In this Comment we question the recent emphasis by Langereis et al. [Phys. Rev. A 60, 2917 (1999)] that excitation of triplet states in double-capture processes is noticeable in the ${\mathrm{Ne}}^{8+}{(1s}^2{)}^{1}S+\mathrm{He}{(1s}^2{)}^{1}S$ collisional system at 80 keV. We demonstrate that all their identified ${\mathrm{Ne}}^{6+}{(1s}^2{3lnl}^{\prime })$ autoionizing transitions can be perfectly explained by excitation of singlet states alone. In our opinion their findings based on electron spectroscopy rely on too inaccurate spectrum analysis and theoretical input data.

We propose a quantum feedback scheme for producing deterministically reproducible spin squeezing. The results of a continuous nondemolition atom number measurement are fed back to control the quantum state of the sample. For large samples and strong cavity coupling, the squeezing parameter minimum scales inversely with atom number, approaching the Heisenberg limit. Furthermore, ceasing the measurement and feedback when this minimum has been reached will leave the sample in the maximally squeezed spin state.

We show that the four states $a|00〉+b|11〉,\hspace{0.5em}\overline{b}|00〉-ā|11〉,\hspace{0.5em}c|01〉+d|10〉,$ and $\overline{d}|01〉-\overline{c}|10〉$ cannot be discriminated with certainty if only local operations and classical communication (LOCC) are allowed and if only a single copy is provided, except in the case when they are simply $|00〉,\hspace{0.5em}|11〉,\hspace{0.5em}|01〉,$ and $|10〉$ (in which case they are trivially distinguishable with LOCC). We go on to show that there exists a continuous range of values of $a,\hspace{0.5em}b,\hspace{0.5em}c,$ and d such that even three states among the above four are not locally distinguishable, if only a single copy is provided. The proof follows from the fact that logarithmic negativity is an upper bound of distillable entanglement.

We consider the effect of classical stochastic noise on control laser pulses used in a scheme for transferring quantum information between atoms, or quantum dots, in separate optical cavities via an optical connection between cavities. We develop a master equation for the dynamics of the system subject to stochastic errors in the laser pulses, and use this to evaluate the sensitivity of the transfer process to stochastic pulse shape errors for a number of different pulse shapes. We show that under certain conditions, the sensitivity of the transfer to the noise depends on the pulse shape, and develop a method for determining a pulse shape that is minimally sensitive to specific errors.

We investigate the statistical properties of a prototype of a “hollow atom,” i.e., an atom having a large number of empty inner shells. In particular, we have carried out ab initio calculations of the positions and widths of the ${1s}^{2}4{\mathcal{l}}^5$ states of nitrogen. These states give rise to a dense spectrum of strongly overlapping resonances. Due to the large number of open channels, the statistical description of the system simplifies considerably. We find that the distribution of the nearest-neighbor energy-level spacings follows a Wigner distribution, while the widths of the states are narrowly distributed about the average perturbative width.

In this paper we briefly review the basic steps that allow the calculation of the scattering length in the collision of two alkali-metal atoms in a well defined magnetic polarization state, and in the presence of a static magnetic field. Calculations are actually done for the low-field seeking state $F=1,\hspace{0.5em}\hspace{0.5em}{\mu }_F=-1$ of bosonic potassium atoms. The electrostatic potentials obtained through Rydberg-Klein-Rees data are connected to a dispersive, long range tail in which the dominant dipole-dipole $C_6$ term may take different values within a specified range. We show the occurrence of Feshbach resonances in the ultra cold collision of two identical atoms, belonging either to the bosonic species ${}^{39}\mathrm{K}$ or ${}^{41}\mathrm{K}.$ Our results demonstrate that there is a range of $C_6$ values for which the collision of two ${}^{39}\mathrm{K}$ atoms displays a single resonance, while for other values of $C_6$ no resonance occurs. On the other hand, Feshbach resonances are present in the collision of two ${}^{41}\mathrm{K}$ atoms for almost all values of the dispersion coefficient $C_6$ in that range. We also show the origin of the different types of Feshbach resonances that occur in the cold collision of two ${}^{41}\mathrm{K}$ atoms. The detection of such resonances can help establish the actual value of the dispersive coefficient.

