A simple scheme is presented that allows the generation and detection of nonclassical states of the electromagnetic (em) field with controllable (predetermined) photon-number and phase distributions. It is based on the two-photon resonant interaction of a single em field mode in a high-Q cavity with initially excited atoms crossing the cavity sequentially (one at a time). The sequence duration should be much shorter than the cavity-mode lifetime. Nonclassical states of the field are generated conditionally, by selecting only those sequences wherein each atom is measured to be in the excited state after the interaction. The field distribution resulting from a sequence of N such measurements is peaked about 2N positions in the phase plane, which evolve sinusoidally as a function of the atomic transit times and are therefore simply controlled. When these peaks are chosen not to overlap, the field state constitutes a generalized Schrödinger cat. By choosing them to overlap, we can make parts of the field distribution strongly interfere, giving rise to decimation of the photon-number distribution. In particular, this process can prepare Fock states with controlled photon numbers. The generated phase distribution can be detected by monitoring the pattern of revivals in the excitation of a ‘‘probe’’ atom.

A systematic study of the high-order harmonic generation in He, Ne, Ar, Kr, and Xe has been made using subpicosecond XeCl laser pulses at a maximum laser intensity of 3.5×${10}^{15}$ W/${\mathrm{cm}}^2$. The highest orders of harmonics observed are the 15th in He, the 13th in Ne, and the 9th in Ar, Kr, and Xe, and no broad plateau is formed in the harmonic distributions. The ultraviolet laser pulse, which has a large multiphoton ionization rate, was observed to induce a strong dielectric breakdown of the nonlinear medium at the high intensity. Multiphoton ionization and the subsequent dielectric breakdown of the medium are shown to have a significant influence on the harmonic-generation processes, as well as on the harmonic distribution. The laser-wavelength dependence of the high-order harmonic generation is discussed by comparing the results with those obtained by the subpicosecond visible dye-laser pulses.

Recently demonstrated methods for resonance imaging of moving atoms in the potential due to a spatially varying light shift have yielded spatial resolution of 200 nm, with linearity of a few percent over several micrometers. With single-atom detection and a potential uncertainty-principle limited resolution of a few nanometers, this method can be used to perform spatial correlation experiments in beams and traps, with ultrahigh spatial resolution. In this paper we present a theoretical treatment for methods to extend the resonance imaging technique to include position measurements of moving atoms at multiple points, and thereby to measure appropriately defined atomic correlation functions which depend generally on both position and momentum. Results are given for both fermions and bosons and simple examples show how correlated position measurement by resonance imaging reveals the atomic statistical properties at the long length scales which arise at low temperature.

We argue that for moving atoms, the conventional dipole interaction must be supplemented by a so-called Röntgen term in order to obtain results which are trustworthy to order V/c in the atomic velocity. As an illustration, we include the Röntgen interaction in a Hamiltonian model to derive the angular distribution of photons spontaneously emitted by a freely moving atom. We find agreement with an independent calculation which is based on the transformation properties of such distribution under Lorentz boosts. This resolves the previously reported inconsistency of the conventional dipole interaction for moving atoms [Phys. Rev. A 47, 671 (1993)].

Wave propagation in optical media with strong dispersion and weak quadratic nonlinearity is analyzed using the method of multiple scales. This method shows that the evolution of the envelope for a single nondepleted pump wave is described by the nonlinear Schrödinger equation. Hence various self-modulation effects, due to an effective intensity-dependent refractive index, are possible to observe in materials with quadratic nonlinearity. That is, materials that are known to generate ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ wave processes may also support, for example, soliton propagation. Physical conditions and numerical examples are given for observing solitons, self-defocusing, and spectral broadening. Other self-modulation effects are also discussed as well.

In the present article we have found the complete energy spectrum and the corresponding eigenfunctions of the Dirac oscillator in two spatial dimensions. We show that the energy spectrum depends on the spin of the Dirac particle.

Damped harmonic-oscillator pseudostationary-state wave functions are used to calculate transitions probabilities for a simple harmonic oscillator (SHO) subjected to damping from time t=0. The mean and variance of the energy operator are obtained in the state which was initially an SHO stationary state. This state is an instantaneous eigenstate of the energy at times when sin(ωt)=0, ω being the reduced frequency.

For a dissipative system with Ohmic friction, we obtain a simple and exact solution for the wave function of the system plus the bath. It is described by the direct product in two independent Hilbert spaces. One of them is described by an effective Hamiltonian, the other represents the effect of the bath, i.e., the Brownian motion, thus clarifying the structure of the wave function of the system whose energy is dissipated by its interaction with the bath. No path-integral technology is needed in this treatment. The derivation of the Weisskopf-Wigner linewidth theory follows easily.

