We measure fully differential cross sections for photo-double-ionization of helium at energies 1, 6, and 20 eV above threshold. The data have been obtained by measuring in coincidence the momentum vector of the He${}^{2+}$ ion and one of the electrons. Using time-of-flight and imaging techniques, we cover a solid angle of 25–100 % 4$\pi$ of the final-state continuum of all particles. Therefore the experiment is not confined to any particular set of angles or energy sharing, and allows for a reliable absolute calibration. We present momentum distributions of the ions and a comprehensive set of differential cross sections for electron emission. The latter are on an absolute scale and cover both equal and unequal energy sharing—for both the fast and the slow electron fixed—and a wide range of polar angles. We also present the first data for noncoplanar geometry. For all energies the cross section is sharply peaked around the coplanar emission, i.e., both electrons are preferentially emitted in the plane of the recoiling ion and the photon polarization direction. For most of the geometries the shape of the cross sections is well described by fourth-order Wannier theory calculations.

The Temkin-Poet (TP) model of electron-hydrogen scattering is here generalized to $L>\mathrm{}0\mathrm{}$ partial waves in such a way as to be a clear generalization of the exchange approximation (EA). This generalized exchange approximation (GEA) leads to a pair of coupled partial differential equations (PDE’s). Boundary conditions are formulated, and the PDE’s are solved by a finite element method program adapted from a previous partial wave calculation of the full problem [Shertzer and Botero, Phys. Rev. A 49, 3673 (1994)]. Calculations are carried out for ${}^{1,3}P$ and ${}^{1,3}D$ partial waves in the elastic region. Phase shifts are bounded from below, as is rigorously required, by exchange approximate phase shifts. But the GEA can yield resonances: in the elastic region, in addition to the ${}^{1}S$ resonance of the TP model, there is a ${}^{3}P$ resonance whose position and width are in close proximity to the lowest ${}^{3}P$ resonance of the full theory. The GEA distinguishes between singlet and triplet scattering for all $L,$ and it contains inelastic and ionization channels in the appropriate energy regions. It is expected that the GEA will have its greatest utility in the ionization domain, as a nontrivial test of the many recent methods being developed.

We report a study on single scattering of 500–1950-eV ${\mathrm{Ne}}^{+}$ ions from a Si surface. Our results show a sharp increase in the inelastic energy loss suffered by backscattered ${\mathrm{Ne}}^{+}$ for the distance of closest approach $R_{\min }<~$0.59 Å. A detailed data analysis which considers both the continuous interactions with the target valence electrons and the discrete inelasticity $Q_o$ in the binary Ne-Si collisions reveals a constant $Q_o=45\mathrm{}\pm$4 eV for $R_{\min }<~$0.47 Å. This is attributed to the simultaneous excitation of two electrons from the neutralized Ne to the 2$p^4{(}^1{D)3s}^2$ autoionization state. A small doubly charged ${\mathrm{Ne}}^{2+}$ single-scattering peak has also been observed for $R_{\min }<~$0.59 Å. In this case, the inelasticity of 86±5 eV in the binary collisions is ascribed to the two-electron excitation of surviving ${\mathrm{Ne}}^{+}$ to ${\mathrm{Ne}}^{2+\mathrm{*}}$ 2$p^{3}3s$. These assignments are consistent with all previously reported experimental results of autoionization electron emission, and the charge fraction, intensity, and energy spectral line shape of backscattered singly and doubly charged ions, for ${\mathrm{Ne}}^{+}$ and ${\mathrm{Ne}}^0$ impact on Si, Al, Mg, and Na surfaces. Our results indicate that in low-energy collisions the excited electrons can be located in bound atomic outer shells without being transferred to the conduction band of the solid. The similar threshold internuclear distances for the excitation of Ne 2$p$ electrons for both ${\mathrm{Ne}}^{+}$-Si and ${\mathrm{Ne}}^0$-Si indicate that transitions occur at similar crossings of the promoted 4$f\sigma$ molecular orbital (correlated to Ne 2$p$) with high-lying empty orbitals.

Lamb shifts and Casimir energies, often thought of as long-range and short-range effects, respectively, and studied separately, are each a manifestation of quantum electrodynamics and can be studied together. We do so for a dielectric medium between two parallel ideal conducting plates. We extract the usual Casimir energy and a bulk Lamb shift by studying the quantum fluctuations of the radiation field in the dielectric. We derive finite expressions for the Casimir energy and the bulk Lamb shift valid for any permittivity satisfying the Kramers-Krönig relation; some of the Casimir shifts obtained are simpler in form than any in the literature. We separate the divergent and finite contributions to the bulk Lamb shift. For the dilute nonrelativistic gas we show that the divergent contribution to the bulk Lamb shift defines the bare electron mass in terms of the physically observed free-electron mass. Although we lack a physical interpretation for the necessary subtraction in the case of an arbitrary dielectric, it is natural to interpret the finite part of the bulk energy as a “Lamb shift” in this case too. We show that the derived finite bulk Lamb shift and Casimir energies in the limit of a dilute homogeneous gas are consistent with earlier results for a single atom between two ideal conductors, and for an atom near one of the walls. As an application, the radiative contribution to the interaction energy of a single electron with uniform probability density between two ideal walls is obtained.