The differential cross section in angle and the total cross sections for the excitation of atomic discrete levels in Compton scattering are investigated. Results are presented for the valent $\mathrm{np}-n,(n+1\mathrm{})d$ and $\mathrm{np}-\mathrm{}(n+1\mathrm{}),(n+2\mathrm{})p$ levels of the outer subshells of the noble-gas atoms Ne, Ar, Kr, and Xe, covering the range of the momentum transferred to the atom up to 8 a.u., which is sufficiently large for the calculation of the total Compton excitation cross sections. Calculations were performed in one-electron Hartree-Fock approximation and with many-electron effects taken into account in the random-phase approximation with exchange for monopole, dipole, quadrupole, and octupole transitions. Contributions from higher multipoles proved to be unimportant and many-electron effects were found to be quite noticeable in the differential cross section, while almost negligible in the total excitation cross sections. We conclude that the contributions of discrete excitations are comparable to those of the ionization process.

Size selected, positively charged sodium clusters $({\mathrm{Na}}_n^{+},$ $n=31\mathrm{}$–500) have been studied by photoelectron spectroscopy using photons of 6.42 eV. The spectra clearly exhibit the expected shell-like electronic density of states that in this size range up to now has only been observed indirectly. The overall agreement of the measured structure with jellium model predictions is excellent. One prominent exception is ${\mathrm{Na}}_{55}^{+}$ for which jellium models predict a prolate shape, while here strong evidence for an icosahedral structure has been found.

We present a quantun-mechanical treatment of the coherence properties of a single-mode atom laser. Specifically, we focus on the quantum phase noise of the atomic field as expressed by the first-order coherence function, for which we derive analytical expressions in various regimes. The decay of this function is characterized by the coherence time, or its reciprocal, the linewidth. A crucial contributor to the linewidth is the collisional interaction of the atoms. We find four distinct regimes for the linewidth with increasing interaction strength. These range from the standard laser linewidth, through quadratic and linear regimes, to another constant regime due to quantum revivals of the coherence function. The laser output is only coherent (Bose degenerate) up to the linear regime. However, we show that application of a quantum nondemolition measurement and feedback scheme will increase, by many orders of magnitude, the range of interaction strengths for which it remains coherent.

Due to interaction with the vacuum of the radiation field, near-degenerate lower levels in a $\Lambda$ system have an additional coherence term, the spontaneously generated coherence term. In this paper, we investigate effects of spontaneouly generated coherence on inversionless gain in the presence of a weak probe, a strong coherent field, and an incoherent pump. We find that the inversionless gain stems from both spontaneously generated coherence and dynamically induced coherence, but the former contributes more to the inversionless gain. In particular, we can modulate the inversionless gain just by changing the relative phase between the two fields.

Relativistic configuration-interaction calculations predict the ${\mathrm{Tc}}^{-}$ ${4d}^6{5s}^2$ $J=4,3,2,1,0\mathrm{}$ levels are bound to the neutral Tc I ground state by 636, 552, 503, 481, and 460 meV, respectively. The $J=4\mathrm{}$ value is in good agreement with a revised semiempirical estimate presented here.

The method for analytic evaluation of four-particle integrals, proposed by Fromm and Hill, is generalized to include complex exponential parameters. An original procedure of numerical branch tracking for multiple valued functions is developed. It allows high precision variational solution of the Coulomb four-body problem in a basis of exponential-trigonometric functions of interparticle separations. Numerical results demonstrate high efficiency and versatility of this method.

We report the quantum dynamical close-coupling equations relevant for vibrationally inelastic processes in low-energy collisions between a beam of positrons and the ${\mathrm{CH}}_4$ molecule in the gas phase. The interaction potential is described in detail and we report also our numerical technique for solving the scattering equations. The cross sections are obtained for the excitations of all the modes of the title molecule and are compared both with simpler computational approximations and with the recent experiments for the two distinct energy regions that correspond to the combined symmetric and antisymmetric stretching modes and to twisting and scissoring modes, respectively. Our calculations reproduce well the shape and the values of the experimental findings and give useful insights into the microscopic dynamics for molecular excitation processes activated by low-energy positron scattering.

The method of generating a family of new solutions starting from any wave function satisfying the nonlinear Schrödinger equation in a harmonic potential proposed recently [J. J. García-Ripoll, V. M. Pérez-García, and V. Vekslerchik, Phys. Rev. E 64, 056602 (2001)] is extended to the many-body theory of mutually interacting particles. Our method is based on a generalization of the displacement operator known in quantum optics, and results in the separation of the center-of-mass motion from the internal dynamics of many-body systems. The center-of-mass motion is analyzed for an anisotropic rotating trap and a region of instability for intermediate rotational velocities is predicted.

An ultrabright source of polarization-entangled photons has been realized using type-II phase matching in the spontaneous parametric down-conversion process in two cascaded crystals. The optical axes of the crystals are aligned in such a way that the extraordinarily (ordinarily) polarized cone from one crystal overlaps with the ordinarily (extraordinarily) polarized cone from the second crystal. This spatial overlapping removes the association between the polarization and the output angle of the photons that exists in a single type-II down-conversion process. Hence, entanglement of photon pairs originating from any conjugate points on the output cones is possible if a suitable optical delay line is used. This delay line is particularly simple and easy to implement.

