The squeezing generated in a lossless nondegenerate parametric amplifier with pump quantization has been numerically simulated in a previous paper [G. Drobný and I. Jex, Phys. Rev. A 46, 499 (1992)]. The report squeezing in a quadrature of up to 90%. We give analytic and numeric results that show that the quadratures studied by Drobný and Jex do not exhibit squeezing if the standard technique of homodyne detection is employed. This is simply shown by a calculation that reveals that the variance in both quadratures is equal for all times. On the other hand, if homodyne detection is not used, the variance would oscillate at the optical carrier frequency—hence, squeezing would be unobservable. We believe that this illustrates the importance of using analytical and physical checks of computer-generated results.

Several quantum proper time derivatives are obtained from the Beck one in the usual framework of relativistic quantum mechanics (spin-1/2 case). The ‘‘scalar Hamiltonians’’ of these derivatives should be thought of as the conjugate variables of the proper time. Then, the Hamiltonians would play the role of mass operators, suggesting the formulation of an adequate extended indefinite mass framework. We propose and briefly develop the framework corresponding to the Feynman parametrization of the Dirac equation. In such a case we derive the other parametrizations known in the literature, linking the extension of the different proposals of quantum proper time derivatives again.

The rotationally resolved zero-kinetic-energy electron spectra for the ${\mathit{v}}^{+}$=1, 2, and 3 vibrational levels of the predissociating ${\mathit{A}}^2$${\mathrm{\Sigma }}^{+}$ state of ${\mathrm{HBr}}^{+}$ are reported. The results for the rapidly predissociating ${\mathit{v}}^{+}$=2 and 3 levels show that the high principal quantum number Rydberg states involved in the zero-kinetic-energy spectroscopy are unperturbed by ion core fragmentation. These data demonstrate the general applicability of this technique for rotationally resolved photoelectron spectroscopy.

Relativistic distorted-wave calculations have been made of the cross sections for electron-impact ionization of ${\mathrm{U}}^{90+}$ and ${\mathrm{U}}^{91+}$ ions with the generalized Breit interaction included between bound and free electrons. Good agreement is obtained with recent electron-beam ion-trap experiments [R. E. Marrs, S. R. Elliott, and D. A. Knapp, Phys. Rev. Lett. 72, 4082 (1994)].

We have demonstrated the Talbot effect, the self-imaging of a periodic structure, with atom waves. We have measured the successive recurrence of these self-images as a function of the distance from the imaged grating. This is a near-field interference effect, which has several possible applications that are discussed.

We report here measurements of two-body photoassociative ionization collisions between sodium atoms within an ultranarrow velocity class selected from a well-collimated, thermal atomic beam. Doppler-shifted excitation of the Na(3s${\mathrm{}}^2$${\mathit{S}}_{1/2}$;F=1)→Na(5p${\mathrm{}}^2$${\mathit{P}}_{3/2}$) transition at 285 nm by a single-mode laser defines the narrow velocity class that subsequently populates the F=2 hyperfine level of the Na ground state by optical pumping. Probe laser beam excitation tuned near the Na(3s${\mathrm{}}^2$${\mathit{S}}_{1/2}$;F=2)→Na(3p${\mathrm{}}^2$${\mathit{P}}_{3/2}$;F=3) transition produced photoassociative ionization with an average collision energy ${\mathit{E}}_{\mathit{K}}$ corresponding to a temperature of 5.3 mK (${\mathit{E}}_{\mathit{K}}$=3/2kT). We determine the rate constant for the process as a function of probe beam intensity and polarization.

We report the trapping of neutral atoms in a permanent magnet trap. Approximately 1×${10}^8$ ground-state lithium atoms have been confined in a nonzero magnetic-field minimum produced by six permanent magnets in an Ioffe configuration. These atoms have a kinetic temperature of 1.1 mK and a peak density of approximately 3×${10}^9$ ${\mathrm{cm}}^{\mathrm{-}3}$. The trapped-atom lifetime is 240 s, limited by collisions with background gas. This trap provides an environment in which quantum-statistical effects, atomic collisions, and other ultralow-temperature phenomena can be studied.

