We compare the multiple ionization of atomic and molecular iodine using 100-fs laser pulses at 610 nm over a wide range of laser intensities (2×${10}^{12}$ W/${\mathrm{cm}}^2$-3×${10}^{15}$ W/${\mathrm{cm}}^2$). We show that the elongation of the molecular ion to a critical distance drastically enhances the multiple ionization probability of the molecule compared to that of the atom. In particular, the yield of the ten-times-ionized molecule is higher than that of the three-times-ionized atom around ${10}^{14}$ W/${\mathrm{cm}}^2$. This observation supports recent theoretical work on the role of the electron localization in intense-field molecular ionization. Around ${10}^{15}$ W/${\mathrm{cm}}^2$, the quintuple ionization of atoms is observed, whereas fast ${\mathrm{I}}^{2+}$ fragments arising from the ${\mathrm{I}}_2$ Coulomb explosion are not further ionized, even with 300- or 500-fs laser pulses. This result supports the concept of molecule stabilization in strong laser fields.

In this Rapid Communication we present a method of extending the harmonic generation plateau to high energies with very high conversion efficiencies using moderate intensities. Preparing the initial state as a coherent superposition of the ground state and an excited state we can induce dipole transitions between the continuum and the ground state via the intermediate (excited) state responsible for the ionization. We solve numerically the Schrödinger equation and show that the spectrum contains two distinct plateaus, with cutoffs at $U_e+3\mathrm{}{U}_p$ and $U_g+3\mathrm{}{U}_p$. Using an essential states method we demonstrate that the plateaus are due to recombination into the excited and ground states. We briefly discuss possible experimental realizations of the scheme we present.

A method for the experimental reconstruction of the quantum state of motion for a single trapped ion is proposed. It is based on the measurement of the ground-state population of the trap after a sudden change of the trapping potential. In particular, we show how the $Q\left(\alpha \right)$ function and the quadrature distribution $P(x, \theta )$ can be measured directly. In an example we demonstrate the principle and analyze the sensitivity of the reconstruction process to experimental uncertainties as well as to finite grid limitations. Our method is not restricted to the Lamb-Dicke Limit and works in one or more dimensions.

We show that spontaneous emission can significantly alter the dynamics of a two-atom microlaser. This feature can persist even for very small decay rates and is a consequence of the existence of two coherently decoupled sets of two-atom states. We find, however, that under favorable conditions (as are found in ion traps) spontaneous emission can increase atom-atom correlations by optically pumping the atoms into an entangled two-atom state.

We show that the occupation probabilities of the energy eigenstates excited in a wave packet moving in an arbitrary one-dimensional potential can be determined directly from the time-averaged position distribution. The sampling functions are the derivative of the product of the usual eigenfunctions and the linearly independent (non-normalizable) solutions of the Schrödinger equation for the same energy eigenvalue. This is the same structure as those for the harmonic-oscillator case.

We demonstrate that the preparation of a very well localized atom beam is possible without physical interaction. The preparation is based on the selection of an adequate ensemble of atoms of an originally wide beam by means of information obtained with a neutron interferometer. In such a case, the uncertainty relation can no longer be interpreted as a by-product of the interaction between the system and the preparation apparatus. © 1996 The American Physical Society.

The tests of Bell’s inequality to date have failed to be definitive because of the ‘‘detection loophole,’’ due to the inefficiency of photodetectors. An idealized experiment using pairs of two-level Rydberg atoms, correlated with the help of a quantized cavity field, was proposed by Oliver and Stroud [J. Opt. Soc. Am. B 4, 1426 (1987)] for the purpose of blocking this loophole. We develop their proposal by removing their idealizations. We carefully define the ensemble of atom pairs by imposing conditions on arrival times at the analyzers of the atoms. We take into account the spread of velocities of the atoms, which implies that the ensemble must be described quantum mechanically by a statistical operator rather than a pure state, and we show that with detector efficiencies of 0.9 or better, quantum mechanics implies a strong violation of Bell’s inequality in the ensemble. Upper and lower bounds on ensemble averages can be inferred from experimental averages, thereby permitting an experimental test of Bell’s inequality in the ensemble. © 1996 The American Physical Society.

Making use of a generating-function approach, an effective mathematical procedure is derived for the compensation of detection-loss induced errors in quantum-state measurements at any value of the overall detection efficiency η. The connection with the solution of the time-reversed damping equation is discussed. © 1996 The American Physical Society.

