The time-dependent Schrödinger equation for atoms in an intense laser field is solved in scaled coordinates. Starting with the time propagation of a free particle, we show that scaling removes the spreading and rapid phase variation of a wave packet. By solving the one-dimensional model atom in an intense laser field, we show that stable numerical results are best calculated in the acceleration gauge using scaled coordinates. The wave function thus calculated has the least oscillations and does not spread at large time so that there is no need to introduce absorbers at the boundaries. We show the method is suitable for calculations at any laser field strength. We also show that the scaling method permits propagation to large times thus revealing above threshold ionization structure directly in the wave function.

From exact non-Born-Oppenheimer simulations of dynamics of ${\mathrm{H}}_2^{+}$ and ${\mathrm{D}}_2^{+}$ in an intense $(I>\mathrm{}{10}^{15}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2)$ ultrashort laser pulse ${(t}_p<5\mathrm{}\mathrm{fs}),$ we show that it is possible to measure the time evolution of the probability distribution $|\psi \mathrm{}(R,t)\mathrm{}{|}^2$ of a dissociating wave packet using laser Coulomb-explosion imaging (LCEI). In our numerical simulation, a pump-probe technique is used: first, a weaker laser $(I<\mathrm{}{10}^{14}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2)$ photodissociates the molecule and next, with experimentally controlled time delay $t_0,$ a second intense $(I>\mathrm{}{10}^{15}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2)$ ultrashort ${(t}_p<5\mathrm{}\mathrm{fs})$ laser pulse is applied. The latter, ionizes “instantaneously” the dissociating molecule. Measurement of the kinetic-energy spectra of exploding nuclear fragments allows us, with the help of an inversion based on Coulomb’s law and classical conservation of energy, to reconstruct the shape of the probability distribution $|\psi \mathrm{}(R,t)\mathrm{}{|}^2$ at time ${t=t}_0.$ By repeating this experiment for many time delays $t_0,$ one can thus obtain detailed information about the time-dependent dynamics of the photoinduced dissociation. The theory of LCEI for moving nuclear wave packets and the limitations of the above classical inversion method are presented.

With two interfering femtosecond pulses it is possible to produce an ultrafast transient refractive-index grating with relatively high contrast in a transparent material. The grating has a significant impact on nonlinear optical effects, it is responsible for a loss of surface sensitivity in second-harmonic generation from centrosymmetric materials, an enhancement of the generated third harmonic due to self-phase matching, and for the diffraction of the generated harmonics. The latter phenomenon is determined by the nonlinear equivalent of the diffraction law. In a nonresonant material, the refractive-index grating is a thin slide with the thickness of the spatial equivalent of the pulse duration, propagating through the crystal with the group velocity. The duration of the grating depends only on the pulse width, in our case 80–100 fs. Besides offering a fundamental point of view, this opens the way to a variety of interesting applications, in particular in telecommunications, such as any kind of beam manipulation, optical switching, or demultiplexing, all of them on a femtosecond time scale.

We analyze the implications of the molecular structure of a target and the angular scattering effects on projectile-target collisions within the Electron-Nuclear Dynamics (END) approach. We show the suitability of the END method for the analysis of molecular scattering processes such as differential cross sections, charge exchange, and energy loss as required for the study of the stopping cross section. As a consequence of these effects, we show that the rovibronic energy loss becomes of greatest importance at low projectile energies. Furthermore, we find that the Bragg additivity rule and the linear-velocity dependence of the stopping cross section are not fulfilled at low projectile energies. Finally, we analyze the differences in the scattering processes for molecular and atomic targets, and show that in a transmission experiment with small exit window, the acceptance angle corresponds to different impact parameter selection for molecular targets than for atomic ones. Thus, the measured stopping cross section becomes a function of the acceptance angle of the experimental setup. We present results for hydrogen beams on ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$ gas targets.

We demonstrate efficient replication of an incoherent fluorescent light with the ${1770-\mathrm{c}\mathrm{m}}^{\mathrm{-}1}$ broad bandwidth into its Raman sidebands with frequency spacing of 4150 ${\mathrm{cm}}^{\mathrm{-}1}$ in a thin hydrogen crystal. We achieve a high conversion efficiency of 22% per sideband using a sufficiently large Raman coherence prepared by two collinearly propagating ns laser fields.

In a two-dimensional world, a free quantum particle of vanishing angular momentum experiences an attractive force. This force originates from a modification of the classical centrifugal force due to the wave nature of the particle. For positive energies the quantum anticentrifugal force manifests itself in a bunching of the nodes of the energy wave functions towards the origin. For negative energies this force is sufficient to create a bound state in a two-dimensional δ-function potential. In a counterintuitive way, the attractive force pushes the particle away from the location of the δ-function potential. As a consequence, the particle is localized in a band-shaped domain around the origin.