We study the radiative distortion of the lowest two potential surfaces of ${\mathrm{H}}_2^{+}$ and ${\mathrm{H}}_3^{2+}$ molecular ions in a superintense (I≳${10}^{16}$ W/${\mathrm{cm}}^2$), high-frequency, linearly polarized laser field, using the space-translation or acceleration representation of laser-matter interaction. The electron clouds undergo field-induced redistribution in the molecular ions due to the presence of field-induced ‘‘dichotomous’’ dressed Coulomb potentials. Such super-field-dressed systems have a greater tendency to transfer electronic charge into the region between the nuclei and hence become more ‘‘stable’’ than the field-free ones. For example, at the equilibrium nuclear separation the dissociation energy of the superdressed ${\mathrm{H}}_2^{+}$ is found to increase by about 20% compared with the field-free ${\mathrm{H}}_2^{+}$. More dramatically, the lowest two surfaces of ${\mathrm{H}}_3^{2+}$ that are repulsive in zero field become attractive (bonding) in the presence of an intense, high-frequency field. The possibility of molecules becoming stabilized against both ionization and dissociation in superintense fields is discussed.

The dynamic Kingdon trap is a trap designed for the permanent storage of charged particles. While the Paul trap is based on the principle of strong focusing, the dynamic Kingdon trap uses strong defocusing to achieve trapping. It is shown that the dynamic Kingdon trap exhibits a sequence of period-doubling bifurcations. A numerical solution of the Laplace equation for a finite-length dynamic Kingdon trap with holding caps shows that this trap can be implemented in the laboratory.

Recent measurements in laser-assisted elastic electron-atom scattering at small angles are not consistent with Kroll-Watson theory. The added effect of the polarization of the atom by the laser field is studied for a typical atomic static field and polarizability. It is found that this effect makes a negligible contribution in the ${\mathrm{CO}}_2$ laser intensity range used in the measurements.

We give the exact bright spatiotemporal soliton solutions of the two-dimensional nonlinear Schrödinger equation with or without two-photon absorption (TPA) and the bandwidth-limited optical gain, analyzing the physical origin of the bandwidth-limited optical gain that compensates for TPA. The results show that bright spatiotemporal solitons can occur not only in the anomalous dispersion region, but also in the normal dispersion region. The effect of temporal dispersion on the peak power required to form bright spatiotemporal solitons is much less than that of spatial diffraction, and the effect of TPA on the spatial soliton is not neglected and can be compensated for by the frequency-dependent optical gain.

It is generally believed that interaction between dark solitons is repulsive, and two solitons cannot form a bound state. Recently, it has been pointed out that parametric interactions in a diffractive quadratic nonlinear medium can support one-dimensional twin-hole spatial dark solitons [K. Hayata and M. Koshiba, Phys. Rev. A 50, 675 (1994)]. We demonstrate numerically and analytically that this twin-hole dark soliton is modulationally unstable. Instead, we show that, in the other physical context, wave mixing between the first and second harmonics due to cascaded second-order processes in a dispersive quadratic media can support stable twin- (or multi-) hole dark solitons. We explain the physical mechanism that allows these solitons to exist and analyze their stability numerically and analytically.

The standard dimensional continuation of the Schrödinger equation, in which the kinetic energy is generalized to arbitrary D while the potential energy remains unchanged, leads to dissociation in the limit D→∞ for systems that are only weakly bound at D=3. Using the bound states of ${\mathrm{H}}^{\mathrm{-}}$ as an example, we show that accurate energies can be obtained from large-order perturbation theory in 1/D if the repulsive part of the potential is attenuated with a D-dependent factor that prevents the large-D dissociation.

We have investigated the effects of the Mo/ller interaction in relativistic distorted-wave calculations of cross sections for electron-impact ionization of high-Z hydrogenlike ions. We found that the Mo/ller interaction significantly increases the cross section for hydrogenlike uranium, and brings our calculated results into very good agreement with experimental results reported by Marrs, Elliott, and Knapp [Phys. Rev. Lett. 72, 4082 (1994)]. We found similar increases in the cross sections for other hydrogenlike ions. Our results also show that these effects become important at much lower collision energy than previously reported [D. L. Moores and M. S. Pindzola, Phys. Rev. A 41, 3603 (1990)]. With the Mo/ller interaction included, our cross sections for these ions are in good agreement with preliminary results obtained in recent experiments on the electron-beam ion trap (EBIT).