The resonant coherent excitation (RCE) of surface channeled ions has been theoretically investigated. Solving the Schrödinger equation numerically along the ion trajectory, the excitation probability of the surface channeled ion due to the periodic components of the surface potential is calculated. The mixing and energy shift of the electronic states in the vicinity of the surface due to both the continuum surface potential and the induced surface wake potential are included. The result is compared with the recent experimental result of the RCE of surface channeled ${\mathrm{B}}^{4+}$ ions at a SnTe(001) surface. Using a freezing distance model for the charge exchange processes, the characteristic features of the observed result can be well reproduced. This indicates that the observed RCE occurs mainly in the outgoing trajectory.

We evaluate quantitatively the role of Auger and radiative recombination processes in the neutralization of slow multicharged ions in metals. The strong perturbation of the valence-band electrons by the ion requires a nonlinear treatment which is carried out using density functional theory. We find that this perturbation creates an electronic cloud around the ion which has an atomiclike character. We show that it is this phenomenon which determines the order of magnitude of the transition rates, as illustrated by the evaluation of Auger and radiative rates for Ne and Ar ions.

We have trapped ${}^{40}\mathrm{K}$ in a vapor-cell magneto-optical trap starting from a natural abundance sample. This rare, weakly radioactive atom is a fermion. The number of trapped atoms is approximately 8000, with a density of $\sim {10}^8$ atoms/${\mathrm{cm}}^3$. Contrary to what is observed for the other isotopes of potassium, our data indicate that temperatures lower than the Doppler-cooling limit can be reached for ${}^{40}\mathrm{K}$. We discuss the interest of these results in view of possible experiments to study a degenerate Fermi gas.

We present a many-body theory of the dipole-dipole interaction in three-dimensional optical lattices generated by a four-beam configuration, specializing to the case of $J_g=\frac{1}{2}\to J_e=$$\frac{3}{2}$ transitions. We construct a many-body interaction Hamiltonian in coordinate representation for an antiferromagnetic fcc optical lattice, the Schrödinger field operators being expanded on a basis of Wannier functions. We discuss the main characteristics of the dipole-dipole matrix elements giving rise to bound-bound and bound-free atom interactions in the lattice. Because of the anisotropy of the dipole-dipole interaction, specific directions can be favored for transport and scattering processes. Furthermore, since the dipole-dipole interaction depends on atomic magnetic quantum numbers, the dipole-dipole potential resembles a spin-dependent potential, and can give rise to atomic hopping with simultaneous change in the magnetic quantum number.

For the hydrogen atom in combined magnetic and electric fields we investigate the dependence of the quantum spectra, classical dynamics, and statistical distributions of energy levels on the mutual orientation of the two external fields. Resonance energies and oscillator strengths are obtained by exact diagonalization of the Hamiltonian in a complete basis set, even far above the ionization threshold. At high excitation energies around the Stark saddle point the eigenenergies exhibit strong level repulsions when the angle between the fields is varied. The large avoided crossings occur between states with the same approximately conserved principal quantum number, $n,$ and this intramanifold mixing of states cannot be explained, not even qualitatively, by conventional perturbation theory. However, it is well reproduced by an extended perturbation theory, which takes into account all couplings between the angular momentum and Runge-Lenz vector. The large avoided crossings are interpreted as a quantum manifestation of classical intramanifold chaos. This interpretation is supported by both classical Poincaré surfaces of section, which reveal a mixed regular-chaotic intramanifold dynamics, and the statistical analysis of nearest-neighbor-spacing distributions.

We use the formalism of complex scaling to construct an energy-space treatment of resonances embedded in a continuum. We then use this formalism to study the nature of coherent population transfer through a resonant intermediate state. It is found that in the limit of rapid decay to the continuum, there is strong nonadiabatic coupling between the eigenstates of the matter-field Hamiltonian, which leads to imperfect population transfer.

We develop a systematic scheme to treat binary collisions between ultracold atoms in the presence of a strong laser field, tuned to the red of the trapping transition. We assume that the Rabi frequency is much less than the spacing between adjacent bound-state resonances. In this approach we neglect fine and hyperfine structures, but consider fully the three-dimensional aspects of the scattering process, up to the partial $d$ wave. We apply the scheme to calculate the $S$ matrix elements up to the second order in the ratio between the Rabi frequency and the laser detuning. We also obtain, for this simplified multichannel model, the asymmetric line shapes of photoassociation spectroscopy, and the modification of the scattering length due to the light field at low, but finite, entrance kinetic energy. We emphasize that the present calculations can be generalized to treat more realistic models, and suggest how to carry out a thorough numerical comparison to this semianalytic theory.