Quantum canonical transformations of the second kind and the non-Hermitian realizations of the basic canonical commutation relations are investigated with a special interest in the generalization of the conventional ladder operators. The operator ordering problem is shown to be resolved when the non-Hermitian realizations for the canonical variables that cannot be measured simultaneously with the energy are chosen for the canonical quantizations. Another merit of the non-Hermitian representation is that it naturally allows us to introduce the generalized ladder operators with which one can solve eigenvalue problems quite neatly. © 1996 The American Physical Society.

We study the time propagation of an initially localized wave packet for a generic one-dimensional time-independent system, using the ‘‘nonlinear wave-packet dynamics’’ [S. Tomsovic and E. J. Heller, Phys. Rev. Lett. 67, 664 (1991)], a semiclassical approximation using a local linearization of the wave packet in the vicinity of classical reference trajectories. Several reference trajectories are needed to describe the behavior of the full wave packet. The introduction of action-angle variables allows us to obtain a simple analytic expression for the autocorrelation function, and to show that a universal behavior (quantum collapses, quantum revivals, etc.) is obtained via interferences between the reference trajectories. A connection with the standard WKB approach is established. Finally, we apply the nonlinear wave-packet dynamics to the case of the hydrogen atom in a weak magnetic field, and show that the semiclassical expressions obtained by nonlinear wave-packet dynamics are extremely accurate. © 1996 The American Physical Society.

This paper presents two kinds of applications of the Jaynes-Cummings model to improve detection schemes for the binary phase-shift-keyed signals of the coherent states ‖α〉 and ‖-α〉. The first application raises the amount of exact retrodiction of a mixture made by choosing at random from ‖α〉 and ‖-α〉. The second application is concerned with realizing the optimum receiver to achieve a low decision error. Instead of optical detection, atomic level detection after mapping from them to two-level states of an atom will be proposed. © 1996 The American Physical Society.

In the present work, we propose the method of state-dependent diagonalization to find the energy eigenvalues and eigenstates of a quantum anharmonic oscillator. The example of a cubic-quartic anharmonic oscillator is used to illustrate its validity. Unlike the conventional exact diagonalization, this method is shown to be very efficient for calculating the energy eigenvalues of the excited states as well as the corresponding eigenfunctions. That is, no huge matrix needs to be diagonalized in this approach. © 1996 The American Physical Society.

A semiclassical expression for matrix elements of an arbitrary operator with respect to the eigenstates of an integrable Hamiltonian is derived. This is essentially the Heisenberg correspondence principle, and it is shown via the Weyl correspondence that the approximation is valid through the lowest two orders in ħ. The result is used to prove that an asymptotic form of the Clebsch-Gordan coefficients for two large and one small angular momenta is valid through two orders. © 1996 The American Physical Society.

We present several schemes for preparing and detecting coherent superpositions of classically distinct states of the electromagnetic field in one or two high-Q cavities. These proposals are based on two-atom correlation measurements, to be performed on circular Rydberg atoms interacting dispersively with the cavity fields. Changing the time interval between the two detected atoms allows a monitoring of the decay of quantum coherence due to dissipation. © 1996 The American Physical Society.

Starting with the same form of atomic nonlinearity, Weinberg [Ann. Phys. (NY) 194, 336 (1989)] and Wódkiewicz and Scully [Phys. Rev. A 42, 5111 (1990)] obtained contradictory results concerning an evolution of the atomic inversion w in a two-level atom in Weinberg’s nonlinear quantum mechanics: If the atom is initially in a ground state then either the evolution of w (1) can be linear if one uses a nonlinear generalization of the Jaynes-Cummings Hamiltonian, or (2) is always nonlinear if one uses the nonlinear Bloch equations derived from the nonlinear atomic Hamiltonian function. It is shown that the difference is rooted in inequivalent descriptions of the composite ‘‘atom-plus-field’’ system. The linear evolution of w results from a ‘‘faster-than-light communication’’ between the atom and the field. If one applies a description without the ‘‘faster-than-light telegraph’’ then the calculations based on a suitably modified Jaynes-Cummings Hamiltonian lead to the same dynamics of w as is found in semiclassical calculations based on Bloch equations. It is shown also that a nonlinear quantum mechanics based on a nonlinear Schrödinger equation does not possess a natural probability interpretation.

A time-dependent generalization of current density-functional theory in the form introduced by by Vignale, Rasolt, and Geldart [Adv. Quantum Chem. 21, 235 (1990)] is used. This theory is then applied to the case where an external harmonic electric field is present, and the changes are considered by perturbation theory. Finally, expressions for the frequency-dependent polarizabilities are derived in terms of the so-called electric and magnetic hessians. The theory is contrasted with time-dependent coupled Hartree-Fock theory; this demonstrates how the theory can be implemented. © 1996 The American Physical Society.