We present a succinct and compact formalism for the solutions of certain Gel’fand-Levitan and Marchenko equations associated with the theories of isospectral Hamiltonians and of continuum bound states.

We compare three procedures for constructing bound states whose energies are embedded in the continuous part of the energy spectrum. We use methods based on the Gel’fand-Levitan and Marchenko equations to generate new potentials which look superficially similar to potentials supporting continuum bound states, but which instead produce isolated energies embedded in the continuum for which no physically acceptable wave function exists. Two examples are used to illustrate these results.

The displaced parity operators are shown to have properties that bear a deep relationship with those of the Wigner functions. By exploiting these properties we show that these operators play an important role in linking together many of the aspects of the various exact phase-space mappings of quantum mechanics. These include the Wigner and Weyl representations, coherent states and the Bargmann representation, the P and Q representations, the Weyl correspondence, and the Moyal star product formalism. We also introduce corresponding displaced Fourier operators and show that their squares are just the displaced parity operators. The formalism is extended to squeezed and displaced parity operators, and their corresponding central role in the theory of squeezed coherent states and general squeezing is explained. We also elucidate the part played by the displaced parity operators in the Moyal star product and its extensions, as a first step towards a potential application of these operators in such modern developments as deformation theory and quantum groups. Finally, we indicate how the apparatus developed might also find applications in other recent exact classical mappings of many-particle quantum mechanics or quantum field theory, which are not special cases of deformation theory. Prime examples here include the powerful so-called independent-cluster method techniques, which incorporate the coupled-cluster method formalism with its inbuilt supercoherent states. Throughout the work we stress the central and unifying role played by the displaced parity operator and its generalizations.

Quantum nonlocality is explored in a proposed experiment simpler than most in that only one photon is detected and no polarizations are measured. A pair of multilevel atoms is irradiated by a weak tuned laser pulse, exciting a certain level in one of them that subsequently decays to a metastable level, emitting a photon. The photon is detected on a distant screen, producing an interference pattern. In the delayed-choice option a second tuned laser pulse that indirectly deexcites the metastable level is sent in later, but while the photon is in flight toward the screen. The interference pattern is found to be erased. A feature is that this ‘‘memory erasure’’ is partial, and its degree is controlled by varying the distance between the pair of atoms.

The perturbed ladder-operator method is applied to the solution of the perturbed Morse- oscillator eigenequation, i.e., the radial Schrödinger equation with a total potential U(r)=${\mathit{D}}_{\mathit{e}}$(1-${\mathit{e}}_{\mathit{e}}^{\mathrm{-}\mathrm{\beta }(\mathit{r}\mathrm{-}\mathit{r}}$)${)}^2$+${\mathit{D}}_{\mathit{e}}$ t${sum}_{\mathit{t}}$${\mathit{g}}_{\mathit{t}}$(1-${\mathit{e}}_{\mathit{e}}^{\mathrm{-}\mathrm{\beta }(\mathit{r}\mathrm{-}\mathit{r}}$)${)}^{\mathit{t}}$. This method, which is an extension of the original Schrödinger-Infeld-Hull factorization method within the perturbative scheme, allows an analytical solution of perturbed eigenequations in almost the same way as factorizable ones. After expanding each perturbation term in a series of ${\mathit{y}}_{\mathit{s}}$(r)=${\mathit{e}}_{\mathit{e}}^{\mathrm{-}\mathit{s}\mathrm{\beta }(\mathit{r}\mathrm{-}\mathit{r}}$), analytical expressions of the perturbed Morse energies are obtained in terms of the anharmonicity constant and of the vibrational quantum number without having to calculate either the excited unperturbed spectra or any matrix element. Analytical expressions of the perturbed Morse eigenfunctions are then obtainable by iterated application of the perturbed ladder operator on the key eigenfunction, or on any one of them. Illustrative examples are given.