed, and the case has been studied in detail, in which we have found it to be due to interferences of a scattered electron from different scattering centers. Therefore, we have examined a possibility of utilizing the undulation as a means for molecular structure analysis. For these observed features, a simple, intuitively correct interpretation based on the underlying molecular structure and scattering physics has been given.

High-resolution resonant Auger electron spectra of HBr are reported at the Br $3d\to 5p$ and Br $3d\to 4d$ resonances. Subnatural linewidths of ∼40 meV, due to the Auger resonance Raman effect, reveal complex multiplet features. By recording spectra at closely spaced energies, the resonant Auger spectra from the resonantly excited core Br $3d$ to $4d,$ $5p\sigma ,$ and $5p\pi$ Rydberg states are obtained. The well-resolved resonant Auger spectra are used to confirm the assignments of the complex unresolved Br $3d\to$Rydberg photoabsorption spectrum.

We develop a method of finding analytical solutions of the Bogolyubov–de Gennes equations for the excitations of a Bose condensate in the Thomas-Fermi regime in harmonic traps of any asymmetry and introduce a classification of eigenstates. In the case of cylindrical symmetry we emphasize the presence of an accidental degeneracy in the excitation spectrum at certain values of the projection of orbital angular momentum on the symmetry axis and discuss possible consequences of the degeneracy in the context of new signatures of Bose-Einstein condensation.

We calculate the reflection probability for ultracold atoms incident on an evanescent-wave atomic mirror, and analyze the optimum conditions to observe quantum reflection. We find that averaging over the Gaussian profile of the laser beam dramatically reduces the quantum signature, and consider the effects of an appropriate aperture that limits the variation of beam intensity. We show that quantum reflection is particularly sensitive to details of the atom-surface potential, and could be used to resolve retardation effects.

Using the stimulated force exerted by counterpropagating π pulses from a mode-locked Ti:sapphire laser we have focused a beam of laser-cooled cesium atoms along one dimension to about 57% of its original width in the detection zone. We determined the force profile outside and inside the overlap region of the pulses and found agreement with an earlier theoretical prediction. The scheme does not require an effective two-level system and is therefore suitable for a large variety of elements.

Fully quantum and classical trajectory Monte Carlo calculations are performed for a Rydberg alkali-metal atom that is kicked by a pulsed electric field. The two calculations are compared to recent experimental results through the ionization probability versus peak field strength. The energy distributions of the final electrons are compared between the two calculations. There is a qualitative difference between the classical and quantum momentum distributions which is measurable in principle. An experiment to detect the time-dependent precession of the orbital angular momentum in Cs is also proposed.

We describe a method for obtaining population trapping and electromagnetically induced transparency in atoms with hyperfine structure and where, therefore, more than three states are coupled by two applied fields.

We report on the existence of various periodic transverse patterns and stable localized structures in the optical field of a planar resonator, which exhibits the defocusing saturable nonlinearity of a semiconductor near the band edge. We predict multistability of all feasible patterns as well as of the localized states. Being equal as well as different, stable localized states can organize as clusters or new kinds of periodic patterns (superlattices). The interaction of localized states via their oscillating tails allows the formation of patterns with the same basic units but with different lattice spacing.

We measure experimentally the statistical distribution of time intervals between power-dropout events occurring in a semiconductor laser with time-delayed optical feedback operating in the low-frequency fluctuation regime. Near the laser threshold, the time-interval probability distribution displays a low-probability region, or dead zone, for short times, followed by a slow rise, and an exponential decay for long times. At higher injection currents, the distributions develop considerable structure. We compare our results to the predictions of approximate analytic models of the laser dynamics and find that no single model accurately captures the details of the observed distributions, indicating that our physical understanding of the long-term dynamics of the laser in this regime is less than complete.

Quantum-mechanical entropies of position and momentum operators in a given state are shown to be reasonable and sensitive measures for squeezing of quantum fluctuations. It is shown to be true not only for states having Gaussian wave functions but also for more general, both pure and mixed, quantum states. A simple proof that the squeezing exhibited by the variance is always accompanied by a corresponding entropy reduction below the entropy vacuum level is given. These results show that the information entropy is not only a theoretically satisfactory concept but can also be useful as a tool for more practical quantum-optics applications.

We show how to reconstruct the quantum state of one-dimensional wave packets in the continuous part of the spectrum. We assume that the position probability distribution is measured for a sufficiently long time interval and that the potential is known, but otherwise arbitrary. Our paper fills the gap between the tomographic state reconstruction based on free evolution [J. Bertrand and P. Bertrand, Found. Phys. 17, 397 (1987)] and the state determination of moving bound states [U. Leonhardt and M. G. Raymer, Phys. Rev. Lett. 76, 1985 (1996)]. Our result may be relevant with respect to the state determination of atomic beams [Ch. Kurtsiefer, T. Pfau, and J. Mlynek, Nature (London) 386, 150 (1997)] moving in arbitrary potentials.

The dynamics of the spin-boson Hamiltonian is considered in the stochastic approximation. The Hamiltonian describes a two-level system coupled to an environment, and is widely used in physics, chemistry, and the theory of quantum measurement. We demonstrate that the method of stochastic approximation, a general method for consideration of dynamics of an arbitrary system interacting with environment, is powerful enough to reproduce qualitatively the striking results by Leggett et al. [Rev. Mod. Phys. 59, 1 (1987)] found earlier for this model system. The results include an exact expression of the dynamics in terms of the spectral density, and show the appearance of two interesting regimes for the system, i.e., pure oscillating and pure damping ones. Correlators describing the environment are also computed.

The effect of a canonical Lorentz boost on the Newton-Wigner-Pryce position operator of a spin zero system is calculated. The resulting equations differ significantly from those corresponding to the Lorentz boost of a position coordinate in classical special relativity. The components of the boosted Newton-Wigner-Pryce position operator are interpreted in terms of a classical analog. It is seen that the transformed operator corresponds not to the coordinates of the same event in two reference frames, but to the coordinates of the intersection of the worldline of the system’s center of momentum with hyperplanes of the same coordinate time in the two frames.

We present relaxed criteria for quantum error correction that are useful when the specific dominant quantum noise process is known. As an example, we provide a four-bit code that corrects for a single amplitude damping error. This code violates the usual Hamming bound calculated for a Pauli description of the error process and has no simple explanation in terms of the usual Pauli basis GF(4) codes.

We develop here a simple formalism that converts second-class constraints into first-class ones for a particle moving on an $n$-dimensional sphere. The Poisson algebra generated by the Hamiltonian and the constraints closes and by quantization transforms into a Lie algebra. The observable of the theory is given by the Casimir operator of this algebra and coincides with the square of the angular momentum.

The time-dependent total electric- and magnetic-field operators in the neighborhood of a molecule are calculated in the minimal-coupling formalism of Coulomb gauge quantum electrodynamics. The spatial variations of the vector potential are taken into account, enabling the fields correct to second order in the electronic charge to include magnetic-dipole- and electric-quadrupole-dependent terms in addition to contributions arising from the electric-dipole interaction term. The minimal-coupling Maxwell fields are compared and contrasted with their analogs previously derived in the multipolar framework. The electric- and magnetic-radiation-field operators derived in the minimal-coupling formalism are then used to calculate the expectation values of the Thomson energy density and the Poynting vector, and the results obtained are shown to be identical to those of the multipolar theory.