We investigate the superfluid–Mott-insulator quantum phase transition of spin-1 bosons in an optical lattice created by pairs of counterpropagating linearly polarized laser beams, driving an $F_g=1$ to $F_e=1$ internal atomic transition. The whole parameter space of the resulting two-component Bose-Hubbard model is studied. We find that the phase transition is not always second order as in the case of spinless bosons, but can be first order in certain regions of the parameter space. The calculations are done in the mean-field approximation by means of exact numerical diagonalization as well as within the framework of perturbation theory.

We consider the photoassociation of a low-density gas of quantum-degenerate trapped fermionic atoms into bosonic molecules in a spherically symmetric harmonic potential. For a dilute system and the photoassociation coupling energy small compared to the level separation of the trap, only those fermions in the single shell with Fermi energy are coupled to the bosonic molecular field. Introducing a collective pseudospin operator formalism we show that this system can then be mapped onto the Tavis-Cummings Hamiltonian of quantum optics, with an additional pairing interaction. By exact diagonalization of the Hamiltonian, we examine the ground state and low excitations of the Bose-Fermi system, and study the dynamics of the coherent coupling between atoms and molecules. In a semiclassical description of the system, the pairing interaction between fermions is shown to result in a self-trapping transition in the photoassociation, with a sudden suppression of the coherent oscillations between atoms and molecules. We also show that the full quantum dynamics of the system is dominated by quantum fluctuations in the vicinity of the self-trapping solution.

The phase matching for the nonlinear process of frequency-degenerated spontaneous parametric downconversion in tunneling-coupled channel waveguides is analyzed. The use of type II nonlinear interaction with individual photons in each pair appearing in different output channels allows for constructing polarization entangled states for quantum information processing applications.

Two methods for creating arbitrary two-photon polarization pure states are introduced. Based on these, four schemes for creating two-photon polarization mixed states are proposed and analyzed. The first two schemes can synthesize completely arbitrary two-qubit mixed states, i.e., control all 15 free parameters: scheme I requires several sets of crystals, while scheme II requires only a single set, but relies on decohering the pump beam. Additionally, we describe two further schemes which are much easier to implement. Although the total capability of these is still being studied, we show that they can synthesize all two-qubit Werner states, maximally entangled mixed states, Collins-Gisin states, and arbitrary Bell-diagonal states.

Besides the traditional circuit-based model of quantum computation, several quantum algorithms based on a continuous-time Hamiltonian evolution have recently been introduced, including for instance continuous-time quantum walk algorithms as well as adiabatic quantum algorithms. Unfortunately, very little is known today about the behavior of these Hamiltonian algorithms in the presence of noise. Here, we perform a fully analytical study of the resistance to noise of these algorithms using perturbation theory combined with a theoretical noise model based on random matrices drawn from the Gaussian orthogonal ensemble, whose elements vary in time and form a stationary random process.

Four basis vectors of the Hilbert space of two qubits have the property that if three of them are product states, then the fourth one has to be a product state as well. We address the following situation: Consider a set of orthogonal vectors, each exhibiting a certain degree of entanglement. What is the bound on entanglement of the rest of the basis vectors to form a complete orthonormal basis? Specifically, we present an orthonormal basis, the $\Xi$ basis in the Hilbert space of two qubits, with one product state and three equally entangled states. The maximum of the so available entanglement is quantified. A close-to-optimal protocol is presented for entanglement purification via entanglement swapping of two-qubit states. It is based on a suitably chosen nonmaximally entangled basis and carried out in a single step without any ancillas. A similar application of the $\Xi$ basis is examined. In this latter case, all the involved entangled states have different and nonorthogonal Schmidt decompositions and, except for some possibly resulting states, none of them are maximally entangled. Entanglement of single pair purification is not conserved on average in this case.

A necessary and sufficient condition for one-distillability is formulated in terms of decomposable positive maps. As an application we provide insight into why all states violating the reduction criterion map are distillable and demonstrate how to construct such maps in a systematic way. We establish a connection between a number of existing results, which leads to an elementary proof for the characterization of distillability in terms of two-positive maps.

