Using model potentials to describe the ionic cores, we have approximated the $e^{+}+\mathrm{Li}$ and $e^{+}+\mathrm{Na}$ systems as quasi-three-body problems and performed adiabatic hyperspherical calculations to search for the existence of bound states. We have confirmed the existence of a bound state for $e^{+}+\mathrm{Li}$ that was first predicted by Ryzhikh and Mitroy [Phys. Rev. Lett. 21, 4124 (1997)] with a binding energy of 58 meV. Further, we predict the existence of a stable bound state for $e^{+}+\mathrm{Na}$ with a binding energy of 7 meV and explain why bound states exist for these two systems but not for the $e^{+}+\mathrm{H}$ system, despite the fact that ${\mathrm{H}}^{\mathrm{-}}$ has a higher binding energy than either ${\mathrm{Li}}^{\mathrm{-}}$ or ${\mathrm{Na}}^{\mathrm{-}}.$ Based on this work, we find that it is unlikely that positrons can form stable bound states with any other of the alkali-metal atoms.

In sub-Doppler laser cooling, the application of an additional homogeneous magnetic field gives rise to velocity selective resonances and laser cooling to nonzero velocities. We present a systematic investigation of the resulting structures in two-dimensional momentum space in an atomic beam experiment. The rms width of the resonances is close to one recoil momentum. The analysis of these structures in terms of a resonance condition shows good quantitative agreement with experimental results.

We report the observation of laser-induced structure (LICS) in the flat photoionization continuum of helium. The structure is a strong and spectrally sharp resonance, showing both enhanced and diminished ionization (a Beutler-Fano profile). Our observations show, in an otherwise unstructured continuum, pronounced ionization suppression (as much as 70%), which is due to population trapping associated with LICS. We also show the effect of dynamic Stark shifts upon the LICS profile. A discussed theoretical model, incorporating significant dynamic Stark shifts, gives a quantitatively accurate description of the line profile for a wide range of pulse intensities.

We study the dynamics of a Bose-Einstein condensate in a double-well potential in the two-mode approximation. The dissipation of energy from the condensate is described by the coupling to a thermal reservoir of noncondensate modes. As a consequence of the coupling, the self-locked population imbalance in the macroscopic quantum self-trapping decays away. We show that a coherent state predicted by spontaneous symmetry breaking is not robust and decoheres rapidly into a statistical mixture due to the interactions between condensate and noncondensate atoms. However, via stochastic simulations we find that with a sufficiently fast measurement rate of the relative phase between the two wells the matter wave coherence is established even in the presence of the decoherence.

We present quantitative measurements of the spatial density profile of Bose-Einstein condensates of sodium atoms confined in a 4-Dee magnetic bottle. The condensates are imaged in transmission with near-resonant laser light. We demonstrate that the Thomas-Fermi surface of a condensate can be determined to better than 1%. More generally, we obtain excellent agreement with mean-field theory. We conclude that precision measurements of atomic scattering lengths and interactions between phase-separated cold atoms in a harmonic trap can be performed with high precision using this method.

Stimulated Raman scattering (SRS) is experimentally investigated for solid hydrogen in the context of the strong coupling. Coherence decay behaviors are measured for the Raman transition of $Q\left(0\right)\mathrm{}$ $(\nu =1\mathrm{}-0)$ using the time-resolved coherent anti-Stokes Raman-scattering method. We show that the coherence decay for the Raman transition changes with the evolution of the SRS from the weak-coupling regime to the strong-coupling regime.

Stimulated Raman scattering of light in the regime of laser pulse durations shorter than the period of Raman-active vibrational mode $2\pi /{\Omega }_R$ is investigated. Using full equations for the field and the medium polarization, we obtain an insight into the stage of frequency conversion where the slowly varying amplitude approximation is inapplicable. It is found that the laser pulse experiences a continuous downshift of its spectrum, resulting in the formation of an intense single-cycle electromagnetic pulse. The role of the competing processes is analyzed.

We suggest a quantum state reconstruction scheme. Our proposal is applicable to the field inside a microwave cavity as well as to the harmonic motion of a trapped atom. It will be shown that the inversion of two-level atoms after a resonant interaction with a coherently displaced quantum state is directly related to the Wigner characteristic function of the initial state. This method neither requires the preparation of atoms in a quantum superposition of the upper and lower energy levels nor heavy numerical processing of the measured data. We demonstrate the reconstruction scheme for the example of a Schrödinger-cat superposition state.

