Atomic stabilization against photoionization is numerically investigated in two spatial dimensions. It is demonstrated that the stabilization, prevented by magnetic effects, can be restored by a properly chosen constant magnetic field.

Two-photon excitation of a quantum ladder system by a chirped pulse leads to interferences in the excited-state population, due to the phase differences between direct and sequential paths. First, based on an analytical approach, we separate and discuss the features of the contributions arising from these two paths. Then interferences with two intermediate levels are observed experimentally in atomic sodium vapor. Interplay between the two sequential paths leads to strongly contrasted oscillations and a great enhancement of the transition probability for some values of the chirp.

Fault-tolerant quantum error correction (QEC) networks are studied by a combination of numerical and approximate analytical treatments. The probability of failure of the recovery operation is calculated for a variety of Calderbank-Shor-Steane codes, including large block codes and concatenated codes. Recent insights into the syndrome extraction process, which render the whole process more efficient and more noise tolerant, are incorporated. The average number of recoveries that can be completed without failure is thus estimated as a function of various parameters. The main parameters are the gate $\gamma$ and memory $\epsilon$ failure rates, the physical scale-up of the computer size, and the time $t_m$ required for measurements and classical processing. The achievable computation size is given as a surface in parameter space. This indicates the noise threshold as well as other information. It is found that concatenated codes based on the $\left[\right[23,1,7\left]\right]$ Golay code give higher thresholds than those based on the $\left[\right[7,1,3\left]\right]$ Hamming code under most conditions. The threshold gate noise ${\gamma }_0$ is a function of $\epsilon /\gamma$ and $t_m;$ example values are $\{\epsilon /\gamma {,t}_m,{\gamma }_0\}=\{{1,1,10}^{-3}\},$ $\{0.01,1,3\times {10}^{-3}\},$ $\{{1,100,10}^{-4}\},$ $\{0.01,100,2\times {10}^{-3}\},$ assuming zero cost for information transport. This represents an order of magnitude increase in tolerated memory noise, compared with previous calculations, which is made possible by recent insights into the fault-tolerant QEC process.

The study of quantum cryptography and quantum entanglement has traditionally been based on two-level quantum systems (qubits) and more recently on three-level systems (qutrits). We investigate several classes of state-dependent quantum cloners for four-level systems (quartits). These results apply to symmetric as well as asymmetric cloners, so that the balance between the fidelity of the two clones can also be analyzed. We extend Cerf’s formalism for cloning states in order to derive cloning machines that remain invariant under certain unitary transformations. Our results show that a different cloner has to be used for two mutually unbiased bases which are related by a double Hadamard transformation, than for two mutually unbiased bases that are related by a Fourier transformation. This different cloner is obtained thanks to a redefinition of Bell states that respects the intrinsic symmetries of the Hadamard transformation.

Recently, an unusual predissociation was observed for some vibrational levels of the $B{}^1{\Pi }_u$ molecular state of ${}^6{\mathrm{Li}}^7\mathrm{Li}$ [Bouloufa et al., Phys. Rev. A 63, 042507 (2001)]. It was interpreted as due to the ungerade-gerade symmetry breaking that couples the $B{}^1{\Pi }_u$ quasibound levels to the $1{}^1{\Pi }_g$ continuum. However, the agreement between theory and experiment was not perfect for predissociation rates of three rovibrational levels, occurring for isolated quantum numbers. Here, we identify these additional perturbations as due to the rotational coupling of the $1{}^1{\Pi }_g$ continuum with quasibound levels of the $2{}^1{\Sigma }_g^{+}$ state. In addition, our method allows a calculation of the Λ-doubling in the $1{}^1{\Pi }_g$ state and dissociation rates of quasibound $2{}^1{\Sigma }_g^{+}$ levels for three isotopomers of ${\mathrm{Li}}_2.$ Comparison with experimental data is discussed.

Electron capture by ${\mathrm{Li}}^{+}$ ions from aligned $\mathrm{Na}\mathrm{}\left(25p\right)\mathrm{}$ Rydberg atoms was measured as a function of the approach angle between the alignment axis of the target-atom wave functions and the ion-beam direction, over a range of reduced velocity $\tilde{v}=1.0\mathrm{}–2.0,$ where $\tilde{v}{=v}_{\mathrm{ion}}{/v}_e.$ A Stark barrel was used to generate uniform rotatable electric fields over the collision volume and to align Rydberg atoms along the field at arbitrary angles over a full range of $360°.$ A mixture of $\mathrm{Na}\mathrm{}\left(25p\right)\mathrm{}$ fine-structure levels was prepared in the Stark barrel by two-step pulsed laser excitation in the presence of a moderate electric field (about 56 V/cm) followed by adiabatic switching and rotation to 1.8 V/cm. The relative capture cross section, which varied sinusoidally as a function of the alignment angle, had maxima at $0°$ and $180°$ and minima at $90°$ and $270°$ throughout this velocity range, showing a strong preference for capture from the endwise arrangement. The alignment effect weakened as the projectile velocity was increased. The Rydberg-state results differ in both magnitude and trend from those based on low-lying aligned states. The spin-independent asymmetry parameter was inferred from the angle-dependent capture cross sections after the spin-orbit depolarization effect in the mixed Rydberg p state was fully accounted for so that the results correspond purely to molecular $\Sigma$ and $\Pi$ collision geometries.

