We have discovered that ionization without accompanying electron capture is an important process in slow (v∼0.1–0.2 a.u.) ${\mathrm{Xe}}^{\mathit{q}+}$-Xe collisions at very high projectile charge (q>25). The measured absolute cross sections, although between one and two orders of magnitude lower than the ones for single-electron capture, increase rapidly with q when q>25 and reach a level of ∼1×${10}^{\mathrm{-}15}$ ${\mathrm{cm}}^2$ for q>30. We argue that the reaction mechanism for ionization of the heavier rare gases involves the formation of core-excited, autoionizing, neutral target states.

A rigorous method to calculate the first-order self-energy in a model potential is presented. An alternative straightforward way of renormalization is introduced to avoid the commonly used potential expansion implying a larger number of diagrams in higher-order QED effects. The divergent mass term is defined in coordinate space and decomposed into a sum over finite partial-wave (l) contributions. The unrenormalized bound self-energy is similarly decomposed into a partial-wave sum and the renormalization is performed for each partial wave. The renormalized sum converges fairly rapidly (the asymptotic behavior is ${\mathit{l}}^{\mathrm{-}3}$). The method is applied to lithiumlike uranium, for which the electron self-energy in the potential of a point nucleus, as well as the effects of the finite nucleus and of the screening by the remaining electrons on the self-energy, are obtained with an accuracy better than 0.1 eV. The results are in very good agreement with experiment and with calculations recently performed using other techniques.

A scheme for concentrating a large fraction (∼100%) of the alkali-metal atoms in an atomic vapor in any single magnetic sublevel of the ground state is developed. This is experimentally demonstrated in the ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$ vapor. The atomic vapor is optically pumped to a high degree of spin polarization after which two radio-frequency π pulses are applied to transfer the atomic population from the (2,2) or (2,-2) (F,${\mathit{M}}_{\mathit{F}}$) state to the (2,0) sublevel of the ground state. The resulting distribution is diagnosed using a microwave field tuned to the hyperfine transition (6834 MHz).

We have measured the total collisional loss rate for ultracold sodium atoms held in a magneto-optical trap (MOT) as a function of light intensity in the trap. We extract the rate constant for collisional loss by measuring the temporal behavior of MOT loading from background vapor. The loss rate increases with light intensity in satisfactory agreement with new calculations, which are also presented. The results are interpreted in terms of detailed collision processes.

We confine ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$ atoms in an optical dipole force trap with a very large detuning from resonance of up to 65 nm. Confinement times of 200 ms, limited only by background-gas collisions, are obtained without additional cooling. A typical trap contains 1300 atoms at a temperature of 0.4 mK and a peak density of 8×${10}^{11}$ ${\mathrm{cm}}^{\mathrm{-}3}$. We measure spontaneous photon scatter rates of the trapped atoms to be less than 1.6×${10}^3$ ${\mathrm{s}}^{\mathrm{-}1}$, corresponding to recoil heating rates below 0.6 mK/s. The far-detuned trap confines atoms with a strong, nearly conservative optical force and negligible atomic excitation.

Using the combined configuration-interaction–Hylleraas method, the dc Stark-shift parameter of the lithium D1 line has been calculated. The value of 4.636 kHz/(kV/cm${)}^2$ is in excellent agreement with recent experimental results of 4.6216(21) [L. R. Hunter, D. Krause, Jr., D. J. Berkeland, and M. G. Boshier, Phys. Rev. A 44, 6140 (1991)] and 4.617(41) kHz/(kV/cm${)}^2$ [L. Windholz, M. Musso, G. Zerza, and H. Jäger, Phys. Rev. A 46, 5812 (1992)].

A numerical analysis using the resolvent-operator method shows that the space and time localization of ionization is in fact the key needed to understand the residual population that is left in the excited state in Stark-induced resonant multiphoton ionization. The two viewpoints recently opposed in the literature [Optics and Photonics News 3, 22 (1992) G. N. Gibson, R. R. Freeman, and T. J. McIllrath] are therefore compatible. However, the excited-state population can easily be destroyed if the resonance intensity or the pulse duration is increased.

We show that it is possible to make a logically reversible quantum-nondemolition measurement of an optical-field photon number, where the measurement preserves all the information contained in the premeasurement wave function. The nonunitary dynamics of the proposed scheme is analyzed using a Monte Carlo wave-function approach.