The $(e^{-},e^{+})$-pair annihilation is considered in the positron-helium $e^{+}\left[\mathrm{He}\left(2{}^{3}S\right)\right]$ four-body ion, in which the positron forms a bound state with the helium atom in its lowest triplet state [i.e., in the $2{}^{3}S(L=0)$ state]. A number of bound-state properties of this system have been determined for the $e^{+}\left[\mathrm{He}\left(2{}^{3}S\right)\right]$ ions, where the ${}^{\infty }\mathrm{He}$, ${}^4\mathrm{He}$, and ${}^3\mathrm{He}$ helium nuclei are considered. Some applications related to the positron annihilation in the $e^{+}\left[\mathrm{He}\left(2{}^{3}S\right)\right]$ ion are also discussed.

Time-dependent density-functional theory (TDDFT) employing the exact-exchange functional has been formulated on the basis of the optimized-effective-potential (OEP) method of Talman and Shadwick for second-order molecular properties and implemented into a Gaussian-basis-set, trial-vector algorithm. The only approximation involved, apart from the lack of correlation effects and the use of Gaussian-type basis functions, was the consistent use of the adiabatic approximation in the exchange kernel and in the linear response function. The static and dynamic polarizabilities and their anisotropy predicted by the TDDFT with exact exchange (TDOEP) agree accurately with the corresponding values from time-dependent Hartree-Fock theory, the exact-exchange counterpart in the wave function theory. The TDOEP is free from the nonphysical asymptotic decay of the exchange potential of most conventional density functionals or from any other manifestations of the incomplete cancellation of the self-interaction energy. The systematic overestimation of the absolute values and dispersion of polarizabilities that plagues most conventional TDDFT cannot be seen in the TDOEP.

The Lamb shift in muonic hydrogen continues to be a subject of experimental and theoretical investigation. Here my older work on the subject is updated to provide a complementary calculation of the energies of the $2p\text{−}2s$ transitions in muonic hydrogen.

The experimental and theoretical ratios of the generalized oscillator strength (GOS) for valence excitations of Ne, Ar, and Kr are presented. The excitation selectivity for fast electron impact is elucidated: the $LS$ coupling singlet nature of the ground state selects the $LS$ coupling singlet components from the intermediate coupling wave function of the excited state. According to this rule, the GOS’s for some unresolved transitions were determined. Furthermore, this work provides an experimental method to determine the intermediate coupling coefficients of singlet components.

We present ab initio calculations of multiphoton ionization cross sections—up to four—in atomic magnesium. We have followed a configuration interaction approach with the basis set constructed in terms of ${\mathrm{L}}^2$ integrable B-spline polynomials. The multiphoton ionization cross sections are given for a range of photon energies where the ion is left in its ground state. For the two-photon ionization process we calculate the cross section as a function of the photon energy and compare with known theoretical results. We also provide the corresponding angular asymmetry parameters which determine the angular distribution of the ionized electron. We have extended the energy range of reported theoretical three-photon ionization cross section while we present the four-photon cross section in the region between the 3s and 3p ionization thresholds. In this region the $3p^2{}^{1}S$ autoionizing state is identified through the four-photon absorption process and the related four-photon Fano q parameter is obtained.

The process of strong-field photodetachment of an atomic negative ion is considered with a simple analytical account for the ac dipole moment induced in the atomic core by the external laser field. The method is based on a Keldysh-like saddle-point theory, modified by using dipole-spherical angular wave functions in the initial state of the outer electron. The field-induced dipole results in an increase of the detachment rate and essential modifications in its angular dependence. These modifications are interpreted as destruction of the quantum interference originated from the coherent superposition of the two saddle-point contributions to the transition amplitude.

