Vortex-lattice structures of antiferromagnetic spinor Bose-Einstein condensates with hyperfine spin $F=1\mathrm{}$ are investigated theoretically based on the Ginzburg-Pitaevskii equations near $T_c.$ The Abrikosov lattice with clear core regions is never found to be stable at any rotation drive $\Omega .$ Instead, each component ${\Psi }_i(i=0,\pm 1)$ prefers to shift the core locations away from the others to realize almost uniform order-parameter amplitude with complicated magnetic-moment configurations. This system is characterized by many competing metastable structures so that quite a variety of vortices may be realized with a small change in external parameters.

We obtain the next-to-next-to-leading-logarithmic renormalization-group improvement of the spectrum of hydrogenlike atoms with massless fermions by using potential NRQED. These results can also be applied to the computation of the muonic hydrogen spectrum where we are able to reproduce some known double logarithms at $O\left(m{\alpha }_s^6\right).\mathrm{}$ We compare with other formalisms dealing with logarithmic resummation available in the literature.

A three-dimensional, fully correlated ab initio method for calculating the ionization rates and Stark shifts of molecular hydrogen oriented parallel to an external electric or low-frequency electromagnetic field is presented. With its aid, the occurrence of bond softening and enhanced ionization in ${\mathrm{H}}_2$ is investigated. Based on a simple quantum-mechanical explanation for those effects, their occurrence is also predicted for any neutral covalently bound molecule. The ab initio results are used to investigate the applicability of simpler numerical models for predicting those phenomena in larger molecules.

Ionization rates are calculated for molecular hydrogen oriented parallel to an external electric or low-frequency electromagnetic field using a three-dimensional, fully correlated ab initio method. The calculation includes also the range of field intensities where barrier suppression leads to over the barrier instead of tunneling ionization. The resulting ionization rates (considering also the influence of vibrational motion and excitation) are compared to those predicted by the (semiclassical) Ammosov-Delone-Krainov (ADK) model. In agreement with earlier findings for helium it is found that the ADK model predicts very accurately ionization rates in the tunneling regime, but overestimates the rate in the over-the-barrier regime. This conclusion is, however, only true, if the tunnel-ionization rate of ${\mathrm{H}}_2$ is (at least to a good approximation) isotropic.

We have performed a nonperturbative Floquet study of the angular distributions of the emitted electrons in the two-photon detachment of ${\mathrm{H}}^{-}$ driven by strong infrared laser fields. The external field parameters are chosen to correspond to the recent experiment by R. Reichle, H. Helm, and I. Yu. Kiyan, Phys. Rev. Lett. 87, 243001 (2001). We discuss the laser-frequency and -intensity effects on the shape of the angular distribution in the vicinity of the ionization threshold. We show that the angular distribution pattern can be interpreted in terms of the interference of the s and d partial waves in the final state and the Wigner threshold law.

The configuration-interaction (CI) method is used to investigate the interactions of positrons and positronium with copper at low energies. The calculations were performed within the framework of the fixed-core approximation with semiempirical polarization potentials used to model dynamical interactions between the active particles and the $(1s-3d)$ core. Initially, calculations upon the $e^{+}\mathrm{Li}$ system were used to refine the numerical procedures and highlighted the extreme difficulties of using an orthodox CI calculation to describe the $e^{+}$ Li system. The positron binding energy of $e^{+}\mathrm{Cu}$ derived from a CI calculation which included electron and positron orbitals with $\mathcal{l}<~18$ was 0.005 12 hartree while the spin-averaged annihilation rate was $0.507\times {10}^9{\mathrm{s}}^{-1}.$ The configuration basis used for the bound-state calculation was also used as a part of the trial wave function for a Kohn variational calculation of positron-copper scattering. The positron-copper system has a scattering length of about ${13.1a}_0$ and the annihilation parameter $Z_{\mathrm{eff}}$ at threshold was 72.9. The dipole polarizability of the neutral copper ground state was computed and found to be ${41.6a}_0^3.$ The structure of CuPs was also studied with the CI method and it was found to have a binding energy of 0.0143 hartree and an annihilation rate of $\sim 2\times {10}^9{\mathrm{s}}^{-1}.$

We present a theory of hysteretic phenomena in Bose gases, using superfluidity in one-dimensional rings and in optical lattices as primary examples. Through this study we are able to give a physical interpretation of swallow-tail loops recently found by many authors in the mean-field energy structure of trapped atomic gases. These loops are a generic sign of hysteresis, and in the present context are an indication of superfluidity. We have also calculated the rate of decay of metastable current-carrying states due to quantum fluctuations.