We have measured the $2^3{P}_1–2^3{P}_0$ interval in atomic helium to be 29 616.966(13) MHz (an accuracy of 400 ppb). The microwave transition is driven using a laser-excited thermal beam of metastable helium atoms. The result of the measurement resolves the discrepancy between a previous, less-precise microwave measurement and recent laser measurements of this interval. Comparison of measured and theoretical predictions for this interval allows for a determination of the fine-structure constant.

A general method for extending a nondissipative nonlinear Schrödinger and Liouville–von Neumann one-particle dynamics to an arbitrary number of particles is described. It is shown at a general level that the dynamics so obtained is completely separable, which is the strongest condition one can impose on dynamics of composite systems. It requires that for all initial states (entangled or not) not only can a subsystem not be influenced by any action undertaken by an observer in a separated system (strong separability), but additionally the self-consistency condition ${\mathrm{Tr}\mathrm{}}_2\circ {\phi }_{1+2}^t={\phi }_1^t\circ {\mathrm{Tr}\mathrm{}}_2$ is fulfilled. It is shown that a correct extension to $N$ particles involves integro-differential equations, which, in spite of their nonlocal appearance, make the theory fully local. As a consequence, a much larger class of nonlinearities satisfying the complete separability condition is allowed than has been assumed so far. In particular all nonlinearities of the form $F\left(|\psi \mathrm{}\right(x\left)\mathrm{}|\right)$ are acceptable. This shows that the locality condition does not single out logarithmic or one-homogeneous nonlinearities.

It is argued that the time of arrival cannot be precisely defined and measured in quantum mechanics. By constructing explicit toy models of a measurement, we show that for a free particle it cannot be measured more accurately then $\Delta t_A\sim {1/E}_k,$ where $E_k$ is the initial kinetic energy of the particle. With a better accuracy, particles reflect off the measuring device, and the resulting probability distribution becomes distorted. It is shown that a time-of-arrival operator cannot exist, and that approximate time-of-arrival operators do not correspond to the measurements considered here.

A formalism for minimal irreversible quantum mechanics is extended from pure states to mixed states. In the latter case the problem of their diagonal singularity is explained and solved. In addition to the pure and mixed states of the usual approach, more general states are obtained. The Friedrichs model is studied. Decoherence is found and decoherence characteristic times are computed.

Noisy quantum channels may be used in many information-carrying applications. We show that different applications may result in different channel capacities. Upper bounds on several of these capacities are proved. These bounds are based on the coherent information, which plays a role in quantum information theory analogous to that played by the mutual information in classical information theory. Many new properties of the coherent information and entanglement fidelity are proved. Two nonclassical features of the coherent information are demonstrated: the failure of subadditivity, and the failure of the pipelining inequality. Both properties arise as a consequence of quantum entanglement, and give quantum information new features not found in classical information theory. The problem of a noisy quantum channel with a classical observer measuring the environment is introduced, and bounds on the corresponding channel capacity proved. These bounds are always greater than for the unobserved channel. We conclude with a summary of open problems.

The interference pattern of the resonance fluorescence from a $J=1/2\mathrm{}$ to $J=1/2\mathrm{}$ transition of two identical atoms confined in a three-dimensional harmonic potential is calculated. The thermal motion of the atoms is included. Agreement is obtained with experiments [U. Eichmann et al., Phys. Rev. Lett. 70, 2359 (1993)]. Contrary to some theoretical predictions, but in agreement with the present calculations, a fringe visibility greater than 50% can be observed with polarization-selective detection. The dependence of the fringe visibility on polarization has a simple interpretation, based on whether or not it is possible in principle to determine which atom emitted the photon.

The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as strength and range. Shape-invariance algebras, in general, are shown to be infinite dimensional. The conditions under which they become finite dimensional are explored.

Explicit kinetic-energy density functionals for noninteracting electron systems that are based on reproducing the linear response function in the homogeneous limit are the most accurate approximations to the exact Kohn-Sham functional. In this work we study several such models for one-dimensional systems. In this case, the geometrical simplicity allows the calculation of the static linear response resulting from these functionals for inhomogeneous systems. Likewise, the discussion of the energies and density profiles obtained is easier and clearer than that for more realistic problems. Special attention is paid to the application of explicit kinetic energy functionals to systems with odd and noninteger number of particles.

