We have theoretically investigated the effects of self-phase-modulation on multiphoton nonlinear optical processes in semiconductors, utilizing multiple-order perturbation theory based on a set of coupled nonlinear-wave equations. Our results clearly demonstrate that the self-phase-modulation in the fundamental field induces spectral broadening in the harmonic fields (cross-phase modulation) and alleviates phase mismatch by providing a distribution of wave vectors. These results are consistent with our recent observation of extreme nonlinear optical behavior in bulk semiconductors under intense mid-infrared radiation.

High-order harmonic generation by metallic carbon nanotubes exposed to an intense ultrashort pulse has been theoretically investigated in the semiclassical approximation. The mechanism of nonlinearity provided by the motion of π electrons has been considered. It has been shown that the high density of conduction electrons in metallic carbon nanotubes and the specific dispersion law inherent in hexagonal crystalline structure result in the efficient generation of high-order harmonics with intensities that fall down smoothly with harmonic number, without cutoff, and with efficiency much larger than in gases with the same pump intensity. We have also studied phase matching for different harmonics in a rope of parallel-aligned carbon nanotubes dependent on the angle of incidence.

A formalism that utilizes the analytic transfer matrix technique is applied to the Schrödinger equation. This approach leads to proofs that the phase loss at a turning point is exactly equal to π. We also show the existence of the phase contributions devoted by the scattered subwaves, which to our knowledge, have never been taken into account in previous works. Subsequently, an exact quantization condition, which differs essentially from the WKB method, is introduced for arbitrary potential wells.

We present a method for the determination of the completely positive (CP) map describing a physical device based on random preparation of the input states, random measurements at the output, and the maximum-likelihood principle. In the numerical implementation the constraint of completely positivity can be imposed by exploiting the isomorphism between linear transformations from Hilbert spaces $\mathcal{H}$ to $\mathcal{K}$ and linear operators in $\mathcal{K}\otimes \mathcal{H}.$ The effectiveness of the method is shown on the basis of some examples of reconstruction of CP maps related to quantum communication channels for qubits.

Recently measured radiative lifetimes of the Rydberg series $6pnd\frac{1}{2}[\frac{5}{2}{]}_2^o$ and $\frac{1}{2}[\frac{3}{2}{]}_2^o$ $(n=6\mathrm{}–13)$ of Pb I [Li et al., Phys. Rev. A 57, 3443 (1998)] have been compared with theoretical values obtained by means of multichannel quantum defect theory (MQDT) analyses. The MQDT parameters were obtained from experimentally determined energy levels. The channel admixture coefficients were calculated and used to evaluate the theoretical lifetimes. In addition, lifetime values for highly excited Rydberg states have been predicted.

Considering Bohr’s correspondence principle and energy conservation laws, we derive by means of some elementary classical considerations of electron motion in a laser field an expression for the width of the laser-stimulated x-ray spectrum in electron-ion recombination and we find a classical expression for the power distribution of x-ray radiation, both of which agree surprisingly well with the results of the corresponding quantum-mechanical calculations presented earlier.

A recent paper by Irby [Phys. Rev. A 60, 1135 (1999)] analyzes the effect of using calculated, rather than measured, values of the electron time-of-flight in soft electron imaging. This paper creates the impression that the analysis used by Abdallah et al. [Phys. Rev. A 56, 2000 (1997)] might be suspect and that the saddle-point shifts observed in that paper might be in error. In fact, the analysis used by Abdallah et al. is almost exact, as is shown in this comment, and the conclusions reached in that paper were correct.