Whether or not kinetic energy can be represented in orbital Kohn-Sham equations by an effective local potential has been discussed in several recent publications, reaching conflicting conclusions. It is shown here that this conflict can be resolved by dropping the widespread but unjustified assumption that the existence of a ground-state density functional for the kinetic energy of an N-electron system implies the existence of a density-functional derivative equivalent to a local potential function. For more than two electrons, a density-functional derivative does exist, but has the mathematical character of a linear operator that acts on orbital wave functions.

We report an observation of the strong dependence of the multiple $(6<q<~10)$ ionization cross section on the alignment of the molecular axis in collisions of highly charged Xe ions with ${\mathrm{N}}_2$ molecules at an impact energy of 5.9 MeV/amu. Theoretical calculations based on the statistical-energy-deposition model well describe the experimental data.

We obtain the threshold laws for three-body recombination of particles interacting via short-range potentials, taking into account all combinations of particle symmetry. In particular, we show that the recombination rate is constant at zero energy unless indistinguishable fermions are present. In this case, the rate is suppressed by either a factor of E or $E^2$ for two or three indistinguishable fermions, respectively. In addition, we present the threshold law for collision-induced dissociation.

Explicit expressions for all the transport coefficients have recently been found for a trapped Bose-condensed gas at finite temperatures. These transport coefficients are used to define the characteristic relaxation times, which determine the crossover between the mean-field collisionless and the two-fluid hydrodynamic regime. These relaxation times are evaluated as a function of the position in the trap potential. We show that all the relaxation times are dominated by the collisions between the condensate and the noncondensate atoms, and are much smaller than the standard classical collision time used in most of the current literature. The study [Stamper-Kurn et al., Phys. Rev. Lett. 81, 500 (1998)] of the collective modes at finite temperature is shown to have been well within the two-fluid hydrodynamic regime.

We present an experimental demonstration of extending the high-order harmonic cutoff photon energy more than a factor of 2 when the driving-field wavelength is changed from 0.8 to 1.51 μm with an optical parametric amplifier. With argon gas, the cutoff has been extended from 64 to 160 eV. We predict that coherent keV x rays can be generated by exciting helium gas with the long-wavelength driving pulses. Experiments on xenon gas with several pump wavelengths also showed the dramatic cutoff extension, as well as full tunability of the generated XUV wavelengths.

Ground- and excited-state energies as well as probability densities of quantum-mechanical anharmonic and double-well oscillators are obtained by numerically solving the time-dependent Schrödinger equation (TDSE). The methodology employed is exact in principle and is based on solving the TDSE in imaginary time, coupled with the minimization of energy expectation value. The present method works very well for deep wells and for double-well oscillators with pseudodegenerate energy levels where time-independent methods experience difficulties. The dependence of energy on anharmonicity parameter and the splitting of pseudodegeneracy by an asymmetry parameter as well as probability-density plots are discussed. Several potentials, especially those with pseudodegenerate energy levels, are reported here.

We suggest an interferometric scheme assisted by squeezing and linear feedback to realize the whole class of field-quadrature quantum nondemolition measurements, from Von Neumann projective measurement to a fully nondestructive noninformative one. In our setup, the signal under investigation is mixed with a squeezed probe in an interferometer and, at the output, one of the two modes is revealed through homodyne detection. The second beam is then amplitude-modulated according to the outcome of the measurement, and finally squeezed according to the transmittivity of the interferometer. Using strongly squeezed or antisqueezed probes respectively, one achieves either a projective measurement, i.e., homodyne statistics arbitrarily close to the intrinsic quadrature distribution of the signal, and conditional outputs approaching the corresponding eigenstates, or a fully nondestructive one, characterized by an almost uniform homodyne statistics, and by an output state arbitrarily close to the input signal. By varying the squeezing between these two extremes, or simply by tuning the internal phase shift of the interferometer, the whole set of intermediate cases may also be obtained. In particular, an optimal quantum nondemolition measurement of quadrature may be achieved, which minimizes the information gain versus state disturbance tradeoff.