Difference phase and transmission spectra (DPS and DTS) due to induced phase modulation of probe pulses in ${\mathrm{CS}}_2$ were measured with a femtosecond frequency-domain interferometer. Signals that satisfy the Kramers-Kronig (KK) relations with opposite signs were observed. At zero time delay, DTS and DPS were both even functions with respect to the probe center frequency due to the fifth- and third-order nonlinearities, respectively. The conditions for applying the KK relations to time-resolved data were obtained theoretically and verified experimentally.

A general method to decouple multicomponent linear wave equations is presented. First, the Weyl calculus is used to transform operator relations into relations between c-number valued matrices. Then it is shown that the symbol representing the wave operator can be diagonalized systematically up to arbitrary order in an appropriate expansion parameter. After transforming the symbols back to operators, the original problem is reduced to solving a set of linear uncoupled scalar wave equations. The procedure is exemplified for a particle with a Born-Oppenheimer-type Hamiltonian valid through second order in ħ. The resulting effective scalar Hamiltonians are seen to contain an additional velocity-dependent potential. This contribution has not been reported in recent studies investigating the adiabatic motion of a neutral particle moving in an inhomogeneous magnetic field. Finally, the relation of the general method to standard quantum-mechanical perturbation theory is discussed.

We consider a quantum interference experiment in which two incident electrons, moving in complementary regions of space, give rise to a nonseparable two-electron state. Multielectron interference experiments have been considered previously, but it is shown here that a two-electron interference experiment is within the reach of existing laboratory techniques. It is also shown that an electromagnetic action exerted on one of the electrons can result in observable effects involving both electrons, although the conditions of the experiment are chosen such that during or after the exertion of this action on one of the electrons there is no exchange of energy, momentum, or angular momentum between the two electrons. This brings into evidence the importance of the single phase common to all particles of a system for the description of interactions involving multiparticle states which are nonseparable.

The perturbation required to vary the normalization constants of the chosen energy levels and to shift individual levels in the rectangular well for the finite-difference Schrödinger equation is shown. The peculiarities of the discrete case in comparison with the equation of motion with the continuous coordinate are found. The ordinary potential parameters ${\mathit{v}}_{\mathit{n}}$ (on the diagonal of the matrix Hamiltonian) determine the shape of the lower boundary of the allowed zone, and ${\mathit{u}}_{\mathit{n}}$ on the neighbor diagonals of the matrix Hamiltonian determine the width of the zone. It is found that ${\mathit{v}}_{\mathit{n}}$ and ${\mathit{u}}_{\mathit{n}}$ produce a different influence on the shifts of the energy levels in the rectangular well. The potential v pushes in the same direction the levels symmetrically placed with respect to the middle of the spectrum, and u pushes them in the opposite directions.

Finite quantum systems are considered and dual quantities are defined with a finite Fourier transform. Ladder operators that translate the eigenstates of these quantities are shown to form a finite Weyl group. Dual measurements are introduced and shown to obey certain entropic inequalities. A factorization of these systems into subsystems with the use of number-theoretic results is also presented.

A method is presented for the construction of WKB wave functions that avoids explicit consideration of any matching between results pertaining to classically allowed and classically forbidden regions. The formalism is based on the maximization of a suitably defined quantal pseudoentropy, subject to the constraints posed by the expectation values of a reduced number of operators, which are evaluated according to special WKB techniques that consider expansions up to orders ħ and ${\mathrm{ħ}}^2$. The algorithm is tested with reference to the harmonic and quartic anharmonic oscillators.

We consider the spin-boson model as a measurement device, with the 1/2-spin system acting as a pointer and the influence of the environment simulated by means of the interaction between the 1/2-spin system and a dissipative oscillator. In accordance with the recent finding of Bonilla and Guinea [L. L. Bonilla and F. Guinea, Phys. Rev. A 45, 7718 (1992)] the assumption that the oscillator is classical results, under specific conditions, in the occurrence of a wave-function collapse. However, our theoretical analysis shows that the wave-function collapse is provoked by the action exerted by the 1/2-spin system on the oscillator (reaction field) and that the reaction field is as intense as the quantum-mechanical fluctuation neglected by the semiclassical approximation. A numerical treatment shows that no collapse occurs within a fully-quantum-mechanical treatment.

