In our recent publication [D. O’Dell et al., Phys. Rev. Lett. 84, 5687 (2000)] we proposed a scheme for electromagnetically generating a self-bound Bose-Einstein condensate with $1/r$ attractive interactions: the analog of a Bose star. Here we focus upon the conditions necessary to observe the transition from external trapping to self-binding. This transition becomes manifest in a sharp reduction of the condensate radius and its dependence on the laser intensity rather than the trap potential.

Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)] approximated the correlation energy of a many-electron system as a functional of the Hartree-Fock one-particle density matrix. The most fundamental and least approximate version of this functional [their Eq. (9)] is found to yield only 25% of the true correlation energy of a uniform electron gas, and not 100% as previously believed. While short-range correlations are described surprisingly well by this approach, important long-range correlations are missing. Such correlations are energetically negligible in atoms, but cannot be ignored in more extended systems, including solids as well as molecules.

Theoretical distorted-wave calculations and experimental crossed-beam measurements are carried out for the electron-impact ionization of atomic ions in the Ga isonuclear sequence. For ${\mathrm{Ga}}^{+}$ and ${\mathrm{Ga}}^{2+}$ the indirect process of $3d$ subshell excitation followed by autoionization is calculated to make a significant contribution to the total ionization cross section near threshold. For ${\mathrm{Ga}}^{3+},$ ${\mathrm{Ga}}^{4+},$ and ${\mathrm{Ga}}^{5+}$ the total ionization cross section is calculated to be dominated by direct ionization of the $3d$ subshell. For ${\mathrm{Ga}}^{6+},$ ${\mathrm{Ga}}^{7+},$ ${\mathrm{Ga}}^{8+},$ and ${\mathrm{Ga}}^{9+}$ the indirect process of $3p$ subshell excitation followed by autoionization is calculated to make a sizable contribution to the total ionization cross section. The distorted-wave predictions for the Ga ions are generally confirmed by the reasonable agreement found between theory and experiment along the isonuclear sequence.

Single-electron (SC) and double-electron capture (DC) in collisions of metastable ${\mathrm{Ar}}^{8+}$ ions with ${\mathrm{H}}_2$ have been studied by using X-VUV and Auger spectroscopy at 10 keV per charge. SC by the long-lived metastable ion ${\mathrm{Ar}}^{8+}{(2p}^5{3s)}^3{P}_{0.2}$ mostly populates inner-shell excited Na-like ${\mathrm{Ar}}^{7+**}[{(2p}^5{3s)}^{3}P,nl{]}^{2.4}{L}_j$ levels with $n=5,$ a small fraction going to $n=4.\mathrm{}$ With the use of radiative and Auger decay rates, the observed X-VUV and Auger spectra are analyzed and compared with the spectra obtained by other authors. It is shown that the stabilization of these core-excited states is both radiative and autoionizing. DC by the metastable projectile reveals the formation of triply excited ${\mathrm{Ar}}^{6+***}$ ions. They stabilize along two Auger decay steps: the first one gives a low-energy electron, associated with the decay to the intermediate continua ${\mathrm{Ar}}^{7+}{(2p}^5{3l3l}^{\prime }),$ while the second step—originating from these ${\mathrm{Ar}}^{7+}{(2p}^5{3l3l}^{\prime })$ levels—gives a higher-energy electron, characteristic of the decay to the only available continuum ${\mathrm{Ar}}^{8+}{(2p}^6{)}^1{S}_0.$

Photodesorption of impurity ions is studied in the framework of a truncated harmonic oscillator model and is considered as a direct photon absorption process without substrate heating. The desorption rate is found by methods of quantum statistics, using the system’s evolution operator. The desorption rates estimates appear realistic. Our results predict a series of new physical effects in desorption processes.

The delocalized π electrons of a ${\mathrm{C}}_{60}$ cluster can be well described as an electron gas. Electronic friction experienced by a multicharged ion colliding with a fullerene might then be modeled in terms of the electronic stopping power. We investigated such collisions for projectile atomic numbers Z ranging from 2 to 18 and charge states $q=2,3.\mathrm{}$ Direct mass-spectrometric evidence of the clear oscillatory behavior of electronic-stopping-related processes such as multifragmentation and ionization of ${\mathrm{C}}_{60}$ was observed as a function of Z. From the positions of the maxima of the corresponding cross sections, two classes of trajectories can be distinguished: close collisions through the high electron density of the cage inducing multifragmentation, and glancing collisions through the lower electron densities of the fullerene “atmosphere” inducing direct ionization.

