We show that nonlocality of quantum mechanics cannot lead to superluminal transmission of information, even if most general local operations are allowed, as long as they are linear and trace preserving. In particular, any quantum-mechanical approximate cloning transformation does not allow signaling. On the other hand, the no-signaling constraint on its own is not sufficient to prevent a transformation from surpassing the known cloning bounds. We illustrate these concepts on the basis of some examples.

Large-scale multiconfiguration Dirac-Hartree-Fock calculations of intercombination transition rates are sensitive to many factors. Earlier calculations for the ${3s}^2{}^1{S}_0–3s3p{}^3{P}_1$ transition optimized simultaneously on the ${}^3{P}_{0,1,2}$ levels using statistical weights of $2J+1.$ In this paper, different optimization strategies are investigated for Mg-like ${\mathrm{Al}}^{+},$ as well as a correction to the transition rate from the nonrelativistic limit. After correcting the transition rates for the transition energy, singlet-triplet separation, and the nonrelativistic limit, the deviation of the different intercombination rates reduces to $0.7\%.$ The best strategy was also applied to ${\mathrm{Si}}^{2+},\hspace{0.5em}{\mathrm{P}}^{3+},$ and ${\mathrm{S}}^{4+}.$ Compared with the available experiment, the intercombination rate of ${\mathrm{Si}}^{2+}$ is in excellent agreement with observation and the rate for ${\mathrm{Al}}^{+}$ is underestimated by $7\%.$ The latter may be attributed to the core-core correlation.

Single ionization of the HD molecule by fast ion impact is used to populate the vibrational continuum of the ${\mathrm{HD}}^{+}$ electronic ground state $\left(1s\sigma \right).\mathrm{}$ The resulting dissociation leads to two final states, the lower $1s\sigma$ state or the first excited $2p\sigma$ state, which is 3.7 meV higher at the separated atom limit due to the finite nuclear mass correction to the Born-Oppenheimer approximation. We find dissociation to the lower ${\mathrm{H}}^{+}+\mathrm{D}\mathrm{}\left(1s\right)\mathrm{}$ state to be about 7% more likely than to the upper $\mathrm{H}\mathrm{}\left(1s\right)+{\mathrm{D}}^{+}$ final state. The major experimental difficulty in this measurement is the determination of the ${\mathrm{H}}_2$ contamination in the HD target. Two different methods of determining this contamination are presented, and the details of the measurement of the relative yields of the final two ground-state dissociation channels are discussed. The experimental results are compared to our coupled channels calculation and to a model based on Meyerhof’s approximate formulation.

Energy loss and straggling has been measured for hydrogen and deuterium ions in thin solid aluminum foils in the low-energy range $E<\mathrm{}10\mathrm{}\mathrm{keV}$ and in the forward direction, both as a function of the energy, and at fixed energies as a function of the observation angle. Whereas no isotopic effect in the energy loss at the forward direction was observed, significant differences appeared when observing at nonzero angles. Monte Carlo simulations and model calculations of the energy loss as a function of the observation angle using a frictional-type energy loss, taking into account the path-length enlargement, the elastic energy loss, and the foil roughness, led to an understanding of the main physical features at these energies. The observed isotopic effect at nonzero angles can be fully accounted for by differences in the foil roughness influence and in the elastic energy loss.

Electron collisions with neutral sodium clusters in the 0–3 eV energy range have been studied in a crossed-beam geometry, and direct evidence for the formation of ${\mathrm{Na}}_n^{-}$ anions has been obtained. The dependence of ion formation efficiency on the electron energy is well represented by the Langevin cross section, suggesting that the electrons are captured by the polarization field of the cluster. This is consistent with the highly polarizable nature of alkali-metal clusters.

We test the accuracy of the semiclassical approximation for a completely chaotic system, the strongly magnetized hydrogen atom. We study a quantity of direct experimental interest, the photoabsorption cross section. The standard semiclassical approximation using periodic orbits is used (without any additional trick to improve convergence) and is shown to agree very well with a fully resolved ab initio quantum “exact” calculation. We also study the families of periodic orbits giving the dominant contributions to the spectrum.

We describe a decomposition of the resolvent $G\left(E\right)=1/\left(E-H\right)$ into two parts, $G_{\mathrm{int}}\mathrm{}\left(E\right)\mathrm{}$ and $G_{\mathrm{ext}}\mathrm{}\left(E\right),$ each of which can be computed, potentially, with moderate cost. Using an integral representation, $G_{\mathrm{int}}\mathrm{}\left(E\right)\mathrm{}$ is built from a Hermitian Hamiltonian matrix constructed on a real discrete basis, and it incorporates the interaction in the interior region where the dynamics take place. The term $G_{\mathrm{ext}}\mathrm{}\left(E\right)\mathrm{}$ takes into account the flux passing into the exterior region, and it can be replaced by a Padé approximant by means of a simple connection between $G_{\mathrm{int}}\mathrm{}\left(E\right)\mathrm{}$ and $G_{\mathrm{ext}}\mathrm{}\left(E\right).$ We illustrate the method by application to the examples of photoionization of a hydrogen atom and scattering of a particle from a ${1/(1+r)\mathrm{}}^4$ potential.

