We compare calculations of the fully differential cross section for ionization of atomic hydrogen by electron impact using two different theories—the perturbative CDW-EIS (continuum distorted wave with eikonal initial state) approximation and the nonperturbative ECS (exterior complex scaling) method. For this comparison, we chose an impact energy of 54.4 eV, since this is near the lowest energy that our perturbative approach would be applicable and near the highest energy that can be tackled by the ECS method with our present computational resources. For the case of equal-energy outgoing electrons investigated here, the two theories predict nearly identical results except that CDW-EIS underestimates the ECS values nearly uniformly by about 30%. Interestingly, when initial-state projectile-target interactions are neglected by replacing the eikonal initial state with the unperturbed initial state (the approximation of Brauner, Briggs, and Klar [J. Phys. B $22,$ 2265 (1989)]), the cross section oscillates by $\pm 50\%$ about the ECS values.

We introduce phase operators associated with the algebra su(3), which is the appropriate tool to describe three-level systems. The rather unusual properties of this phase are caused by the small dimension of the system and are explored in detail. When a three-level atom interacts with a quantum field in a cavity, a polynomial deformation of this algebra emerges in a natural way. We also introduce a polar decomposition of the atom-field relative amplitudes that leads to a Hermitian relative-phase operator, whose eigenstates correctly describe the corresponding phase properties. We claim that this is the natural variable to deal with quantum interference effects in atom-field interactions. We find the probability distribution for this variable and study its time evolution in some special cases.

We extend the theory of diffraction in time to particles with angular momentum. We consider the problem of the sudden release of a particle which initially was inside a spherical trap. The particle’s free time evolution is described by spherical waves, which have amplitudes diffracted in time. The time-dependent density pattern is, for high or low energies, one of Fresnel or Fraunhofer diffraction by a single slit respectively.

High-resolution measurements of the photoionization cross sections of the Na-isoelectronic ions ${\mathrm{Mg}}^{+}$ and ${\mathrm{Al}}^{2+}$ are presented, to be compared with earlier measurements in which structure in the most prominent peaks was unresolved. These measurements have been normalized to the earlier ones in order to provide values of the oscillator strengths of the newly resolved peaks, and comparison is made with multiconfiguration Hartree-Fock calculations.

Absolute total destruction cross sections of ${\mathrm{B}}_n^{-}\mathrm{}(n=1,2\mathrm{})\mathrm{}$ and ${\mathrm{Al}}_n^{-}(n=1\mathrm{}–4)$ clusters colliding with ${\mathrm{N}}_2$ were measured for relative velocities in the interval 0.2–1.0 a.u. All cross-section curves may be described as a single curve, presenting a maximum around the velocity of 0.3 a.u., multiplied by a projectile-dependent factor. For the ${\mathrm{Al}}_n^{-}$ case, this factor increases linearly with the projectile size n. These findings agree with previous works for anionic atoms and clusters being destroyed in noble gases, where the single curve contains the data target dependence and the scaling factors are also linear in n.

We analyze the existence and stability of spatially extended (Bloch-type) and localized states of a Bose-Einstein condensate loaded into an optical lattice. In the framework of the Gross-Pitaevskii equation with a periodic potential, we study the band-gap structure of the matter-wave spectrum in both the linear and nonlinear regimes. We demonstrate the existence of families of spatially localized matter-wave gap solitons, and analyze their stability in different band gaps, for both repulsive and attractive atomic interactions.

We investigate theoretically the mode-locking properties of an erbium-doped birefringent fiber laser in a unidirectional cavity containing an optical isolator. The mode-locking is achieved through nonlinear polarization rotation. The approach is based on a master equation which takes explicitly into account the angles between the eigen axis of the fiber at each side of the polarizer. The stability conditions of both the stationary and localized solutions are determined. This allows to establish a stability diagram versus the angles which gives the domains where the laser operates in continuous, mode-locked or unstable regime. The model also allows to calculate the pulse duration together with the pulse energy as a function of the orientation of the eigen axis of the fiber with respect to the polarizer.

In this paper, we discuss the problem of splitting of the total correlations for a bipartite quantum state described by the Von Neumann mutual information into classical and quantum parts. We propose a measure of the classical correlations as the difference between the Von Neumann mutual information and the relative entropy of entanglement. We compare this measure with different measures proposed in the literature.

In this paper we focus on a special framework for quantum coin-flipping protocols, bit-commitment-based protocols, within which almost all known protocols fit. We show a lower bound of 1/16 for the bias in any such protocol. We also analyze a sequence of multiround protocols that tries to overcome the drawbacks of the previously proposed protocols in order to lower the bias. We show an intricate cheating strategy for this sequence, which leads to a bias of 1/4. This indicates that a bias of 1/4 might be optimal in such protocols, and also demonstrates that a more clever proof technique may be required to show this optimality.

The hyperfine structure of the ${}^2{S}_{1/2}{-}^2{D}_{5/2}$ quadrupole transition at 674 nm in ${}^{87}{\mathrm{Sr}}^{+}$ has been observed. The ion was confined in a Paul trap and cooled using laser radiation at 422 and 1092 nm. The quadrupole transition was observed by monitoring quantum jumps in the 422-nm fluorescence. The odd isotope of strontium has “clock” transitions independent of the first-order Zeeman shift and the ${}^2{D}_{5/2}$ state hyperfine structure constants have been determined as $A_{D_{5/2}}=2.1743\mathrm{}\left(14\right)\mathrm{}\mathrm{MHz}$ and $B_{D_{5/2}}=49.11\mathrm{}\left(6\right)\mathrm{}\mathrm{MHz}.$ Standard uncertainties have been added in parentheses. These values allow the second-order Zeeman shifts to be calculated. The ${}^{88}{\mathrm{Sr}}^{+}{-}^{87}{\mathrm{Sr}}^{+}$ isotope shift for the 674-nm quadrupole transition has been measured to be 247.99(4) MHz.