The time-dependent Schrödinger equation for the one-dimensional ${\mathrm{H}}_2^{+}$ molecule (with both nuclear and electronic degrees of freedom included) was solved numerically to study dissociative ionization. A wave-function splitting technique was used with projections onto Volkov states, which allows one to circumvent the problem of lost information on electron flux due to absorbing boundary methods. This technique allows us to calculate the above-threshold ionization (ATI) photo electron kinetic-energy spectra in the presence of moving nuclei, as well as complete spectra of dissociating protons, beyond the Born-Oppenheimer approximation. The ATI spectra are considerably enhanced with respect to the H-atom spectra due to electron molecule interaction. The peaks seen in calculated Coulomb explosion spectra of protons agree well with recent theoretical and experimental work related to the phenomenon of charge-resonance-enhanced ionization in molecules.

By studying the time evolution of wave packets on diamagnetic Rydberg atoms, initially localized on classical periodic hydrogenic trajectories, the influence of core scattering can be shown. Outside the core region the wave packet follows a hydrogenic torus, but is ejected on different hydrogenic tori due to core scattering.

The low-lying hydrodynamic normal modes of a dilute Bose-Einstein gas in an isotropic harmonic trap determine the corresponding Bogoliubov amplitudes. In the Thomas-Fermi limit, these modes have large low-temperature occupation numbers and they permit an explicit construction of the dynamic structure function $S(\mathbf{q},\omega )$. The total noncondensate number $N^{\prime }\mathrm{}\left(0\right)\mathrm{}$ at zero temperature increases like $R^6$, where $R$ is the condensate radius measured in units of the oscillator length. The lowest dipole modes are constructed explicitly in the Bogoliubov approximation.

We consider modification of an atom-field nonresonant interaction due to the motion of the atom (ion) in a confining potential of the trap. We study the electromagnetic field emitted by the trapped atom for various states of its center of mass. In particular, we study the radiation emitted by the atom when its center of mass is in a superposition of two quantum states and in a statistical mixture of the two states. We show that the differences between these cases are rather elusive, but they can be detected when some particular conditions are satisfied. We point out that they can be used as a way to detect the coherence of the state of the center of mass.

We propose a scheme to create a macroscopic “Schrödinger-cat” state formed by two interacting Bose condensates. In analogy with quantum optics, where the control and engineering of quantum states can be maintained to a large extent, we consider the present scheme to be an example of quantum atom optics at work.

It is shown that symmetry breaking of light counterpropagation through a system of two thin films of a resonance medium may lead to nonreciprocal transverse optical patterns in the form of positive hexagons for one direction of propagation, and in the form of negative hexagons for the opposite. Analogies with the period-2 Ikeda instability and the polarization symmetry breaking are discussed. Results may be relevant to other pattern-forming systems undergoing a pitchfork bifurcation of the homogeneous static mode.

We propose and analyze a way in which effective multicomponent condensates can be created inside high-$Q$ multimode cavities. In contrast to the situation involving several atomic species or levels, the coupling between the various components of the dressed condensates is linear. We predict analytically and confirm numerically the onset of instabilities in the quasiparticle excitation spectrum.

In this paper we use microscopic arguments to derive a nonlinear Schrödinger equation for trapped Bose-condensed gases. This is made possible by considering the equations of motion of various anomalous averages. The resulting equation explicitly includes the effect of repeated binary interactions (in particular ladders) between the atoms. Moreover, under the conditions where dressing of the intermediate states of a collision can be ignored, this equation is shown to reduce to the conventional Gross-Pitaevskii equation in the pseudopotential limit. Extending the treatment, we show first how the occupation of excited (bare particle) states affects the collisions, and thus obtain the many-body $T$-matrix approximation in a trap. In addition, we discuss how the bare particle many-body $T$ matrix gets dressed by mean fields due to condensed and excited atoms. We conclude that the most commonly used version of the Gross-Pitaevskii equation can only be put on a microscopic basis for a restrictive range of conditions. For partial condensation, we need to take account of interactions between condensed and excited atoms, which, in a consistent formulation, should also be expressed in terms of the many-body $T$ matrix. This can be achieved by considering fluctuations around the condensate mean field beyond those included in the conventional finite temperature mean field, i.e., Hartree-Fock-Bogoliubov, theory.

A three-component vector quantum field theory is developed to describe the electronic-spin-resonance interaction of a magnetically trapped Bose-Einstein condensate with a radio frequency field. The theory is directly applied to simulate the recent experiment of Mewes et al. for an output coupler for a Bose-Einstein condensate in a magnetic trap [Phys. Rev. Lett. 78, 582 (1997)]. By employing the mean-field approach, we study the collective dynamics of the multicomponent matter field via the nonlinear Schrödinger equation. Including the effect of gravity, we study the spin-resonance Rabi oscillations for the three-component Bose-Einstein condensate in three ground-state hyperfine levels and simulate the dynamic expansion of the condensate components coupled out of the magnetic trap.