I present a derivation of the many qualitative changes to basic scattering theory that result when a (partially) coherent matter beam inelastically interacts with a quantum target. The weak beam limit, where only one object in the beam interacts with the quantum target, is developed. Some of the basic changes to scattering theory are as follows. (1) The transition probability can increase as the square of the number of particles in the beam. (2) The transition probability is not proportional to the convolution of the total inelastic cross section with the momentum distribution of the beam. (3) The transition probability to different final states of the target does not depend on the population in the initial states but depends on the amplitudes for the initial states. (4) The total transition probability depends on the differential cross section integrated over all final angles and on the differential cross section only in the forward scattering direction. (5) The transition probability can be nonzero even when the beam misses the target. (6) In the perturbative limit, the transition probability can be related to classical, large scale properties of the beam (such as the average density).

We present a physical picture explaining the asymmetries between absorption and stimulated emission occurring in the driven three-level systems. Based on a dressed-state picture, we obtain transition rates for absorption and stimulated emission separately, and show that the cancellation of absorption in the $\Lambda$- and V-type systems are originated from different physical mechanisms. Furthermore, a simple analogy can be applied to cascade-type systems to show the absorption enhancement at two-photon resonance.

We use Thomson’s classical concept of mode of a leaky cavity to develop a quantum theory of cavity damping. This theory generalizes the conventional system-reservoir theory of high-$Q$ cavity damping to arbitrary Q. The small system now consists of damped oscillators corresponding to the natural modes of the leaky cavity rather than undamped oscillators associated with the normal modes of a fictitious perfect cavity. The formalism unifies semiclassical Fox-Li modes and the normal modes traditionally used for quantization. It also lays the foundations for a full quantum description of excess noise. The connection with Siegman’s semiclassical work is straightforward. In a wider context, this theory constitutes a radical departure from present models of dissipation in quantum mechanics: unlike conventional models, system and reservoir operators no longer commute with each other. This noncommutability is an unavoidable consequence of having to use natural cavity modes rather than normal modes of a fictitious perfect cavity.

It is shown that a neutral particle with an electric dipole moment acquires a quantum phase of Aharonov-Bohm type which is induced by a magnetic dipole field, in addition to the He-McKellar-Wilkens phase which requires a magnetic monopole field. Therefore this phase is measurable in principle. This phase is related to the Casella phase in the sense of the electromagnetic duality.

Using a phase-locked laser pair we have observed dark resonances with linewidths below 30 Hz in a rubidium cell filled with neon as buffer gas. A model allowing for pressure broadening correctly reproduces the dependence of the width on the laser intensity. Consideration of velocity changing collisions reveals the absence of Doppler effects in the position and width of the dark resonance at high buffer-gas pressure.

The standard Born-Oppenheimer theory does not give an accurate description of the wave function near points of level crossing. We give such a description near an isotropic conic crossing, for energies close to the crossing energy. This leads to the study of two coupled second-order ordinary differential equations whose solution is described in terms of the generalized hypergeometric functions of the kind ${}_0{F}_3\mathrm{}(;a,b,c;z).$ We find that, at low angular momenta, the mixing due to crossing is surprisingly large, scaling like ${\mu }^{1/6},$ where μ is the electron to nuclear mass ratio.