We investigate a four-state system interacting with long and short laser pulses in a weak probe beam approximation. We show that when all lasers are tuned to the exact unperturbed resonances, part of the four-wave mixing (FWM) field is strongly absorbed. The part that is not absorbed has the exact intensity required to destructively interfere with the excitation pathway involved in producing the FWM state. We show that with this three-photon destructive interference, the conversion efficiency can still be as high as 25%. Contrary to common belief, our calculation shows that this process, where an ideal one-photon electromagnetically induced transparency is established, is not most suitable for high-efficiency conversion. With appropriate phase matching and propagation distance, and when the three-photon destructive interference does not occur, we show that the photon flux conversion efficiency is independent of probe intensity and can be close to 100%. In addition, we show clearly that the conversion efficiency is not determined by the maximum atomic coherence between two lower excited states, as commonly believed. It is the combination of phase matching and constructive interference involving the two terms arising in producing the mixing wave that is the key element for the optimized FWM generation. Indeed, in this scheme no appreciable excited state is produced, so that the atomic coherence between states |0〉 and |2〉 is always very small.

Term values of 14 levels of $\mathrm{EF}{}^1{\Sigma }_g^{+}\mathrm{}(v=19\mathrm{}),$ $\mathrm{GK}{}^1{\Sigma }_g^{+}\mathrm{}(v=0\mathrm{}),$ $I{}^1{\Pi }_g\mathrm{}(v=0\mathrm{}),$ and $J{}^1{\Delta }_g\mathrm{}(v=0\mathrm{})\mathrm{}$ states in ${\mathrm{H}}_2$ have been calibrated in a two-step laser excitation experiment with an accuracy of $0.006\hspace{0.5em}{\mathrm{cm}}^{-1}.$ Combined with literature data on inter-Rydberg transitions these highly accurate values on g symmetry levels yield an independent determination of the ionization potential in ${\mathrm{H}}_2$ at $124417.476\hspace{0.5em}\mathrm{}\left(12\right)\mathrm{}\hspace{0.5em}{\mathrm{cm}}^{-1},$ which is consistent with previous experimental values and with ab initio calculation.

An experimental technique for the determination of the metastable $1s2s{}^{3}S$ fraction f of two-electron ion beams is reported. The method utilizes the electron yields of the ${1s2p}^2{}^{2}D$ and $1s2s2p{}^{4}P$ doubly excited states, produced in collisions of two-electron ion beams with ${\mathrm{H}}_2$ or He targets. The metastable beam fraction f is determined in two successive measurements at the same beam energy but having different metastable fractions. The technique is applied to the case of ${\mathrm{B}}^{3+}$ ions in collisions with ${\mathrm{H}}_2$ targets. The results are in good agreement with those from our recent paper on similar metastable fraction measurements [M. Zamkov et al., Phys. Rev. A 64, 052702 (2001)]. The method can be safely applied in cases where the two different metastable fractions differ significantly.

We examine the long-term time dependence of Gaussian wave packets in a circular infinite well (billiard) system and find that there are approximate revivals. For the special case of purely $m=0\mathrm{}$ states (central wave packets with no momentum) the revival time is $T_{\mathrm{rev}}^{\mathrm{}(m=0\mathrm{})\mathrm{}}=8\mathrm{}\mu R^2/ħ\pi ,$ where $\mu$ is the mass of the particle, and the revivals are almost exact. For all other wave packets, we find that $T_{\mathrm{rev}}^{\left(m\ne 0\right)}=({\pi }^2{/2)T}_{\mathrm{rev}}^{\mathrm{}(m=0\mathrm{})\mathrm{}}\approx {5T}_{\mathrm{rev}}^{\mathrm{}(m=0\mathrm{})\mathrm{}}$ and the nature of the revivals becomes increasingly approximate as the average angular momentum or number of $m\ne 0$ states is increased. The dependence of the revival structure on the initial position, energy, and angular momentum of the wave packet and the connection to the energy spectrum is discussed in detail. The results are also compared to two other highly symmetrical two-dimensional infinite well geometries with exact revivals, namely, the square and equilateral triangle billiards. We also show explicitly how the classical periodicity for closed orbits in a circular billiard arises from the energy eigenvalue spectrum, using a WKB analysis.

Mixed states of samples of spin s particles which are symmetric under permutations of the particles are described in terms of their total collective spin quantum numbers. We use this description to analyze the influence on spin squeezing due to imperfect initial-state preparation.