The photoassociation and bound-bound excitation processes of alkali-metal–group-IIB molecules have been studied for the LiZn, LiCd, and NaZn molecules. We considered two main factors relevant to these processes, namely, the densities of collision complexes and the relevant absorption coefficients. Densities in the vapor mixture were manipulated by preparation of different metal alloys, whereas the free-bound or bound-bound absorption is selected by changing a laser wavelength used for the excitation. The 2${\mathrm{}}^2$Π states were directly excited by the laser wavelength in the spectral range 435–450 nm. The densities of the LiZn, LiCd, and NaZn excimers were estimated from alkali-metal and Zn (Cd) densities using the dissociation equilibrium equation for the corresponding excimers in the ground state. The experimentally observed LiZn excimer band at 477 nm was satisfactory compared with the appropriate theoretical simulation, assuming free-bound excitation of the 2${\mathrm{}}^2$Π state at 438.5 nm. © 1996 The American Physical Society.

Perturbation theory via the Riccati equation is applied to the analytical solution of the isotropic oscillator in a spherical three-space {1/${\mathit{R}}^2$(${\mathit{d}}^2$/d${\mathrm{\chi }}^2$+2 cotχd/dχ)-l(l+1) /${\mathit{R}}^2$${\sin }^2$χ-${\mathrm{\omega }}^2$${\mathit{R}}^2$${\tan }^2$χ+V(χ) /${\mathit{R}}^2$+2${\mathit{E}}_{\mathit{n}}$}Φ(χ)=0,where 1/R is the curvature of the space, ω is the vibrational constant, and V(χ) is a perturbation. This perturbation procedure, well adapted to the use of computer algebra, relies on the solution of the Riccati equation associated with the given equation and on the choice of suitable χ-basis functions for expanding the perturbation V(χ). Provided a Sturm-Liouville equation can be viewed as a Infeld-Hull factorizable equation with an additional perturbation, an analytical determination of the perturbed eigenvalues and eigenfunctions can be carried out, up to a rather high order of the perturbation, by means of simple algebraic manipulations. When expanding V(χ) in a series of (tanχ${)}^{\mathit{s}}$ terms, the curved-space isotropic oscillator is relevant to the procedure and closed-form expressions of the perturbed energies and functions can be obtained. Space-curvature contributions to the isotropic oscillator energies are put in evidence from the comparison of their curved-space expression with their flat-space limit. Further applications of the results are pointed out. © 1996 The American Physical Society.

We investigate the polarization anisotropy of resonant x-ray emission using one-step, two-step, and classical formulations. It is shown, analytically and numerically, that these models in general give different polarization anisotropies. We compare also the results of the one- and two-step models for the integrated unpolarized cross sections over the same set of test molecules. These include two of the chlorofluoromethanes used originally to experimentally verify the polarization anisotropy in resonant x-ray emission. The test molecules also represent species with core-level chemical shifts and species with symmetry-adapted and quasidegenerate core levels. It is shown that only in the case of energy-isolated and localized symmetry-non-adapted core levels do the two-step model and the — in that case identical—classical model apply, while in all other cases, the one-step model is required either for the polarization anisotropy or for the total cross section, or for both these quantities. © 1996 The American Physical Society.

We have made careful measurements of Stark resonances in ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ Rydberg states above and below the classical saddle point to test various theories and to obtain a precise calibration of the electric field. Rydberg states were populated by two-step diode laser excitation to the 3${\mathrm{}}^2$S state followed by He-Ne or diode laser excitation to Stark sublevels near the n=15 manifold energy. Calibration was performed by comparing measured resonance positions with theoretical results. For zero-field energies, the theoretical calculations were made using quantum defect parameters obtained by fitting available spectral data on Li, and from recent polarization model results of Drachman and Bhatia [Phys. Rev. A 51, 2926 (1995)]. Three theoretical methods were used: (1) matrix diagonalization over a basis of spherical coordinate states, for which the precision declines as one approaches the saddle point; (2) frame transformation theory, which makes very economical use of computer resources but is not reliable beyond a precision of about 500 ppm in an electric field; (3) a recently developed R-matrix method. The last of these was most accurate and, like the second, could be used both below and above the saddle point. From the measured resonance positions and an optimum set of Li quantum defect parameters, the R-matrix calculations provided a calibration of the electric field to about ± 2 ppm ±4 mV/cm. We briefly discuss certain refinements and shortcomings of the other two theoretical methods, and the special procedures used to obtain high accuracy with the R-matrix method. © 1996 The American Physical Society.