The four-wave-mixing signal at $2{\omega }_1-{\omega }_2$ from a collective system of $N$ two-level atoms dissipating through spontaneous emission and dephasing and driven by weak external fields of frequencies ${\omega }_1$ and ${\omega }_2$ in a cavity of arbitrary $Q$ is found by evaluating exactly the susceptibility ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}({\omega }_1,{\omega }_1,-{\omega }_2)$. The exact results show that the customarily employed secular approximation for treating the problem of a strongly coupled atom-cavity system is hopelessly inadequate for describing the process of four-wave mixing.

In this paper detector efficiency conditions are derived for the Greenberger-Horne-Zeilinger (GHZ) paradox. The conditions will be necessary and sufficient, i.e., the GHZ paradox is explicable in terms of a local-variable model if the efficiency is below the bounds, and the GHZ prerequisites are inconsistent at higher efficiencies. The derivation does not make use of any of the symmetry assumptions usually made in the literature, most notably the assumption of independent errors. The errors in local-hidden-variable models are governed by the “hidden variable” and, therefore, one cannot in general assume that the errors are independent. It will be shown that this assumption is not necessary. Moreover, bounds are presented that do not need the emission rate of particle triples to be known. An example of such a bound is the ratio of the triple coincidence rate and the double coincidence rate at two detectors, which needs to be higher than 75% to yield a contradiction.

The nonrelativistic convergent close-coupling (CCC) method is applied to the calculation of 20-eV electrons scattering from the barium ground state. Very good agreement is found with measurements of the elastic, ${\mathrm{}\left(6s6p\right)\mathrm{}}^1{P}^o,$ and ${\mathrm{}\left(6s5d\right)\mathrm{}}^1{D}^e$ differential cross sections. In addition, good agreement is found with the measurements of the ${\mathrm{}\left(6s6p\right)\mathrm{}}^1{P}^o$ orientation and alignment parameters. The agreement between the CCC theory and experiment is substantially better than with other relativistic and nonrelativistic theories.

Single and double $K$-shell excitation of Li by 10.6-MeV/nucleon ${\mathrm{N}}^{7+}$ projectiles is investigated by measuring Li autoionization spectra in the energy range from 50 to 90 eV. The ratio for double $K$-shell excitation to single $K$-shell excitation is determined to be about 0.36%. The measured ratio for double-to-single $K$-shell excitation of Li is about a factor of 2 larger than calculations based on independent interactions between the projectile nucleus and each of the Li target electrons, indicating that the electron-electron interaction plays a dominant role in the double $K$-shell excitation of Li in these collisions.

State-specific configuration interaction in the continuum calculations, with electron correlation included, shows that shape resonances in polyelectronic atoms can be computed systematically to a high degree of accuracy. Specifically, the ${\mathrm{B}}^{\mathrm{-}}{1s}^2{2s}^2{2p}^2{}^{1}D$ state is computed to be a shape resonance with ${\rm E}=95\mathrm{}\mathrm{meV}$ and $\Gamma =54\mathrm{}\mathrm{meV},$ confirming the tentative identification given recently by Lee et al. [Phys Rev. A 53, R633 (1996)] for the lowest resonance structure observed in scattering experiments.

We present a combined experimental and theoretical study of 32.6-eV electron-impact ionization of helium. The measured absolute coplanar triply differential cross sections are in the equal-energy-sharing ${(E}_A{=E}_B=4\mathrm{}\hspace{0.5em}\mathrm{eV})$ kinematical region, and have been obtained in the fixed ${\theta }_A,$ fixed ${\theta }_B-{\theta }_A,$ and symmetric geometries. The convergent close-coupling calculations are in excellent agreement with experiment.

The collision between a cluster and a highly charged ion, and the subsequent production of the highly charged cluster, are theoretically investigated in the time-dependent local-density approximation. The multiple electron transfer passing over the saddle of the potential barrier is seen in the calculation and is in good agreement with an estimate by the simple classical overbarrier model. The measured electron transfer in the ${\mathrm{C}}_{60}{+\mathrm{A}\mathrm{r}}^{8+}$ collision is reasonably reproduced in the calculation.

Single light beam transmission spectroscopy in an ultrathin dilute vapor cell (10–100 μm) reveals sub-Doppler features. Indeed, atoms with fast (normal) velocity undergo a short interaction between the cell walls, and are shown to be less absorbing because they have not reached their steady state of interaction with light. The effect is observed in the linear-response regime with a simple two-level system, as ensured from the ultralow level of light irradiation ($<~1\mu {\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ for the Cs $D_2$ line). The effect, known for a long time in the microwave domain, is demonstrated here in the optical domain, and is extended to cell thicknesses large relative to the optical wavelength.

Ground-state ${}^{52}\mathrm{Cr}$ atoms have been magnetically trapped using buffer-gas loading. The atoms are produced by laser ablation of solid ${}^{52}\mathrm{Cr},$ thermalized by collisions with a cryogenically cooled helium buffer gas, and trapped by an anti-Helmholtz quadrupole magnetic field. The atoms are detected by absorption spectroscopy on the $a^7{S}_3\leftrightarrow z^7{P}_3$ transition at 427.6 nm. Using this technique, approximately ${10}^{11}$ atoms are loaded into the trap in a single ablation pulse. Loading has been demonstrated at temperatures from 0.3 to 1.4 K.