As pointed out in the preceding Comment, computer simulations presented by Irby [Phys. Rev. A 60, 1135 (1999)] analyzed the effect of using constant rather than kinematically dependent values of the electron time of flight in assessment of ejected-electron momentum from recorded micro channel plate detector-impact positions. The article raised questions of possible error in the analysis used recently by Abdallah et al. [Phys. Rev. A 56, 2000 (1997)]. In this reply, we present the results of more sophisticated Monte Carlo computer simulations, which show that the error due to the assumptions used in the analysis by Abdallah et al. are indeed quite miniscule. However, and equally as important, our simulations also confirm experimental projectile-charge dependent shifts reported earlier by Irby et al. [Phys. Rev. A 37, 3612 (1988)] and Gay et al. [J. Phys. B 23, L823 (1990)] in which conclusions opposite that of Abdallah et al. were reached. While still confirming the earlier experimental results, the simulations, on the other hand, support the conclusions of Abdallah et al. and not the conclusions of Irby et al. and Gay et al.

We discuss how generalized measurements may be performed on various atomic systems including cold ions and Rydberg atoms. The suggested methods rely on the fact that any generalized measurement can be identified with a unitary transformation followed by a projective measurement in a higher-dimensional Hilbert space. If the information to be measured is stored in the form of atomic qubits this unitary transformation can be accomplished by redistributing the population of the relevant atomic levels.

The variational time-independent density-functional theory for an individual excited state introduced recently [M. Levy and Á. Nagy, Phys. Rev. Lett. 83, 4361 (1999)] is extended to degenerate states.

The measurement of the dielectronic recombination (DR) cross section of ${\mathrm{C}}^{4+}$ with a high resolution [S. Mannervik et al., Phys. Rev. A 55, 1810 (1997)] provides a rigorous test case for various theoretical methods. In the earlier work, the relativistic multichannel theory was applied to the DR process on the ${\mathrm{He}}^{+}$ ion for both the $\Delta N=1\mathrm{}$ and $\Delta N=2\mathrm{}$ transitions with a principal quantum number of the outermost electron up to 5. In principle, that method can be applied to resonances with any high principal quantum numbers. Practically, however, the calculations become very time consuming. In the present work, the method is extended by incorporating the Bell-Seaton theory. The DR cross sections of ${\mathrm{C}}^{4+}$ for the resonances with $2<~n<~25$ are calculated. The results are in good agreement with those of the experiment except for the $n=6\mathrm{}$ and $7$ resonances. According to the present calculation, the Rydberg cutoff due to field ionization could be about $n_{\max }=25\mathrm{}$ instead of $n_{\max }=16\mathrm{}$ to take into account the effect of the radiative decay during the time of flight. A sudden decrease is observed between the $n=7\mathrm{}$ and $8$ resonances due to the opening of the $1s2s{}^{1}S\epsilon l$ continuum. From the agreement with experiment, it would appear that the present method is applicable to both the low-$n$ and high-$n$ resonances.

van der Waals coefficients for the heteronuclear alkali-metal dimers of Li, Na, K, Rb, Cs, and Fr are calculated using relativistic ab initio methods augmented by high-precision experimental data. We argue that the uncertainties in the coefficients are unlikely to exceed about 1%.

We present the zero-temperature phase diagram of bosonic atoms in an optical lattice, using two different mean-field approaches. The phase diagram consists of various insulating phases and a superfluid phase. We explore the nature of the insulating phase by calculating both the quasiparticle and quasihole dispersion relation. We also determine the parameters of our single band Bose-Hubbard model in terms of the microscopic parameters of the atoms in the optical lattice.

We derive optimal N-photon two-mode input states for interferometric phase measurements. Under canonical measurements the phase variance scales as $N^{-2}$ for these states, as compared to $N^{-1}$ or $N^{-1/2}$ for states considered by previous authors. We prove that it is not possible to realize the canonical measurement by counting photons in the outputs of the interferometer, even if an adjustable auxiliary phase shift is allowed in the interferometer. However, we introduce a feedback algorithm based on Bayesian inference to control this auxiliary phase shift. This makes the measurement close to a canonical one, with a phase variance scaling slightly above $N^{-2}.$ With no feedback, the best result (given that the phase to be measured is completely unknown) is a scaling of $N^{-1}.$ For optimal input states having up to four photons, our feedback scheme is the best possible one, but for higher photon numbers more complicated schemes perform marginally better.