We consider the interaction of a three-level system with phase-modulated resonant fields in the Λ excitation scheme. We treat theoretically the case of a sinusoidal phase modulation, a phase step perturbation, and a stochastic phase modulation. The appearance of a Rabi resonance both in the spectrum of the optical transmitted signal (electromagnetically induced transparency) and in the spectrum of the microwave emission (coherent population trapping maser) is considered in detail. All the theoretical results are compared with the analogous ones reported for the two-level system and with our experimental observations obtained for the case of rubidium in a buffer gas.

We discuss the application of dipole blockade techniques for the preparation of single-atom and single-photon sources. A deterministic protocol is given for loading a single atom in an optical trap, as well as ejecting a controlled number of atoms in a desired direction. A single-photon source with an optically controlled beamlike emission pattern is described.

We report the measurement of the photoionization cross section for the ${5S}_{1/2}$ state of rubidium, using atoms confined in a magneto-optical trap. A single-photon rate at $\lambda =266\mathrm{}\mathrm{nm}$ was found by monitoring the decay of trap fluorescence after exposure to ionizing radiation from a quadrupled ${\mathrm{N}\mathrm{d}:\mathrm{Y}\mathrm{V}\mathrm{O}}_4$ laser. In order to eliminate excited-state ionization, the photoionization and trapping lasers were alternately chopped, so that only ground-state atoms were ionized. We determine that the photoionization cross section at $\lambda =266\mathrm{}\mathrm{nm}$ is $\sigma =1.7\mathrm{}\left(2\right)\mathrm{}\times {10}^{-20}{\mathrm{cm}}^2.$

The impact of control field fluctuations on the optimal manipulation of quantum dynamics phenomena is investigated. The quantum system is driven by an optimal control field, with the physical focus on the evolving expectation value of an observable operator. A relationship is shown to exist between the system dynamics and the control field fluctuations, wherein the process of seeking optimal performance assures an inherent degree of system robustness to such fluctuations. The presence of significant field fluctuations breaks down the evolution of the observable expectation value into a sequence of partially coherent robust steps. Robustness occurs because the optimization process reduces sensitivity to noise-driven quantum system fluctuations by taking advantage of the observable expectation value being bilinear in the evolution operator and its adjoint. The consequences of this inherent robustness are discussed in the light of recent experiments and numerical simulations on the optimal control of quantum phenomena. The analysis in this paper bodes well for the future success of closed-loop quantum optimal control experiments, even in the presence of reasonable levels of field fluctuations.

We derive ultracold atom-atom photoassociation line shapes valid for intense light fields and investigate laser power effects in sodium and rubidium photoassociation to the purely long-range $0_g^{-}$ symmetry state. We consider intensities up to a few hundreds ${\mathrm{W}/\mathrm{c}\mathrm{m}}^2,$ a strongly saturating intensity for typical transitions of experimental interest. For these intensities the $0_g^{-}$ rotational spectrum is still well resolved; however, it is essential to couple the photoassociation resonance to both s- and d-wave ground-state channels. A low-energy d-wave shape resonance can have a profound effect on the line shape. Understanding the line shape is essential for precision spectroscopic analysis and could improve the extraction of ground-state scattering properties such as scattering lengths.

Experiments in coherent spectroscopy correspond to control of quantum mechanical ensembles guiding them from initial to final target states by unitary transformations. The control inputs (pulse sequences) that accomplish these unitary transformations should take as little time as possible so as to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we present a novel approach for efficient control of dynamics in spin chains of arbitrary length. The approach relies on creating certain three spin encoded states, which can be efficiently transferred through a spin chain. The methods presented are expected to find applications in control of spin dynamics in coherent spectroscopy and quantum information processing.

We present a conditional quantum eraser that erases the a priori knowledge or the predictability of the path a photon takes in a Young-type double-slit experiment with two fluorescent four-level atoms. This erasure violates a recently derived erasure relation which must be satisfied for a conventional, unconditional quantum eraser that aims to find an optimal sorting of the system into subensembles with particularly large fringe visibilities. The conditional quantum eraser employs an interaction-free, partial which-way measurement which not only sorts the system into optimal subsystems with large visibility, but also selects the appropriate subsystem with the maximum possible visibility. We explain how the erasure relation can be violated under these circumstances.