The possibility of modulation of an Autler-Townes doublet structure in an atomic continuum by changing the phase difference between two incident femtosecond laser pulses is investigated theoretically. Numerical simulations are carried out by solving the three-dimensional time-dependent Schrödinger equation for a Na atom interacting with a two-color field, a fundamental, and its second harmonic. It is found that a sinusoidal modulation of the individual members of the doublet, as a function of the phase difference, can be achieved at low intensities of the order of ${10}^{10}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2.$ Such modulations of the sharply defined electron currents (where the width is of the order of the fine structure of the Autler-Townes levels) may be detected by high-resolution photoelectron spectroscopy. It is also shown that at a higher intensity of the order of ${10}^{12}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ the amplitude of modulation diminishes, indicating that lower intensities are to be preferred for the present purpose.

We investigate the form and stability of a cloud of atoms confined in a harmonic trap when the scattering length is negative. We find that, besides the known low-density metastable solution, a different branch of Bose condensate appears at higher density when nonlocality effects in the attractive part are taken into account. The transition between the two classes of solutions as a function of the number $N$ of atoms can be either sharp or smooth according to the strength and range of the attractive interaction. Use of tight traps is favorable for investigating the evolution of the system, as the strength of the effective interaction increases with $N$.

A previously derived subset of fermion-photon vertices, in which the generalized “energy” state of the fermion changes with respect to the interacting photon, is shown to yield manifestly gauge-invariant Feynman amplitudes, whether the fermions are on or off the mass shell. These “pairlike” vertices account for all low-order electromagnetic phenomena, such as electromagnetic scattering (including Bhabha and Møller scattering), Compton scattering, pair creation and annihilation, and bremsstrahlung. Pairlike vertices also account for weak-interaction phenomena such as charged pion decay, muon decay, and neutrino-quark scattering. If vector interactions are constrained to these gauge-invariant vertices, then self-interactions are restricted (infinite loop momenta are excluded) but not eliminated. We conclude that it is extremely unlikely that the non-gauge-invariant vertices are physically allowable, despite the success of renormalized quantum electrodynamics which includes these vertices ab initio, but clearly removes their effects in the renormalization process.

We present a method for obtaining evolution operators for linear quantum trajectories. We apply this to a number of physical examples of varying mathematical complexity, in which the quantum trajectories describe the continuous projection measurement of physical observables. Using this method we calculate the average conditional uncertainty for the measured observables, being a central quantity of interest in these measurement processes.

We present a canonical formalism facilitating investigations of the dynamical Casimir effect by means of a response theory approach. We consider a massless scalar field confined inside of an arbitrary domain $G\left(t\right)\mathrm{}$, which undergoes small displacements for a certain period of time. Under rather general conditions a formula for the number of created particles per mode is derived. The perturbative approach reveals the occurrence of two generic processes contributing to the particle production: the squeezing of the vacuum by changing the shape and an acceleration effect due to motion of the boundaries. The method is applied to the configuration of moving mirror(s). Some properties as well as the relation to local Green’s-function methods are discussed.

An approximate inference approach is advanced in order to determine the density matrix in cases in which the pertinent Hamiltonian is unknown, and the available expectation values pertain to noncommuting observables. The inference of both pure and mixed states is addressed, and on an equal footing, without facing infinities in the pure state limit. Information-theoretical tools are employed.

The helicity amplitudes of high-energy photon splitting in an external Coulomb field are obtained exactly in the parameter $Z\alpha$. The consideration is based on the quasiclassical approach, valid for small angles between all photon momenta. A new representation of the quasiclassical electron Green function is exploited. General expressions obtained are analyzed in detail when the transverse momenta of both final photons are much larger than the electron mass. It is shown that, at $Z\alpha \sim 1$, Coulomb corrections essentially change the cross section as compared to the Born approximation. Screened and unscreened potentials are considered.

A nonperturbative theory for quasiadiabatic time evolution in quantum systems is presented. The dynamics of the passage through an avoided level crossing is given by a nonperturbative alternative to the Landau-Zener theory used for diatomic predissociation. The theory provides the theoretical framework for a quantitative understanding of the quantum steps in the hyteresis loops observed very recently in manganese acetate crystals. These steps correspond to avoided level crossings for the associated, fully adiabatic problem. A natural extention of the theory yields quasiadiabatic corrections to Berry’s phase.

The dynamics of the harmonic oscillator, with a fluctuating, time-dependent frequency, is studied in the quantum framework. For periodic fluctuations of period τ, it is found that the mean energy diverges exponentially in time, provided τ falls into certain “bands,” centered around “quasiresonant” values, for which the rate of increase is maximum. In agreement with the correspondence principle, this rate is shown to coincide exactly with the one obtained for the classic oscillator, in the same conditions [Loris Ferrari, Phys. Rev. B 56, 593 (1997)]. The notion of adiabaticity has been revisited in the case of exponentially diverging mean energy. It is found that the Heisenberg form of the Hamiltonian operator can be expressed as a new effective Hamiltonian, which is still harmonic, but has exponentially diverging coefficients. It is argued that the same results hold in general (that is, without any quasiresonance condition) if the frequency fluctuation in time is disordered. A brief discussion is presented about nonharmonic interactions leading to dissipative effects. Applications to real physical systems are outlined, with special reference to the electrons in a uniform and constant magnetic field, to which a small fluctuating component is added.