We calculate the momentum distribution and the second-order correlation function in momentum space, $g^{\left(2\right)}(\mathbf{p},{\mathbf{p}}^{\prime },t)$ for molecular dimers that are coherently formed from an ultracold atomic gas by photoassociation or a Feshbach resonance. We investigate using perturbation theory how the quantum statistics of the molecules depend on the initial state of the atoms by considering three different initial states: a Bose-Einstein condensate (BEC), a normal Fermi gas of ultracold atoms, and a BCS-type superfluid Fermi gas. The cases of strong and weak coupling to the molecular field are discussed. It is found that BEC and BCS states give rise to an essentially coherent molecular field with a momentum distribution determined by the zero-point motion in the confining potential. On the other hand, a normal Fermi gas and the unpaired atoms in the BCS state give rise to a molecular field with a broad momentum distribution and thermal number statistics. It is shown that the first-order correlations of the molecules can be used to measure second-order correlations of the initial atomic state.

All Bloch states of the mean field of a Bose-Einstein condensate in the presence of a one-dimensional lattice are presented in closed analytic form. The band structure is investigated by analyzing the stationary states of the nonlinear Schrödinger, or Gross-Pitaevskii, equation for both repulsive and attractive condensates. The appearance of swallowtails in the bands is examined and interpreted in terms of the condensates superfluid properties. The nonlinear stability properties of the Bloch states are described and the stable regions of the bands and swallowtails are mapped out. We find that the Kronig-Penney potential has the same properties as a sinusoidal potential. Bose-Einstein condensates are trapped in sinusoidal optical lattices. The Kronig-Penney potential has the advantage of being analytically tractable, unlike the sinusoidal potential, and, therefore, serves as a good model for understanding experimental phenomena.

We investigate theoretically the optical properties of an atomic gas that has been cooled by the laser cooling method of velocity-selective coherent population trapping. We demonstrate that the application of a weak laser pulse gives rise to a backscattered pulse, which is a direct signal for the entanglement in the atomic system, and which leads to single-particle entanglement on the few-photon level. If the pulse is applied together with the pump lasers, it also displays the phenomenon of electromagnetically induced transparency. We suggest that the effect should be observable in a gas of rubidium atoms.

We consider a composite particle formed by two fermions or two bosons. We discover that composite behavior is closely related to the quantum entanglement between the constituent particles. By analyzing the properties of creation and annihilation operators, we show that bosonic character emerges if the constituent particles become strongly entangled. Such a connection is demonstrated explicitly in a class of two-particle wave functions.

We propose a scheme to generate a supersinglet of three three-level atoms in microwave cavity quantum electrodynamics based on the resonant atom-cavity interaction. In the scheme, three three-level atoms in suitable initial states are sequentially sent through three cavities originally prepared in their vacuum states. After an appropriate atom-cavity interaction process, in the subsequent measurement on the third cavity field the atoms are projected onto the desired supersinglet. The practical feasibility of this method is discussed.

Typically linear optical quantum computing (LOQC) models assume that all input photons are completely indistinguishable. In practice there will inevitably be nonidealities associated with the photons and the experimental setup which will introduce a degree of distinguishability between photons. We consider a nondeterministic optical controlled-NOT gate, a fundamental LOQC gate, and examine the effect of temporal and spectral distinguishability on its operation. We also consider the effect of utilizing nonideal photon counters, which have finite bandwidth and time response.

We use a disordered antiferromagnetic spin-$1∕2$ chain with anisotropic exchange coupling to model an array of interacting qubits. All qubits have the same level spacing, except two, which are called the defects of the chain. The level spacings of the defects are equal and much larger than all the others. We investigate how the entanglement between the two defects depends on the anisotropy of the system. When the anisotropy coupling is much larger than the energy difference between a defect and an ordinary qubit, the two defects become strongly entangled. Small anisotropies, on the contrary, may decrease the entanglement, which is, in this case, also much affected by the number of excitations. The analysis is made for nearest-neighbor and next-nearest-neighbor defects. The decrease in the entanglement for nearest neighbor defects is not very significant, especially in large chains.