An alternative method for the description of quantum superintegrable systems in two dimensions through the use of quantum algebraic techniques is introduced. It is suggested that such systems can be described in terms of a generalized deformed oscillator, characterized by a structure function specific to the system. The energy eigenvalues corresponding to a state with finite-dimensional degeneracy can then be determined directly from the properties of the relevant structure function. The validity of the method is demonstrated in the case of the isotropic harmonic oscillator in a space with constant curvature. The method can be used for constructing the quantum versions of several classical superintegrable systems, the Holt potential being given as an example.

The process of the electron transfer in collisions of highly excited Rydberg atoms with ground-state atoms is treated in the impulse approximation using the three-body Faddeev-equations approach. The cross section for the electron transfer in ${\mathrm{Ca}}^{\mathrm{*}}$(4snl)-Ca(4${\mathit{s}}^2$) collisions is calculated as a function of the electron affinity of Ca. It is shown that the cross section is extremely sensitive to the electron affinity and thereby a recent experimental observation of this reaction by McLaughlin and Duquette provides a very accurate value of the electron affinity of Ca.

We investigate the energy and angular distribution of electrons emitted in fast collisions with neutral atoms from Rydberg states of the projectile into low-lying continuum states of the projectile. We find highly anisotropic, approximately ellipsoidal angular distributions for large principal quantum numbers (n≃10). The corresponding spherical multipole expansion contains contributions from high-order multipoles ${\mathrm{\beta }}_{\mathit{k}}$ at least up to k≃8 and large values of low-order multipoles ${\mathrm{\beta }}_2$ well beyond the limit for dipole-allowed transitions. Comparison with recent data for ion-solid collisions shows surprisingly good agreement.

We present a path-integral solution for the exact propagation of the Wigner distribution in phase space, which is an improved version of results obtained [Maslov, Bertrand, Combe, and co-workers, J. Sov. Math. 13, 315 (1980); 19, 55 (1982); Lett. Math. Phys. 7, 327 (1983); Physica 124A, 561 (1984)] and is suitable for Monte Carlo simulations. The trajectories involved are purely stochastic processes exhibiting discontinuous jumps in momentum. The applicability of the method is demonstrated for scattering at a one-dimensional barrier.

The ${\mathrm{N}}_2$ C-state lifetime is crucial, for instance, in understanding the action of the nitrogen laser. Although it has been extensively studied in a great number of experiments, the results do not converge and they scatter much more than the individually quoted errors. Thus, a recent measurement with a given error of 1% yields a result which is a 24% higher value than the earlier accepted average value. The present experiments suggest that the scattering among the results is due to a unique systematic error originating from a joint action of resonance trapping and collisional transfer. The recommended weighted average value is τ(${\mathrm{N}}_2$,C, v=0)=37.4±1.0 ns.

Temporal integration of density-matrix equations with quantized translational motion gives alternative results for laser cooling of atoms. For polarization gradient cooling, the average kinetic energy in the cold-atom peak after 1000 radiative lifetimes decreases with increasing ${\mathit{F}}_{\mathit{g}}$, and is <1 recoil energy at low laser intensity. With magnetically induced laser cooling (MILC) and low optical pumping rates, atoms cool slowly within the potential wells, giving minima in the velocity distribution at ν=0. MILC is seen as a cyclic process; optical pumping cools and B-field mixing slightly heats.

We interpret recently measured collisional frequency shifts in a cesium atomic fountain using coupled-channel theory and a simple picture of hyperfine-coupled long-range molecular states. We predict the existence of ${\mathrm{Cs}}_2$ singlet and triplet states very close to threshold with an associated strong influence on ultracold collisions and large negative values for the Cs+Cs scattering lengths. Our results are important for future precision experiments using Cs fountains, and may also have important consequences for attempts to realize a Bose condensate in an ultracold atomic Cs vapor.

We have experimentally determined the harmonic-generation cutoff as a function of the laser intensity in neon using an intense, short-pulse Ti:sapphire laser. The experimental cutoff is lower than that obtained in single-atom calculations. Using a simple quantum-mechanical approach to harmonic generation valid at high intensity, we show that the difference is due to the effect of propagation.

We present results of experiments testing the influence of elliptical polarization on the production of high-order harmonics. Experiments were conducted both with a 600-nm, 1-psec dye laser and with an 825-nm, 140-fsec Cr:${\mathrm{LiSAF}}_6$ (Cr:LiSAF) laser system, over a wide range of intensities and target gases (xenon, argon, and neon), using a detection system with a dynamical range of more than three orders of magnitude. The decrease of the harmonic strength with the ellipticity of the pump beam is rather slow for the low-order harmonics, and becomes much steeper for the high-order harmonics. We compare some of these data with the predictions of lowest-order perturbation theory.

We report on the energy distribution of the electrons emitted in two-color photodetachment of ${\mathrm{H}}^{\mathrm{-}}$ in a highly nonlinear regime, and compare these results with the ones found by averaging the cross section obtained in the presence of a static field over the values taken by the low-frequency field in a cycle. Similarities and differences are discussed.

