I analyze the conditions for the correctness of the formula proposed by Lavoine and Villaeys [Phys. Rev. Lett. 67, 2780 (1991)] for learning about the non-Markovian effects by degenerate four-wave-mixing processes. I show that this dependence does not provide information about non-Markovian relaxation dynamics for the case of the inhomogeneously broadened transition. Such information can be obtained by the modification of a three-pulse four-wave-mixing experiment.

Using Lie-group and prolongation techniques, Baumann and Nonnenmacher [Phys. Rev. A 46, 2682 (1992)] recently studied integrability of a Hamiltonian describing the dynamics of ion traps. It is pointed out that their results can be obtained more simply and directly by recognizing that the problem is separable in each of the integrable limits found by Baumann and Nonnenmacher. Similarities between this system and a hydrogen atom in a generalized van der Waals potential are also considered.

In a recent publication Baumann and Nonnenmacher [Phys. Rev. A 46, 2682 (1992)] analyze the equations of motion of two ions in a Paul trap in the pseudopotential approximation. Chaos and nonzero Liapunov exponents are found for trap asymmetry parameter λ=1/2 and angular-momentum parameter ν≠0. It is pointed out that besides the total energy E, a constant of the motion, G=[${\nu }^2$/ρ+ρζ̇ ${}_{}{}^2{}_{}{}^{}\mathrm{̇}$+ρ/(${\mathrm{\rho }}^2$+${\mathrm{\zeta }}^2$${)}^{1/2}$-${\mathrm{\zeta }}^2$ρ/4${]}^2$ +${\nu }^2$(ρρ̇ +ζζ̇${)}^2$/${\mathrm{\rho }}^2$+${\nu }^2$(${\mathrm{\rho }}^2$+${\mathrm{\zeta }}^2$), exists for λ=1/2 and arbitrary ν. Therefore, and contrary to the claims by Baumann and Nonnenmacher, chaos cannot exist for λ=1/2, and the Liapunov exponents are expected to be zero.

We believe that the criticism in the preceding Comments of Blümel [Phys. Rev. A 48, 854 (1993)] and Farrelly and Howard [Phys. Rev. A 48, 851 (1993)] reflect a misunderstanding of the basis of our claims. Here, we clarify the crucial points of our paper [Phys. Rev. A 46, 2682 (1992)] in order to dispel any ambiguity and misunderstanding.

Electronic continuum angular and radial wave functions are represented in a compact form by expansions over spherical harmonics and the Legendre functions of the first kind, respectively, with separated exponents. Particularly for the continuum radial case, the phase shift is expressed through the characteristic exponent by a formula that generalizes previous asymptotic analytic expressions for small and large intercenter distances.

We extend the quantum key distribution method of Bennett and Brassard [IBM Tech. Discl. Bull. 28, 3153 (1985)] by exploiting a nonconjugate coding scheme. Using this scheme we are able to show that the original method of Bennett and Brassard gives optimal security.

In this paper the second-order nuclear structure correction to the energy of hydrogenlike systems is estimated and previous results are corrected. Both deuterium and hydrogen are considered. In the case of deuterium the correction is proportional to the nuclear polarizability and amounts to about -19 kHz for the 1S state. For hydrogen the resulting energy shift is about -60 Hz.

It is shown that the 1S level hyperfine populations prior to muon capture will be statistical when either target or beam is unpolarized independent of the atomic level at which the hyperfine interaction becomes appreciable. This assertion holds in the absence of magnetic transitions during the cascade and is true because of minimal polarization after atomic capture and selective feeding during the cascade.

Quantum-electrodynamic corrections of O(${\mathit{mc}}^2$${\mathrm{\alpha }}^6$lnα) to the electron-electron interaction in helium are evaluated for several states. The additional energy shift, which is an order of α smaller than the leading Araki-Sucher terms, raises the predicted energy of the 1s2s ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ state by 2.49 MHz to -960 332 039.43(18) MHz relative to ${\mathrm{He}}^{+}$(1s). The new value significantly alters the comparison with recent high-precision experiments.

Using laser double-resonance spectroscopy, we have studied the second dissociation limit of all three stable isotopic variants of molecular hydrogen. Just above threshold, the vibrational continuum exhibits considerable fine-grained structure, differing greatly between isotopes because of varying nonadiabatic couplings between the B, B’, and C states. Significantly improved values of the dissociation energies are obtained from the continuum onsets. We also report preliminary investigations of atomic 2S:2P branching ratios very near threshold.

We report a theoretical calculation for electron-impact ionization of atoms that includes short-range electron-atom effects for wave functions that satisfy the exact asymptotic boundary conditions. Results of this theory, which we label as the three-body distorted-wave Born approximation, are compared with experiment and other theories for ionization of hydrogen and helium for incident-electron energies from 4 to 18 times the ionization energy.

We predict a previously unidentified phenomenon, the drift of a gas mixture arising from the difference in masses of resonant and buffer molecules scattered by a cell-wall surface at velocity-selective excitation. The transverse profile of the mixture flux and pressure drop along the cell with closed ends are calculated. Recent experimental results [R. W. M. Hoogeveen, R. J. van der Oord, and L. J. F. Hermans, in 2 Proceedings of the 15th International Symposium on Rarefied Gas Dynamics, Grado, Italy (Teubner, Stuttgart, 1986), Vol. 1, p. 321] are discussed in connection with the phenomenon.

We discuss semiclassical polarization gradient cooling of a trapped ion with the transition scheme ${\mathit{j}}_1$=1/2→${\mathit{j}}_2$=3/2 in the limits of small vibration amplitude and low light intensity. The minimum excitation energy of the ion reached by laser cooling is about one vibrational quantum above the zero-point energy.

The propagation of limited-bandwidth signals, such as Gaussian wave packets, tuned to a transparent spectral region far below the resonance of an inverted two-level atomic medium, can be superluminal, i.e., with phase, group, and energy velocities all exceeding the vacuum speed of light c. Causality is not violated, however. Little distortion and gain can accompany this propagation.

An experimental observation of field-induced resonances in four-wave mixing is reported. In experiments on Na vapor near the D lines, when the input fields are strong, new resonances appear, confirming recent theoretical predictions based on a nonperturbative approach to wave-mixing processes. The analogy to and differences from the pressure-induced extra resonances are discussed.

A possible way of constructing x-ray lasers of photon energy in the keV range is suggested. An arrangement in which x-ray lasing of photon energies 7.18 and 11.7 keV is expected is also given.

The lifetime of atomic hydrogen exposed to an intense ‘‘high-frequency’’ linearly polarized laser field has been calculated, in a Sturmian-Floquet approach, for the case where the atom is initially in an excited state with m=3, 4, 5, or 6, l=m, m+1, or m+2, and n≤8, for several wavelengths between 455 and 1064 nm. In this range of parameters, the intensity at which the lifetime of the atom reaches a minimum value is given in good approximation by a simple ‘‘empirical’’ law. The lifetime is longer than that predicted by previous approximate Floquet calculations, and its minimum occurs at a smaller intensity. Results for higher-lying Rydberg states are also presented.