The Dyson-Pechukas level dynamics has been reformulated and made suitable for studying avoided level crossings and transition to chaos. The N-level dynamics is converted into a many-body problem of one-dimensional Coulomb gas with N-constituent particles having intrinsic excitations. It is shown that local fluctuation of the level distribution is generated by a large number of avoided level crossings. The role played by avoided level crossings in generating chaoticity in level dynamics is similar to the role played by short-range collisions in causing thermalization in many-body dynamics. Furthermore, the effect of level changing rates in producing avoided level crossings is the same as particle velocities in causing particle-particle collisions. A one-dimensional su(2) Hamiltonian has been constructed as an illustration of the level dynamics, showing how the avoided level crossings cause the transition from a regular distribution to the chaotic Gaussian orthogonal ensemble (GOE) distribution of the levels. The existence of the one-dimensional su(2) Hamiltonian which can show both GOE and Poisson level statistics is remarkable and deserves further investigation.

Measurements of internal energy states of atomic ions confined in traps can be used to illustrate fundamental properties of quantum systems, because long relaxation times and observation times are available. In the experiments described here, a single ion or a few identical ions were prepared in well-defined superpositions of two internal energy eigenstates. The populations of the energy levels were then measured. For an individual ion, the outcome of the measurement is uncertain, unless the amplitude for one of the two eigenstates is zero, and is completely uncertain when the magnitudes of the two amplitudes are equal. In one experiment, a single ${}_{}{}^{199}{}_{}{}^{}\mathrm{Hg}_{}^{+}{}_{}{}^{}$ ion, confined in a linear rf trap, was prepared in various superpositions of two hyperfine states. In another experiment, groups of ${}_{}{}^9{}_{}{}^{}\mathrm{Be}_{}^{+}{}_{}{}^{}$ ions, ranging in size from about 5 to about 400 ions, were confined in a Penning trap and prepared in various superposition states. The measured population fluctuations were greater when the state amplitudes were equal than when one of the amplitudes was nearly zero, in agreement with the predictions of quantum mechanics. These fluctuations, which we call quantum projection noise, are the fundamental source of noise for population measurements with a fixed number of atoms. These fluctuations are of practical importance, since they contribute to the errors of atomic frequency standards.

We study Rydberg molecules taking into account the interaction between the rotational motion of the nuclei and the radial motion of the electron. This situation can be treated to a good approximation in quantum mechanics by the multichannel quantum-defect method which in turn has a well-defined classical limit. We are able to calculate very long sequences of levels and the corresponding amplitudes of wave packets. This allows us to study the statistical properties of both in detail. Our interest focuses on aspects of ‘‘quantum chaos’’ that can be particularly well understood in this case. Our main result is that, in a completely chaotic classical situation, where statistics of quantum-level spacings follow the expected universal Gaussian-orthogonal-ensemble behavior, and statistics of line intensities display the expected universal Porter-Thomas behavior, nonuniversal properties are explicitly contained in correlations between intensities and spacings, determined by the time needed for the classical system to mix on a length scale given by the quantum wavelength.

Using the phase-space picture (Weyl-Wigner-Moyal formalism) of quantum mechanics for time-dependent Hamiltonians, we show that the Ermakov-Lewis invariant of a generalized harmonic oscillator can be derived from the Wigner function of a squeezed coherent state. The geometric meaning of this invariant is clarified and realized via the Wigner ellipse in phase space.

In the framework of Gutzwiller’s theory for nonintegrable Hamiltonian systems the diagonal part of the Green’s function is expressed as a sum over classical trajectories which are closed in configuration space. We can distinguish two types of recurrent trajectories, those which are in the neighborhood of a periodic orbit and those whose lengths vanish as the allotted time continuously approaches zero. For the hydrogen atom in a uniform magnetic field we identify both types of orbits in the path-generating function, i.e, the Fourier transform of the Green’s function with respect to 1/ħ. Projections of the Green’s function onto coherent states eliminate the contributions from recurrent but nonperiodic orbits. The corresponding phase-space representation of the path-generating function shows a strong localization along the classical periodic orbits.