We present correlated-wave-function characteristics, energies, and partial widths with interchannel coupling to all orders, for the ${\mathrm{H}}^{\mathrm{-}}$ two-electron ionization ladder resonances of ${}_{}{}^1{}_{}{}^{}$D symmetry for n=3, 4, and 5. Our computations took into account the interaction of up to 19 open channels. The resulting energies and total widths are compared to earlier computations and with the experimental energy for n=3.

The modified shifted-large-N approach proposed by Bag et al. [Phys. Rev. A 46, 6059 (1992)] for the Morse potential is applied to the exponential (6) [exp(6)] potential, i.e., a potential with an exponential repulsion and an attraction in ${\mathit{r}}^{\mathrm{-}6}$. Although the method does not provide the exact analytic expressions of the vibrational eigenvalues and eigenfunctions as in the Morse case, it is shown to predict quite accurate results for both the energy eigenvalues and eigenfunctions for the vibrational and rovibrational states of the exp(6) potential. In particular, the wave functions are much more accurate than those provided by the usual shifted-1/N method, which fails to yield their correct behavior. Moreover, in the modified approach, the exp(6) eigenfunctions are given in the same analytical form as the Morse ones.

The energy loss of hydrogen beams traversing a helium gas target is calculated using the charge-state approach. The first Born approximation is used for the neutral charge-state and the continuum-distorted-wave–eikonal-initial-state model for the proton charge state. This model takes into account distortion effects due to the long-range Coulomb potential. From the cross sections for the different reaction channels we obtain the equilibrium charge-state fractions, the electronic stopping power associated with each reaction channel, and the mean electronic stopping power. This information allows a detailed study of the velocity dependence at low impact velocities.

We show through close-coupled quantum-scattering calculations that the cross section for fine-structure-changing collisions between excited ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$ and ground ${}_{}{}^2{}_{}{}^{}$${\mathit{S}}_{1/2}$ A atoms of the same species, where A=Rb or Cs, is very sensitive to the molecular potentials and spin-orbit matrix elements of the alkali-metal-dimer species. Spectroscopic studies of these species are needed to extract accurate parameters. New high-resolution photoassociation spectroscopy of trapped atoms could be used for this purpose.

Interaction with a measuring apparatus can cause otherwise interfering paths of a particle to become distinguishable. Under some conditions, however, it is possible to ‘‘erase’’ the distinguishability, thereby restoring interference. The concept of a quantum eraser is useful for understanding the role of entanglement in interference. Several attempts to investigate the phenomenon have been made using the correlated photons from spontaneous parametric down-conversion. However, none of the experiments previously performed in connection with quantum erasure has provided an optimal demonstration. We propose three improved down-conversion schemes, each of which satisfies all the criteria for a true quantum eraser. As the proposed schemes are all modifications or combinations of previously completed experiments, they are deemed to be feasible.

By measuring the phase shift of the response of a modulated laser, we improve upon a previous demonstration of the fit of the dynamics of a ${\mathrm{CO}}_2$ laser to a vibrational-rotation model and extract, rather than assume, the intraband relaxation rate.

We report the observation of anomalous conical emission in the first resonant transition of atomic calcium in the presence of a second probe beam. The observations do not favor the refraction-at-boundary model unless the incoherence between the beams plays a crucial role. On the other hand, an induced defocusing of a blue-shifted beam takes place in the presence of a strong red-shifted beam. This result is rather surprising, since it is observed under circumstances where self-focusing would be expected.

The pure-state evolution of the atomic as well as the field states in the resonant two-photon Jaynes-Cummings model with the field initially in the coherent state is studied. Analytic expressions for various quantities involved are obtained under the large-n¯ approximation. It is shown that the atom as well as the field are approximately in the pure state for gt=kπ/4, where k is an integer and in a completely pure state for gt=kπ. The field states generated at the times gt=kπ/4 are shown to be a quantum superposition of the coherent states for a particular choice of the relative phase. The interference between these states leads to a spiked photon-number distribution but the field is still Poissonian.

The possibility of constructing tunable x-ray lasers of photon energy in the kilo-electron-volt range is discussed. It is shown on the basis of channeling observations that an ∼3.3% change of the photon energy of an x-ray-laser scheme proposed recently can be obtained with a 100-K change of the temperature.

We analyze the phase properties of a strong cavity field interacting with an ensemble of initially excited N two-level atoms. Using the Pegg-Barnett phase formalism [Phys. Rev. A 39, 1665 (1989)], we calculate the phase probability distribution as well as the phase variance. The phase probability density exhibits a (N+1)-peak structure at the initial stages of the evolution. The phase variance is used to illustrate the progressive randomization of the phase on the long-time evolution. The difference in the phase dynamics for the N even and the N odd case is pointed out.

A Pancharatnam phase shift, which is similar to Berry’s topological phase, is introduced into the idler path between two down-converters in an experiment on induced coherence without induced emission. Although the idler beams in such an experiment do not take part in interference, the Pancharatnam phase shift is observable in the interference of the signal beams. This is clearly a nonlocal manifestation of Pancharatnam’s phase.