Absolute generalized oscillator strengths (GOS’s) of the ${3p}^6\to {3p}^5{(4s,4s}^{\prime }),$ ${3p}^6\to {3p}^5{(4p,4p}^{\prime }),$ and ${3p}^6\to {3p}^5{(5s,5s}^{\prime }{,3d,3d}^{\prime })$ valence-shell electronic transitions as well as the ${2p}_{3/2}\to 4s$ inner-shell transition in Ar have been determined as functions of energy loss and momentum transfer (K) at an impact energy of 2.5 keV. Generally good agreement can be found between the present GOS measurement for the ${3p}^6\to {3p}^5{(4s,4s}^{\prime })$ transitions (at 11.8 eV) and the previous experimental profiles for $K<\mathrm{}1\mathrm{}\mathrm{a}.\mathrm{u}.\mathrm{}$ Calculations based on the first Born approximation appear to be in reasonable agreement with the GOS data only in shape and also for $K<\mathrm{}1\mathrm{}\mathrm{a}.\mathrm{u}.\mathrm{},$ while the Yukawa frozen-core calculations based on the Glauber approximation appear to converge to the present data even for $K>\mathrm{}1\mathrm{}\mathrm{a}.\mathrm{u}.\mathrm{}$ The experimental and theoretical results all give consistent values for the K positions of the observed minimum and maximum in the GOS profile of the ${3p}^6\to {3p}^5{(4s,4s}^{\prime })$ transitions. The GOS profile for the ${3p}^6\to {3p}^5{(4p,4p}^{\prime })$ transitions (at 13.4 eV) in Ar has been determined and found to have a shape characteristic of nondipole excitation with a maximum at $K^2\sim 0.7\mathrm{a}.\mathrm{u}.\mathrm{}$ Like the ${3p}^6\to {3p}^5{(4s,4s}^{\prime })$ transitions, the GOS profile for the ${3p}^6\to {3p}^5{(5s,5s}^{\prime }{,3d,3d}^{\prime })$ transitions (at 14.2 eV) has the characteristic dipole-dominated shape with a strong maximum at $K=0\mathrm{}$ but a notably larger width and without any discernible extrema. Finally, the GOS profile for the ${2p}_{3/2}\to 4s$ inner-shell transition (at 244.4 eV) is dominated by a strong maximum at $K=0,$ characteristic of generally dipole-allowed excitations, but with a broad and rather complex shape. The present work illustrates the analytical value of GOS profiles for probing the intricate nature of the valence- and inner-shell electronic excitations.

A general and computationally efficient method for averaging both the time-dependent and the steady-state atomic or molecular state populations over the phases, ${\delta }_1$ and ${\delta }_2,$ of two continuous-wave laser fields involved in an excitation process is developed based on the Floquet formalism. Explicit calculations are presented for the coherent one- and three-photon electronic excitation of a two-level model molecule in order to illustrate the importance of phase averaging in situations where the relative phase difference between the two fields is fixed. While the explicit results involve electronic excitation, they are presented in reduced form so that they can be scaled to other regions of the electromagnetic spectrum and to other field strengths. The results have important implications in situations where the relative phase difference between two intense continuous-wave laser fields is used to control the excitation process.

One-particle properties of noninteracting fermions in a one-dimensional harmonic trap and at zero temperature are studied. Exact expressions and asymptotic results for a large fermion number N are given for the particle density distribution $n_0\mathrm{}(z,N).$ For large N and near the classical boundary at the Fermi energy, the density displays increasing fluctuations. A simple scaling of these tails of the density distribution with respect to N is established. The Fourier transform of the density distribution is calculated exactly. It displays a small but characteristic hump near ${2k}_F,$ with $k_F$ being a properly defined Fermi wave number. This is due to Friedel oscillations, which are identified and discussed. These quantum effects are missing in the semiclassical approximation. Momentum distributions are also evaluated and discussed. As an example of a time-dependent one-particle problem, we calculate exactly the evolution of the particle density when the trap is suddenly switched off, and find a simple scaling behavior, in agreement with recent general results.

We develop a systematical method by which the investigation of the general structure of Bose-Einstein condensates with arbitrary spin has been reduced to solving a one-order linear partial-differential equation of a very simple form. Its general solutions for arbitrary spin are studied and a procedure is also developed to seek systematically the building blocks for constructing the general structure of Bose-Einstein condensates with arbitrary spin.

We have performed an experimental study of the nonlinear dynamics in a Kerr-lens mode-locked Ti:sapphire laser producing $\approx 25\hspace{0.5em}\mathrm{fs}$ pulses. Grassberger-Procaccia and false nearest-neighbor analyses indicate that the pulse trains follow a quasiperiodic route to low-dimensional chaos. The experimental results agree quite well with a simulation based on the Gaussian four-by-four matrix formalism. Pulse-resolved measurements show that the instability in pulse energy is associated with instabilities in the pulse spectral and spatial profile.

A comparison is made of the accuracy with which the electric moments μ, Θ, Ω, and Φ can be calculated by using the finite basis set approach (the algebraic approximation) and finite-difference method in calculations employing the Hartree-Fock model for the ground states of 16 diatomic molecules at their experimental equilibrium geometries. Specifically, the $2^n$-pole moments $n=1,2,3,4,$ for the ${\mathrm{N}}_2,$ CO, BF, ${\mathrm{CN}}^{\mathrm{-}},$ ${\mathrm{NO}}^{+},$ BeF, BO, CN, ${\mathrm{N}}_2^{+},$ AlF, GaF, InF, TlF, MgF, CaF, and SrF molecules are determined using basis sets and grids that have been employed in previous studies of the Hartree-Fock energy.