In this paper the difference between two-photon dipole-forbidden and cascade transitions of an inverted system of atoms is studied. It is shown that the fluctuations of the electromagnetic field (EMF) density in the case of two-photon dipole-forbidden transitions are larger than the ones in the case of cascade emission. In the process of the two-photon dipole-forbidden cooperative emission the photons are created in pairs and there appears coherence between pairs of photons (biphotons). In this situation the distribution of energy between the photons in one pair may be random. For two-photon dipole-forbidden transitions the time-behavior of the square density fluctuations of EMF is similar to those of the density of EMF in the case of cascade emission. When the distance between two atoms excited relative to dipole-forbidden transitions is less than the radiation wavelength, then the kinetics of such atoms is analogous to the cascade emission of a single atom.

A method to study weakly bound three-body quantum systems in two dimensions is formulated in coordinate space for short-range potentials. Occurrences of spatially extended structures (halos) are investigated. Borromean systems are shown to exist in two dimensions for a certain class of potentials. An extensive numerical investigation shows that a weakly bound two-body state gives rise to two weakly bound three-body states, a reminiscence of the Efimov effect in three dimensions. The properties of these two states in the weak binding limit turn out to be universal.

We discuss various aspects of coherence of a Bose-Einstein condensate, and summarize the experimental evidence obtained thus far. It is shown that the mean-field energy of a condensate is a measure of second-order coherence. “Release-energy” measurements therefore provide direct evidence of the suppression of density fluctuations in a condensate compared to a thermal cloud.

Molecular-dynamics simulations have been used to calculate the time-correlation functions and spectra of the depolarized light scattering from a Lennard-Jones argon cluster Ar${}_{13}.$ Three thermodynamic phases of Ar${}_{13}$ have been studied (solid, solid-liquid coexistence region, liquid) and striking differences between the depolarized Rayleigh spectra of these phases were found.

We numerically investigate multiphoton ionization of excited hydrogen atoms in magnetic and microwave fields when up to $N_I=600\mathrm{}$ photons are required for ionization. The analytical estimates for the quantum localization length in the classically chaotic regime are in agreement with numerical data. The excitation is much stronger than the case with microwave field only due to the chaotic structure of eigenstates in a magnetic field.

We reply to suggestions made by Gillespie [Phys. Rev. A 49, 1607 (1994)] that our earlier paper [Phys. Rev. A 45, 4267 (1992)] contained mathematical inconsistencies. By use of a concrete model, we demonstrate explicitly that the behavior of a quantum-mechanical two-state oscillator may be simulated by a classical jump process.

It is argued that the stochastic model of a quantum-mechanical two-state oscillator discussed in the preceding Comment by Hardy et al. [Phys. Rev. A 56, 3301 (1997)] does not constitute a valid classical stochastic process.

A simple scheme for a Bell-inequality experiment employing four spin-$$$\frac{1}{2}$ particles is presented. Two pairs of fermions, say, $P_1-P_2$ and $P_3-P_4,$ are emitted in different directions; then, particles $P_1-P_3$ and $P_2-P_4$ meet at two causally disconnected regions where their phases are shifted. The result is a correlation between the spin states of distant pairs of particles that violates Bell’s inequality. The required phase shifts could be manipulated, for instance, with magnetic fields.

We describe a method for the determination of the quantum state of molecular vibrations in a regime where the anharmonicities are significant. The method is based on the direct analysis of the observed time-resolved spectrum of resonance fluorescence of the molecular sample.

By performing numerically precise calculations on the ${\mathrm{He}}_2,$ ${\mathrm{Ne}}_2,$ ${\mathrm{Ar}}_2,$ ${\mathrm{Kr}}_2,$ HeNe, HeAr, HeKr, NeAr, NeKr, and ArKr diatomic molecules we have determined the capacity of three popular approximations to density-functional theory to accurately describe bonding in these rare-gas systems. The local-density approximation, the Perdew-Wang 1991 generalized-gradient approximation, and the Perdew-Burke-Ernzerhof generalized-gradient approximation are utilized in the calculation of equilibrium bond lengths, atomization energies, and anharmonic and harmonic vibrational frequencies. We also use the density-functional-based determination of atomic polarizabilities and ionization potentials to obtain the coefficients for the long-range ${(1/r}^6)$ attraction. Our calculations suggest that the interaction from the overlap of atomic densities is the primary binding mechanism in these systems at short range but that the long-range ${1/r}^6$ attraction could also contribute to the total binding energy.

In view of the current interest of QED in strong fields, a complete set of one-photon radiative corrections to the bound-electron $g$ factor is evaluated for several hydrogenlike ions. The calculations are performed to all orders in the nuclear potential and compared to earlier results, based on the $\left(Z\alpha \right)$ expansion, which includes the Schwinger and the Grotch terms. For low $Z$ our all-order result approaches the $\left(Z\alpha \right)$ expansion, but for high $Z$ there is a substantial deviation. Furthermore, for high $Z$ our calculations show that the uncertainty due to nuclear structure is small and thus strongly motivate the bound $g$-factor experiment in progress.

This Rapid Communication proposes an experiment with Rydberg atoms resolved simultaneously in energy and time. The occurrence of classical bifurcations can be detected directly from experimental data and, therefore, information about the nonintegrability of classical equations of motion can be obtained. Results for the hydrogen atom subjected to a static uniform magnetic field are presented and discussed in detail.

The radiative correction to the nuclear charge radius contribution to the Lamb shift of order $\alpha (Z\alpha {)}^5{m}_r^3〈r^2〉$ is calculated. In view of the recent high-precision experimental data, this theoretical correction produces a significant contribution to the hydrogen-deuterium isotopic shift.

The ground state of a hydrogen molecule in magnetic fields is investigated using a fully numerical Hartree-Fock approach. We found that between $4.2\times {10}^4$ T and $3\times {10}^6$ T the ground state is ${}^3{\Sigma }_u^{+}$ with very weak interaction between atoms. In this field region the hydrogen can form a superfluid phase, predicted earlier [Korolev and Liberman, Phys. Rev. Lett. 72, 270 (1994)]; the state ${}^3{\Pi }_u$ is metastable and may be responsible for the unknown excitonic line observed by Timofeev and Chernenko [JETP Lett. 61, 617 (1995)]. For magnetic fields stronger than $3\times {10}^6$ T the ground state is the tightly bound ${}^3{\Pi }_u.$

The three-body Coulomb continuum wave function as a product of three two-body Coulomb wave functions is modified by the introduction of an Ansatz for effective Sommerfeld parameters corresponding to the modification of a particular two-body Coulomb interaction by the presence of the third particle. The triple-differential cross sections for electron-impact ionization of atomic hydrogen at incident energies of 54.4 and 150 eV in asymmetric geometry are calculated. We generally find that this approach gives good agreement with experiment, though some small quantitative discrepancies remain.