An accurate finite-element method (FEM) is applied to solve the three-dimensional Schrödinger equation for the $S$ states of the $\mathrm{dt}\mu$ molecular ion. Using an adaptive refinement of the grid and higher-order polynomials the energy eigenvalues are obtained with a relative precision better than ${10}^{-11}.$ The deviation from the virial theorem, the two-body cusp ratios, and the expectation values $〈1/r〉,〈r〉,〈r^2〉,〈\delta \mathrm{}\left(r\right)\mathrm{}〉$ for the three interparticle distances are computed and discussed. The FEM values turn out to be comparable to results obtained with sophisticated global basis sets. Special local refinement techniques are applied to study the expectation values for the Dirac delta functions. New benchmark values for these local properties are presented.

We report measurements of the $5d{}^2{D}_{5/2},$ $5d{}^2{D}_{3/2},$ and $11s{}^2{S}_{1/2}$ state lifetimes in the ${}^{133}$Cs atom to be 1281(9), 909(15), and 351(4) ns, respectively. A pulsed-dye laser selectively excites atomic Cs from the ground state, via a single-photon quadrupole transition, to the $5d$ states and, via a two-photon electric dipole transition, to the $11s$ state. A spectrometer-photomultiplier system detects the fluorescence from the decay of interest and a digitizing oscilloscope records the direct output of the photomultiplier. The data are fit to an exponential function to yield a value for the mean lifetime of the selected state.

Spherically averaged center-of-mass-motion (extracule) densities $d\left(R\right)\mathrm{}$ in position space and $\overline{d}\mathrm{}\left(P\right)\mathrm{}$ in momentum space represent probability densities of finding center-of-mass radii $|{\mathbf{r}}_j+{\mathbf{r}}_k|/2\mathrm{}$ and $|{\mathbf{p}}_j+{\mathbf{p}}_k|/2\mathrm{}$ of any pair of electrons $j$ and $k$ to be $R$ and $P,$ respectively. Theoretical analysis shows that in the Hartree-Fock approximation, the individual spin-orbital-pair component of the extracule density has a definite relation with the corresponding one of the relative-motion (intracule) density, but the total extracule and intracule densities are not related in a simple manner. Using the numerical Hartree-Fock method, the extracule densities $d\left(R\right)\mathrm{}$ and $\overline{d}\mathrm{}\left(P\right)\mathrm{}$ are constructed and examined systematically for the atoms from He to Xe in their ground state. In position space, the extracule density $d\left(R\right)\mathrm{}$ is a monotonically decreasing function for all the atoms. In momentum space, however, the extracule densities $\overline{d}\mathrm{}\left(P\right)\mathrm{}$ are found to be classified into two types according to the location of a maximum. These different behaviors of the densities $d\left(R\right)\mathrm{}$ and $\overline{d}\mathrm{}\left(P\right)\mathrm{}$ are studied in detail based on the contributions of electrons in a pair of atomic subshells and spin orbitals.

The contracted Schrödinger equation (CSE) technique through its direct determination of the two-particle reduced density matrix (2RDM) without the wave function may offer a fresh alternative to traditional many-body quantum calculations. Without additional information the CSE, also known as the density equation, cannot be solved for the 2RDM because it also requires a knowledge of the 4RDM. We provide theoretical foundations through a reconstruction theorem for recent attempts at generating higher RDMs from the 2RDM to remove the indeterminacy of the CSE. With Grassmann algebra a more concise representation for Valdemoro’s reconstruction functionals [F. Colmenero, C. Perez del Valle, and C. Valdemoro, Phys. Rev. A 47, 971 (1993)] is presented. From the perspective of the particle-hole equivalence we obtain Nakatsuji and Yasuda’s correction for the 4RDM formula [H. Nakatsuji and K. Yasuda, Phys. Rev. Lett. 76, 1039 (1996)] as well as a corrective approach for the 3RDM functional. A different reconstruction strategy, the ensemble representability method (ERM), is introduced to build the 3- and 4-RDMs by enforcing four-ensemble representability and contraction conditions. We derive the CSE in second quantization without Valdemoro’s matrix contraction mapping and offer the first proof of Nakatsuji’s theorem for the second-quantized CSE. Both the functional and ERM reconstruction strategies are employed with the CSE to solve for the energies and the 2RDMs of a quasispin model without wave functions. We elucidate the iterative solution of the CSE through an analogy with the power method for eigenvalue equations. Resulting energies of the CSE methods are comparable to single-double configuration-interaction (SDCI) energies, and the 2RDMs are more accurate by an order of magnitude than those from SDCI. While the CSE has been applied to systems with 14 electrons, we present results for as many as 40 particles. Results indicate that the 2RDM remains accurate as the number of particles increases. We also report a direct determination of excited-state 2RDMs through the CSE. By circumventing the wave function, the CSE presents new possibilities for treating electron correlation.