The entanglement of excitonic states in a system of N spatially separated semiconductor microcrystallites is investigated. The interaction among the different microcrystallites is mediated by a single-mode cavity field. It is found that the symmetric sharing of the entanglement (measured by the concurrence) between any pair of the excitonic state with N qubits defined by the number states (vacuum and a single-exciton states) or the coherent states (odd and even coherent states) can be prepared by the cavity field for this system.

The entanglement in a pure state of N qudits (d-dimensional distinguishable quantum particles) can be characterized by specifying how entangled its subsystems are. A generally mixed subsystem of m qudits is obtained by tracing over the other $N-m$ qudits. We examine the entanglement in the space of mixed states of m qudits. We show that for a typical pure state of N qudits, its subsystems smaller than $N/3\mathrm{}$ qudits will have a positive partial transpose and hence are separable or bound entangled. Additionally, our numerical results show that the probability of finding entangled subsystems smaller than $N/3\mathrm{}$ falls exponentially in the dimension of the Hilbert space. The bulk of pure state Hilbert space thus consists of highly entangled states with multipartite entanglement encompassing at least a third of the qudits in the pure state.

For finite-dimensional bipartite quantum systems, we find the exact size of the largest balls, in spectral $l_p$ norms for $1<~p<~\infty ,$ of separable (unentangled) matrices around the identity matrix. This implies a simple and intuitively meaningful geometrical sufficient condition for separability of bipartite density matrices: that their purity $\mathrm{tr}{\rho }^2$ not be too large. Theoretical and experimental applications of these results include algorithmic problems such as computing whether or not a state is entangled, and practical ones such as obtaining information about the existence or nature of entanglement in states reached by nuclear magnetic resonance quantum computation implementations or other experimental situations.

We calculate the spectral line shape of an isolated line from first principles, assuming that the translational motion is not statistically correlated with the evolution of the optical coherence, i.e., with the broadening. We use the known, realistic potentials for the influence of collisions on the translational motion and on the internal motion. We show that the calculated profiles do not agree, particularly at low pressures, with very precise experimental profiles of the $P\left(2\right)\mathrm{}$ line of CO in a bath of Ar. We establish that the source of the disagreement lies in the assumption of uncorrelated effects of collisions on the translational motion and the optical coherence associated with the internal degrees of freedom.

Correlation energies and reduced density matrices (RDMs) of atoms and molecules are directly computed by solving the 1,3-contracted Schrödinger equation (1,3-CSE). The solution of the 1,3-CSE synthesizes two optimization strategies recently employed for the direct determination of the 2-RDM: (i) variational minimization of the energy with respect to a 2-RDM constrained by positivity conditions [D. A. Mazziotti, Phys. Rev. A $65,$ 062511 (2002)] and (ii) the contracted power method for solving the 2,4-CSE [D. A. Mazziotti, J. Chem. Phys. $116,$ 1239 (2002)]. While both the 3- and the 4-RDMs in the 2,4-CSE are reconstructed from the 2-RDM by cumulant expansions, similar techniques cannot be directly applied to the 1,3-CSE because constructing the 2-RDM from the 1-RDM with cumulant theory does not improve upon the mean-field approximation. We, however, establish a unique mapping from the 1-RDM to the 2-RDM by searching for the 2-RDM, constrained by contraction and N-representability conditions, which minimizes the energy. The 2-RDM constrained search is practically implemented through recent advances in positive semidefinite programming. With the variational reconstruction of the 2-RDM and a cumulant reconstruction of the 3-RDM, the 1,3-CSE may be solved via a contracted power method for the ground-state energy and RDMs. The initial RDMs, it is shown, need not be N representable for the contracted power method to converge; this allows us to choose the original RDMs from a variational calculation with approximate N-representability conditions on the 2-RDM. Application of the 1,3-CSE algorithm to atoms and molecules yields highly accurate correlation energies both near and far from equilibrium geometries.

Sympathetic cooling of ${\mathrm{Ca}}^{+},$ ${\mathrm{Zn}}^{+},$ ${\mathrm{Sr}}^{+},$ ${\mathrm{Ba}}^{+},$ and ${\mathrm{Yb}}^{+}$ as guest ions with laser-cooled ${}^{24}{\mathrm{Mg}}^{+}$ as host ions in a rf ion trap is carried out, and resonant frequencies of their motion in the trap potential are measured. Various oscillation modes of the sympathetically cooled ions are observed. The resonant frequency of the oscillation mode is different from the frequency of either the collective oscillation frequency of the trapped ions or the oscillation frequency of each ion without host ions. This difference is well explained by a theoretical model in which coupled equations of motion of the host ion cloud with a single guest ion are considered.