We revisit the recollision picture of correlated multiphoton double ionization of atoms in strong laser fields and develop consistent semiclassical model in the tunneling limit. We illustrate the model by applying it to helium and obtain quantitative agreement with recent experiments [B. Walker, E. Mevel, Baorui Yang, P. Breger, J. P. Chambaret, A. Antonetti, L. F. DiMauro, and P. Agostini, Phys. Rev. A 48, R894 (1993); B. Walker, B. Sheehy, L. F. DiMauro, P. Agostini, K. J. Schafer, and K. C. Kulander, Phys. Rev. Lett. 73, 1227 (1994)]. Developing the model, we address several problems of general interest, such as the reduction of intense field-assisted electron-ion collision to the field-free one and the total-cross-sections that include all inelastic channels. We describe a set of important physical effects responsible for the surprisingly high yield of doubly charged ions of noble gas atoms. All effects originate from the key role of the Coulomb potential and its interplay with the laser field. In addition to the Coulomb focusing of the oscillating trajectories onto the parent ion, other effects include transient trapping of electrons after tunneling in the vicinity of the parent ion, the creation of high-velocity electrons at all phases of the laser field, and the dominant role of collisional excitation of the parent ion followed by laser-assisted ionization.

We consider the evolution of a dilute Bose-Einstein condensate in an optical trap formed by a doughnut laser mode. By solving a one-dimensional Gross-Pitaevskii equation and looking at the variance and the statistical entropy associated with the position of the system, we can study the dynamical behavior of the system. It is shown that for small condensates nonlinear revivals of the macroscopic wave function are expected. For sufficiently large and dense condensates irreversible dynamics takes place for which revivals of regular dynamics appear as predicted in P. Villain and M. Lewenstein, Phys. Rev. A 62, 043601 (2000). These results are confirmed by a two-dimensional simulation in which the scales of energy associated with the two different directions mimic the experimental situation.

A model employing five energy levels and a fit linear rising photopumping rate of x-ray source is proposed to analyze the gain of inner-shell photoionization (ISPI) x-ray lasers when the lasing medium is irradiated with a filtered approximate blackbody source. The deduced analytical expressions for the time of the onset of the peak gain and its peak value reveal the effects of Auger decay, electron-impact ionization, the density of lasing medium, and the increase rate of pumping rate on the duration and the peak value of the laser gain. Also the requirements on the intensity of the driving ultrashort pulse laser can be estimated. The model is generally suitable for analyzing ISPI x-ray lasers in low-$Z$ elements from carbon to neon although carbon is analyzed in details as a representative to verify the validity of the model. $K\alpha$ x-ray lasing at 3.2 nm in nitrogen is also discussed as an attractive candidate for experimentally implementing a “water window” ISPI x-ray laser.

In this paper I have drawn out the steps to be followed in order to derive the exact Schrödinger wave function for a particle in a general one-dimensional time-dependent linear potential. To this end I have used the so-called Lewis and Riesenfeld invariant method, which is based on finding an exact quantum-mechanical invariant in whose eigenstates the exact quantum states are found. In particular, I have obtained the wave functions of a particle in the linear potential well, driven by a monochromatic electric field.

We report the transport of magnetically trapped cold atoms over a large distance. Atoms are captured in a magneto-optical trap (MOT) and loaded into a magnetic quadrupole trap. The quadrupole potential is then moved over a distance of 33 cm into an ultra-high-vacuum (UHV) chamber using a chain of quadrupole coils. By running suitable currents through the quadrupole coil pairs the trapping geometry of the potential is maintained during the transport process, thus minimizing heating of the trapped atom cloud. Magnetically trapped ${}^{87}\mathrm{Rb}$ atoms at an initial temperature of $T=125\mathrm{}\hspace{0.5em}\mu \mathrm{K}$ were heated by less than $20\hspace{0.5em}\mu \mathrm{K}$ during the transport process, and up to ${10}^9$ atoms were transferred into the UHV chamber. Due to the spatial separation of the final magnetic trap and the MOT we have been able to capture atoms in the MOT, while storing magnetically trapped atoms in the UHV chamber.

I present a four-party unlockable bound entangled state, that is, a four-party quantum state which cannot be written in a separable form and from which no pure entanglement can be distilled by local quantum operations and classical communication among the parties, and yet when any two of the parties come together in the same laboratory they can perform a measurement which enables the other two parties to create a pure maximally entangled state between them without coming together. This unlocking ability can be viewed in two ways, either as a determination of which Bell state is shared in the mixture or as a kind of quantum teleportation with cancellation of Pauli operators.