Binary $\mathrm{}(e,2e)\mathrm{}$ measurements are reported for ionization-excitation processes of ${\mathrm{H}}_2.$ The experiments were performed at impact energies of 1200, 1600, and 2000 eV using an energy- and momentum-dispersive spectrometer. Momentum profiles for transitions to the $2s{\sigma }_g$ and $2p{\sigma }_u$ excited final ion states are presented as normalized intensities relative to the cross section of the primary ionization to the $1s{\sigma }_g$ ground ion state. The results are compared with theoretical calculations of Lermer et al. [Phys. Rev. A 56, 1393 (1997)] using the first-order plane-wave impulse approximation. Certain features of the discrepancies between experiment and theory can be explained by incorporating contributions from the second-order two-step mechanisms into the $\mathrm{}(e,2e)\mathrm{}$ cross sections. Furthermore, the present results suggest that $2s{\sigma }_g$ and $2p{\sigma }_u$ cross sections approach their high-energy limits in different ways.

An ultrafast pulse shaping scheme is presented that transiently modifies a two-state superposition on the $E{}^1{\Sigma }_g^{+}$ curve of the lithium dimer. At short time delays, the wave-function amplitude of one of the states is forced to undergo a sign change, while the sign of the second state is programmed to remain static, analogous to the operation of a quantum-computational Z gate. This is observed as a π phase shift in the time-dependent wave-packet signal for pump-probe delays <1.5 ps, relative to longer time delays, greater than 2.5 ps. This shift in sign is accomplished by taking advantage of the separability of the resonant and nonresonant light field effects in the creation of the excited-state wave function. The results show that, for a single state, the resonant and nonresonant light field effects can either be added or subtracted to create the total time evolution of the excited-state wave-function coefficient. If the nonresonant contributions are subtracted from the resonant ones at a time delay when the nonresonant term dominates, then for a short time the excited-state coefficient will have a sign opposite to that at long time, where the resonant term dominates. A desired phase function is derived to produce the opposition in sign of resonant versus nonresonant contributions, and the experimental transient Z-gate matrix elements are quantified.

We demonstrate compression of the velocity spread of a stored ion bunch in an electrostatic ion-beam trap, using the $\delta$-kick method. An analytical formula for the optimum pulse is derived and is used in the laboratory. A 20% reduction in the asymptotic velocity spread is observed after application of a single cooling pulse to a bunch of 4.2-keV ${\mathrm{Ar}}^{+}$ ions.

Two-color excitation by spatially coherent and incoherent laser beams has been used to study three-photon-resonant excitation and subsequent ionization of xenon in conditions, when internally generated sum-frequency field plays an important role in excitation of atomic resonances through interfering one-photon excitation pathway. We show that the incoherence in one of the pumping fields reduces the efficiency of generated sum-frequency field, and thus suppresses the interference between the three- and the one-photon excitation channels. The degree of suppression is controlled by varying the crossing angle between coherent and incoherent laser beams. We show that ionization profiles can be analyzed on the basis of the well-studied interference of one- and three-photon transition amplitudes, but with pumping field decomposed into multiple small-scale uncorrelated domains where coherent process of four-wave mixing occurs. The gain length for a coherent process in these domains depends on the coherence degree and excitation geometry. It gives a possibility of controlling the contribution of coherent processes to the excitation of multiphoton resonances.

A scheme is proposed for implementing a desired transformation of the unknown quantum state of a traveling optical multimode signal. The operator describing this transformation is built up as a polynomial in products of the mode operators. There is no limitation to unitary operators realized by the scheme, the implementation is conditional however, i.e., the desired operator can be realized only with a certain success probability which depends on the respective operator and the input state. While the scheme requires the preparation of single-photon and coherent states, it exclusively makes use of beam splitters and zero- and single-photon detections. The setup consists of a number of stations, each controlling one of the signal modes. The stations share an auxiliary entangled state which has been prepared beforehand. This state is then entangled with each of the signal modes and a measurement is performed of each of the auxiliary modes afterwards. In this way, the stations can be spatially separated from one another, similar to a multimode generalization of a quantum teleportation setup. Some examples of application such as the realization of cross-Kerr nonlinearities, multidirectional quantum teleportation (i.e., multimode mirrors), and the preparation of multimode Greenberger-Horne-Zeilinger- and Einstein-Podolsky-Rosen-like states are considered.