The impedance boundary condition is used to calculate the Casimir force in configurations of two parallel plates and a sphere (spherical lens) above a plate at both zero and nonzero temperature. The impedance approach allows one to find the Casimir force between the realistic test bodies regardless of the electromagnetic fluctuations inside the media. Although this approach is an approximate one, it has wider areas of application than the Lifshitz theory of the Casimir force. The general formulas of the impedance approach to the theory of the Casimir force are given and the formal substitution is found for connecting it with the Lifshitz formula. The range of micrometer separations between the test bodies, which is interesting from the experimental point of view, is investigated in detail. It is shown that at zero temperature the results obtained on the basis of the surface impedance method are in agreement with those obtained in framework of the Lifshitz theory within a fraction of a percent. The temperature correction to the Casimir force from the impedance method coincides with that from the Lifshitz theory up to four significant figures. The case of millimeter separations that corresponds to the normal skin effect is also considered. At zero temperature the obtained results have good agreement with the Lifshitz theory. At nonzero temperature the impedance approach is not subject to the interpretation problems peculiar to the zero-frequency term of the Lifshitz formula in dissipative media.

By solving rigorously and accurately the time-dependent Schrödinger equation, we have obtained numerical results for the decay probability, $P\left(t\right),$ of real, multiparticle systems, in the time domain of $t\approx 0.$ Three different types of atomic nonstationary states were examined, the ${\mathrm{He}}^{-}{1s2p}^2{}^{4}P,$ the Ca KLM $3d5p{}^3{F}^o,$ and the ${\mathrm{He}}^{\mathrm{-}}$ $1s2s2p{}^4{P}_{5/2},$ the last one being metastable and decaying via spin-spin interactions. The main results are that there is a $t^2$ dependence of $P\left(t\approx 0\right)$ and that a time-dependent short-time decay rate can be calculated. The computed coefficients of the $t^2$ term reflect the degree of stability of the state, (i.e., the degree of proximity to the notion of the standard stationary state of quantum mechanics), and are named the stationarity coefficients. These, together with the conventional quantity of the lifetime, corresponding to the exponential decay regime, constitute intrinsic properties of each real unstable state. For the herein studied metastable state the onset of exponential decay occurs after about $5\times {10}^{-14}\mathrm{s},$ i.e., after a duration which is achievable experimentally with laser pulses.

The quantum teleportation protocol is extracted directly out of a standard classical circuit that exchanges the states of two qubits using only controlled-NOT gates. This construction of teleportation from a classically transparent circuit generalizes straightforwardly to d-state systems.

We develop a dynamical perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by nonresonant transitions are estimated. We verify our perturbation approach using exact numerical solution for relatively small $\mathrm{}(N=10\mathrm{})\mathrm{}$ number of qubits. A preferred range of parameters is found in which the errors in processing quantum information are reasonably small. Our results can be useful for understanding the mechanisms of errors and for experimental testing of scalable solid-state quantum computers.

We study the fault tolerance of quantum computation by adiabatic evolution, a quantum algorithm for solving various combinatorial search problems. We describe an inherent robustness of adiabatic computation against two kinds of errors, unitary control errors and decoherence, and we study this robustness using numerical simulations of the algorithm.

We provide an example of a distillable bipartite mixed state such that, even in the asymptotic limit, more pure-state entanglement is required to create it than can be distilled from it. Thus, we show that the irreversibility in the processes of formation and distillation of bipartite states, recently proved in [G. Vidal and J. I. Cirac, Phys. Rev. Lett. 86, 5803 (2001)], is not limited to bound-entangled states.

Dynamic dipole and quadrupole polarizabilities as well as shielding factors of the beryllium atom in the ground state were computed at real frequencies by using the variation-perturbation method. The zeroth- and the first-order wave functions were expanded in many-electron basis of exponentially correlated Gaussian functions. The 1600-term expansion of the unperturbed wave function yielded the ground-state energy accurate to $1\hspace{0.5em}{\mathrm{cm}}^{-1}.$ The first-order wave functions were expanded in very large bases (4800 and 4400 terms). The nonlinear parameters of the first-order correction functions were optimized with respect to both the static and dynamic polarizabilities, and with respect to the excited-state energies. The procedure employed ensures a high accuracy of determination of dynamic properties in a wide range of frequencies and correct positions of the transition poles. Test calculations, performed on He and Li, confirmed the ability of this method to obtain the atomic properties with very high accuracy. The final values of the static properties of Be were ${37.755e}^2{a}_0^2{E}_H^{-1}$ and ${300.96e}^2{a}_0^4{E}_H^{-1}$ for the dipole and quadrupole polarizabilities, respectively, and 1.4769 for the quadrupole shielding factor. The convergence of the atomic properties with the size of the expansion of both the zeroth- and first-order functions was checked. Thanks to very high accuracy of the unperturbed wave function and the efficient method of construction of the first-order wave functions, the dynamic polarizability results presented in this work are of benchmark quality. As a by-product of this project, a set of the most accurate upper bounds to the energies of ${}^{1}P$ and ${}^{1}D$ states of Be was obtained.