Hyperspherical elliptic (HSE) harmonics are the eigenfunctions of the generalized angular momentum operator obtained by separating variables in HSE coordinates. These functions depend on accessory parameters characterizing the HSE coordinate system and present a more flexible basis on a hypersphere as compared with more familiar hyperspherical polar harmonics. We discuss a special set of HSE harmonics arising in hyperspherical treatments of the three-body problem in the HSE coordinate system introduced in an earlier paper [Tolstikhin et al., Phys. Rev. Lett. 74, 3573 (1995)]. The separation of variables in these coordinates leads to the Heun equation, which is a generalization of the Gauss hypergeometric equation. We develop an efficient method to solve the corresponding one-dimensional eigenvalue problem and thus construct the HSE harmonics, which opens a way for their application in the studies of various atomic, molecular, and nuclear three-body systems.

We evaluate the contributions of final-state light-by-light scattering to the parapositronium and orthopositronium decay rates. Our results are 1.29392(4) for parapositronium and 0.350(4) for orthopositronium in units of $(\alpha /\pi {)}^2$ times the respective lowest-order rates.

We demonstrate that when laser light is circularly polarized and properly detuned, the ac Stark shift of an alkali-metal atom in its ground state takes the form of a pure Zeeman shift. The condition is satisfied when the laser frequency is between the $D1\mathrm{}$ and $D2\mathrm{}$ transition frequencies, with the size of the detuning from the $D2\mathrm{}$ resonance twice that from the $D1\mathrm{}$ resonance. The direction of the effective magnetic field is along the laser propagation axis, and its magnitude is proportional to the vector polarizability of the atom and to the laser intensity. We use stimulated Raman spectroscopy on an optically pumped slow atomic beam from a magneto-optical trap to measure the vector polarizability and saturated absorption spectroscopy to show that the scalar polarizability vanishes at the particular detuning.

We present results of convergent close-coupling calculations for excitation of the ground $3^{1}S$ state of magnesium to the $3^{1}P$ state for incident electron energies from threshold to 1000 eV. Good agreement is found with measurements of the $3^{1}P$ optical excitation function and polarization of the $3^1{P-3\mathrm{}}^{1}S$ radiation. Good agreement is also found with the available, but limited, experimental electron-photon correlation data. However, occasional significant discrepancies have been identified between theory and experiment for the differential cross sections.

Ultrashort laser pulses have been used to produce nonstationary Ca $4pnl$ autoionizing states via sudden isolated-core excitation of $4snl$ angular Rydberg wave packets. The angular distributions of the electrons ejected into the $4s\epsilon l$ and $3d\epsilon l$ continua are altered by varying the initial orientation of the $4snl$ angular wave packet. While the observed level of control is less than might be expected from an intuitive picture, it is in excellent agreement with R-matrix quantum-defect theory calculations.

We investigate the time evolution of the superposition of macroscopically distinct quantum states in a system of two-level atoms interacting with a thermal environment of photon modes. We show that the atomic coherent states are robust against decoherence; therefore, we call their superpositions atomic Schrödinger cat states. The initial fast regime of the time evolution is associated with the process of decoherence and it is directed toward the statistical mixture of the constituent coherent states of the original state for most of the initial conditions. However, certain superpositions, called symmetric, exhibit exceptionally slow decoherence. By introducing a new measure, we generalize the usual decoherence scheme regarding the evolution of the state to account also for the symmetric case. To stress the fact that the environment preserves symmetric superpositions much longer than the other ones, we present Wigner function images of the decoherence of a suitably oriented four-component cat state.

We present a general method for the derivation of various statistical quantities describing the detection of a beam of atoms emerging from a micromaser. The use of non-normalized conditioned density operators and a linear master equation for the dynamics between detection events is discussed as are the counting statistics, sequence statistics, and waiting time statistics. In particular, we derive expressions for the mean number of successive detections of atoms in one of any two orthogonal states of the two-level atom. We also derive expressions for the mean waiting times between detections. We show that the mean waiting times between detections of atoms in like states are equivalent to the mean waiting times calculated from the uncorrelated steady state detection rates, although like atoms are indeed correlated. The mean waiting times between detections of atoms in unlike states exhibit correlations. We evaluate the expressions for various detector efficiencies using numerical integration, reporting results for the standard micromaser arrangement in which the cavity is pumped by excited atoms and the excitation levels of the emerging atoms are measured. In addition, the atomic inversion and the Fano-Mandel function for the detection of deexcited atoms are calculated for comparison to the experimental results of Weidinger et al. [Phys. Rev. Lett. 82, 3795 (1999)], who report the observation of trapping states.

We describe the NMR implementation of a recently proposed quantum algorithm involving quantum entanglement at the level of two qubits. The algorithm solves a generalization of the Deutsch problem, and distinguishes between even and odd functions using fewer function calls than is possible classically. The manipulation of entangled states of the two qubits is essential here, unlike the Deutsch-Jozsa algorithm and Grover’s search algorithm for two bits.