The problem of radiative heat transfer between two dielectric bodies is analyzed from the point of view of elementary quantum electrodynamics. The dielectric properties of the bodies are assumed to be linear, but dispersion and losses are allowed. Quantization of the electromagnetic field in inhomogeneous, dispersive, and lossy dielectrics is performed with the help of the Huttner-Barnett procedure. The electromagnetic energy flux is expressed through the expectation value of the Poynting vector. In order to compute the Poynting vector, two techniques suitable for nonequilibrium processes are employed: the Heisenberg equations of motion and the diagrammatic Keldysh procedure. They are shown to give identical final results. These quantum-mechanical calculations provide a solid basis for the further, mainly numerical, development of the theory of thermal scanning microscopy.

The static polarizability of the $1s,$ $2p,$ and $3d$ states of the hydrogen atom has been calculated using the B-splines basis set method, and the portion of the polarizability without poles has been calculated using the B-splines Galerkin method. Excellent agreement with exact values has been obtained. The current algorithm improves the efficiency and accuracy over the finite perturbation method. In addition, closure rules are obtained for the static polarizability of these states.

A technique for directly measuring the duration of subfemtosecond extreme ultraviolet (xuv) laser pulses is proposed. Using the numerical solutions of the time-dependent Schrödinger equation for a H atom in the combined field of a near-infrared femtosecond and an xuv attosecond (asec) laser pulse (both linearly polarized), we show that the photoelectrons are emitted preferentially in a forward (or backward) direction, along the laser polarization vector, depending on the delay between two pulses. Our calculations show that the normalized maximal asymmetry $P_3\left({\tau }_{\mathrm{asec}}\right)$ (i.e., the signal difference measured by a forward and a backward detector divided by the total signal) exhibits a simple linear dependence on the duration ${\tau }_{\mathrm{asec}}$ of the attosecond pulse thus allowing one to easily compute the attosecond-pulse duration from measured asymmetry.

The goal of this paper is an extension of the de Broglie wave mechanics model for a single spinless particle in an electromagnetic field. The analysis indicates that the motion of a particle separates naturally into particle dynamics through the classical Hamilton-Jacobi equation and quantum wave behavior through a pilot or interaction wave equation. The interaction wave equation travels at the classical particle velocity. We study gauge invariance and interpret it in the light of the interaction wave. The Heisenberg uncertainty relations are shown to be implicit in the interaction wave. We also develop a complex quantum-mechanical, relativistic energy-momentum conservation expression using a complex quantum-mechanical four-vector.

Complete vacuum polarization calculations incorporating finite nuclear size are presented for hydrogenic ions with principal quantum numbers $n=1\mathrm{}–5.$ Lithiumlike, sodiumlike, and copperlike ions are also treated starting with Kohn-Sham potentials, and including first-order screening corrections. In both cases dominant Uehling terms are calculated with high accuracy, and smaller Wichmann-Kroll terms are obtained using numerical electron Green’s functions.

We propose a direct, coherent coupling scheme that can create massively entangled states of Bose-Einstein-condensed atoms. Our idea is based on an effective interaction between two atoms from coherent Raman processes through a (two-atom) molecular intermediate state. We compare our scheme with other recent proposals for generation of massive entanglement of Bose-Einstein-condensed atoms. We also present explicit calculations that support the possibility of detecting maximally entangled states without requiring single-atom resolved measurements.

We consider a system of two spin-s particles. We show that the reduced density matrix of this system obtained by tracing out over momentum is invariant under Galilean boosts and translations, and covariant under rotations. It implies that the spin entanglement of the system is the same for all Galilean observers.

In polarimetry, a superposition of internal quantal states is exposed to a single Hamiltonian and information about the evolution of the quantal states is inferred from projection measurements on the final superposition. In this framework, we here extend the polarimetric test of Pancharatnam’s relative phase for $\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}-\frac{1}{2}$ proposed by Wagh and Rakhecha [Phys. Lett. A 197, 112 (1995)] to spin $j>~1$ undergoing noncyclic SO(3) evolution. We demonstrate that the output intensity for higher spin values is a polynomial function of the corresponding $\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}-\frac{1}{2}$ intensity. We further propose a general method to extract the noncyclic SO(3) phase and visibility by rigid translation of two $\pi /2\mathrm{}$ spin flippers. Polarimetry on higher spin states may in practice be done with spin polarized atomic beams.