We give a Shor-Preskill-type security proof to quantum key distribution without public announcement of bases [W.Y. Hwang et al., Phys. Lett. A 244, 489 (1998)]. First, we modify the Lo-Chau protocol once more so that it finally reduces to the quantum key distribution without public announcement of bases. Then we show how we can estimate the error rate in the code bits based on that in the checked bits in the proposed protocol, which is the central point of the proof. We discuss the problem of imperfect sources and that of large deviation in the error rate distributions. We discuss when the bases sequence must be discarded.

We provide generalizations of known two-qubit entanglement distillation protocols for arbitrary Hilbert space dimensions. The protocols, which are analogs of the hashing and breeding procedures, are adapted to bipartite quantum states that are diagonal in a basis of maximally entangled states. We show that the obtained rates are optimal, and thus equal to the distillable entanglement, for a $\left(d-1\right)$-parameter family of rank deficient states. Methods to improve the rates for other states are discussed. In particular, for isotropic states it is shown that the rate can be improved such that it approaches the relative entropy of entanglement in the limit of large dimensions.

Local(multiplicative) effective potential energy-theories of electronic structure comprise the transformation of the Schrödinger equation for interacting Fermi systems to model noninteracting Fermi or Bose systems whereby the equivalent density and energy are obtained. By employing the integrated form of the Kato electron-nucleus cusp condition, we prove that the effective electron-interaction potential energy of these model fermions or bosons is finite at a nucleus. The proof is general and valid for arbitrary system whether it be atomic, molecular, or solid state, and for arbitrary state and symmetry. This then provides justification for all prior work in the literature based on the assumption of finiteness of this potential energy at a nucleus. We further demonstrate the criticality of the electron-nucleus cusp condition to such theories by an example of the hydrogen molecule. We show thereby that both model system effective electron-interaction potential energies, as determined from densities derived from accurate wave functions, will be singular at the nucleus unless the wave function satisfies the electron-nucleus cusp condition.

The gas-surface scattering kernel for Na atoms interacting with a dielectric surface is obtained by measuring and theoretically reproducing two-photon evanescent-volume-wave spectra. From a detailed analysis of the spectral line shapes the contribution of inelastically scattered atoms is identified and a mean energy transfer of 36 meV is deduced for atoms having initial mean thermal energies of 79 meV. The mean probability of direct scattering mediated by surface phonons increases from 0.03 to 0.05 by increasing the surface temperature from 386 K to 398 K.

In a recent experiment at JILA [E. A. Donley et al., Nature (London) 417, 529 (2002)] an initially pure condensate of ${}^{85}\mathrm{Rb}$ atoms was exposed to a specially designed time-dependent magnetic-field pulse in the vicinity of a Feshbach resonance. The production of additional components of the gas as well as their oscillatory behavior have been reported. We apply a microscopic theory of the gas to identify these components and determine their physical properties. Our time-dependent studies allow us to explain the observed dynamic evolution of all fractions, and to identify the physical relevance of the pulse shape. Based on ab initio predictions, our theory strongly supports the view that the experiments have produced a molecular condensate.

Generation of resonance-enhanced third harmonic in Bessel and other conical beams is analyzed from a simple picture, where the fundamental light field is decomposed into elementary configurations of crossed plain-wave sub-beams. We show that the overall harmonic output can be derived as a superposition of all partial harmonic components driven by elementary configurations of the fundamental field. Good agreement with experimental observations has been obtained in simulation of spectral and spatial characteristics of the generated third harmonic. Some peculiarities of harmonic generation in conical light fields are discussed.

Using a group-theoretic approach, we investigate some new peculiar features of a general quartic anharmonic oscillator. When the coefficient of the quartic term is positive and the potential is differentiable, we find that continuity of the derivative of the potential forces the nonexistence of an analytic wave function. For the case in which the coefficient of the quartic term is negative, we find that normalizability of the wave function requires non-Hermiticity of the Hamiltonian. Finally, we apply our method to gain some insight on the double well potential.

We analyze theoretically the time-resolved signal detected in three-pulse, photon echo experiments where several independent two-level systems are involved, in a case when the time delay T between the two last pulses is much longer than delay $\tau$ between the two first pulses. A spectral diffusion process on a long time scale is included in the calculation of the $\tau$-dependent response signal. If spectral diffusion occurs between the different systems, the signal exhibits quantum beats instead of the polarization interferences observed without spectral diffusion. This analysis provides different insights on dynamical processes and spectroscopy, as demonstrated in examples of experimental results obtained on vibrational dynamics of molecules embedded in matrices.

We study the error rate of controlled-NOT (CNOT) operations in the Kane solid-state quantum computer architecture [B. Kane, Nature 393, 133 (1998)]. A spin Hamiltonian is used to describe the system. Dephasing is included as exponential decay of the off-diagonal elements of the system’s density matrix. Using available spin-echo decay data, the CNOT error rate is estimated at $\approx {10}^{-3}.$

Two-body systems with pure entangled wave functions are known not to satisfy local realism; that is, they display nonlocality. However, it is noted that the well-known conclusion of the EPR paradox that quantum mechanics is an incomplete theory is inconclusive, and that local quantum-mechanical calculations are sufficient to explain two-body correlations. Such correlations are commonly attributed to an instant nonlocal interaction, but that is neither required nor observable in a two-body system. However, nonlocal transmission could be directly detected in sequential three-body processes, and a test for this is proposed by the direct timing of the teleportation of a wave function. The result of this would help towards establishing a dynamical theory of teleportation.