The quantum dynamics of a two-dimensional charged spin-1/2 particle is studied for general, symmetry-free curved surfaces and general, nonuniform magnetic fields that are, when different from zero, orthogonal to the defining two surface. Although higher Landau levels generally lose their degeneracy under such general conditions, the lowest Landau level, the ground state, remains degenerate. Previous discussions of this problem have had less generality and/or used supersymmetry, or else have appealed to very general mathematical theorems from differential geometry. In contrast our discussion relies on simple and standard quantum-mechanical concepts. The mathematical similarity of the physical problem at hand and that of a phase-space path-integral quantization scheme of a general classical system is emphasized. Adopting this analogy in the general case leads to a general quantization procedure that is invariant under general coordinate transformations—completely unlike any of the conventional quantization prescriptions—and therefore generalizes the concept of quantization to hitherto inaccessible situations. In a complementary fashion, the so-obtained picture of general quantization helps to derive useful semiclassical formulas for a Hall current in the case of a filling factor equal to one for a general surface and magnetic field.

In this paper we employ optimal control theory to design an external driving field which reduces the difference between certain quantum observables and their classical counterparts in addition to achieving some dynamical objective. Because many different driving fields can achieve a similar target, there is the flexibility of asking that the field also cause quantum and classical observables to match. Several examples are shown using a one-dimensional model system which is highly nonclassical in the absence of a driving field. These illustrations demonstrate some of the richness of possibilities for obtaining good quantum-classical agreement for chosen observables even in the presence of other design criteria.

The effect of random perturbation is investigated for a Hamiltonian with systematic degeneracies. It turns out that the influence of the degeneracies remains significant under perturbation. The model simulates quantized versions of classically chaotic systems in that the Fourier transform of the level density shows the characteristic lines which would be associated with the periods of periodic orbits if the system had a classical analogy. The decaying magnitude of the recurring lines is related to the spread of the probability distribution under the influence of perturbation of the degenerate levels.

We calculate both the exact retarded and advanced Green’s function for the one-dimensional step and square-barrier potentials in the space-energy representation. Some of the results for the square barrier are also extended to general symmetric potentials of finite range.

The quantum-mechanical motion of Gaussian wave packets on elliptical and hyperbolic orbits is calculated and shown in plots. The approximation scheme makes explicit use of energy and angular-momentum conservation thus guaranteeing controlled accuracy of the approximation over long-time intervals. This allows the study of the revivals, a phenomenon of particular interest in Rydberg atoms on elliptical orbits. A comparison with the behavior of a classical phase-space distribution of the same position and momentum widths is carried out.

The modified Coleman-Hepp model proposed recently by Nakazato and Pascazio [Phys. Rev. Lett. 70, 1 (1993)] is further generalized so that an ultrarelativistic particle interacts with a linear array of N spins, each of generic magnitude s rather than 1/2. We study the evolution of an appropriately defined measure C(t) of quantum coherence, with t being time, and elucidate the roles played by N and s on the process of decoherence. It is shown that N and s appear in the form of the product Ns in C(∞) at zero temperature, but not in general. It is also noted that the effect of temperature shows up only for s≥1. We study the temperature dependence of C(∞) in detail, and point out in particular that it is not necessarily a monotonic function of temperature. The limiting cases of s→∞ and/or N→∞ are also considered to investigate how the present model tends to a boson model, that is, a model in which the spins are replaced by harmonic oscillators.

We establish a formula for the probability of a quantum adiabatic transition between two permanently degenerate energy levels which do not cross. This formula corresponds to the non-Abelian generalization of the Landau-Dykhne formula that is valid for the nondegenerate case. It applies in particular in cases of symmetry-induced degeneracy, a typical example being the Kramer degeneracy.

In this paper I present an evaluation of the two-loop diagrams, including the closed electron loop, which contribute to the Lamb shift in (α/π${)}^2$(Zα${)}^5$/${\mathit{n}}^3$ order. These corrections sum to 2.710 61(1) for S states, which gives a 37.41-kHz shift for the 1S state of the hydrogen atom.

Contributions of one-loop ladder and crossed-ladder graphs to the ground-state energy of heliumlike ions are calculated in Furry representation QED. With the aid of a contour rotation, the graphs are evaluated to all orders in Zα in the range Z=10–110. Particular attention is given to the relation of this work to recent many-body perturbation theory and configuration-interaction calculations.

In this paper we solve for the quantum propagator of a general time-dependent system quadratic in both position and momentum, linearly coupled to an infinite bath of harmonic oscillators. We work in the regime where the quantum optical master equation is valid. We map this master equation to a Schrödinger equation on super-Hilbert space and utilize Lie-algebraic techniques to solve for the dynamics in this space. We then map back to the original Hilbert space to obtain the solution of the quantum dynamics. The Lie-algebraic techniques used are preferable to the standard Wei-Norman methods in that only coupled systems of first-order ordinary differential equations and purely algebraic equations need only be solved. We look at two examples.