We investigate theoretically and experimentally the operation of a nonlinear system, feedback controlled photorefractive beam coupling. It is shown that the feedback equations used earlier $(\pm \pi /2\mathrm{}$ phase shift between the diffracted and transmitted beam components) are satisfactory only during a relatively short initial stage of development. We have generalized these equations by taking into account the inertia inherent in any real feedback loop. The inertial feedback equations ensure the permanent operation of the nonlinear system and lead to a variety of periodic and quasiperiodic regimes. We investigate the distinctive features of these regimes and transitions between them for moderately thick crystals. Good qualitative agreement between theory and experimental data is obtained for ${\mathrm{LiNbO}}_3$ crystals.

Anomalous dispersion cannot occur in a transparent passive medium where electromagnetic radiation is being absorbed at all frequencies, as pointed out by Landau and Lifshitz. Here we show, both theoretically and experimentally, that transparent linear anomalous dispersion can occur when a gain doublet is present. Therefore, a superluminal light-pulse propagation can be observed even at a negative 7group velocity through a transparent medium with almost no pulse distortion. Consequently, a negative transit time is experimentally observed resulting in the peak of the incident light pulse to exit the medium even before entering it. This counterintuitive effect is a direct result of the rephasing process owing to the wave nature of light and is not at odds with either causality or Einstein’s theory of special relativity.

The normalized state $|\psi \mathrm{}\left(t\right)\mathrm{}〉{=c}_1\mathrm{}\left(t\right)\mathrm{}|1〉{+c}_2\mathrm{}\left(t\right)\mathrm{}|2〉$ of a single two-level system performs oscillations under the influence of a resonant driving field. It is assumed that only one realization of this process is available. We show that it is possible to approximately visualize in real time the evolution of the system as far as it is given by $|c_2\mathrm{}\left(t\right)\mathrm{}{|}^2.$ For this purpose we use a sequence of particular unsharp measurements separated in time. They are specified within the theory of generalized measurements in which observables are represented by positive operator-valued measures. A realization of the unsharp measurements may be obtained by coupling the two-level system to a meter and performing the usual projection measurements on the meter only.

We believe that a useful kinetic-energy functional should not only incorporate known limiting forms but also have accurate functional derivatives, so that it can be used for obtaining the correct ground-state density via variational calculations. Furthermore, an accurate functional for the kinetic energy should be obtained by fitting to smooth pseudoelectron systems rather than to all-electron calculations as is often done. In this paper, by working on simple model atoms and group-IV pseudoatoms, we demonstrate that an accurate kinetic-energy functional with a correct functional derivative, and meeting most limiting forms, cannot be obtained from a simple expression containing only the density and its gradient. At least the Laplacian of the density should also be included in a useful generalized gradient approximation to the kinetic-energy functional.

We present experimental data on the decay of xenon Stark states converging to the upper spin limit. In an electric field the Rydberg electron has two qualitatively different decay paths. If the electron changes the core state from the upper spin state into the lower spin state, it gains sufficient energy to escape the ionic core and autoionizes. Moreover, if the electronic state is above the saddle point, created by the electric field, it can field ionize. The probability to autoionize is nearly constant around the saddle point whereas the probability to field ionize rapidly increases above the saddle point. With the velocity map imaging technique we monitor both ionization channels as a function of (increasing) photoexcitation energy. We observe that the field ionization channel dominates the competition and gains yield at the expense of the autoionization channel. The spectra are explained both with full quantum calculations and with a relatively simple description for the overall behavior. These experiments show that the field ionization can be used in general as a clock for total core-dependent decay.

We study the interference of biphotons generated via spontaneous parametric down-conversion from a pump with several longitudinal modes. It is shown that biphotons can interfere if the time difference between their birth moments is a multiple, to an accuracy of the pump coherence time, of $T\equiv 2L/c,$ where L is the pump cavity length. This effect, although observed with a cw pump, is similar to a recently reported interference of biphotons generated from time-separated pump pulses.