In this paper we present an analysis of how matter waves, guided as propagating modes in potential structures, are split under adiabatic conditions. The description is formulated in terms of localized states obtained through a unitary transformation acting on the mode functions. The mathematical framework results in coupled propagation equations that are decoupled in the asymptotic regions as well before as after the split. The resulting states have the advantage of describing propagation in situations, for instance matter-wave interferometers, where local perturbations make the transverse modes of the guiding potential unsuitable as a basis. The different regimes of validity of adiabatic propagation schemes based on localized versus delocalized basis states are also outlined. Nontrivial dynamics for superposition states propagating through split potential structures is investigated through numerical simulations. For superposition states the influence of longitudinal wave-packet extension on the localization is investigated and shown to be accurately described in quantitative terms using the adiabatic formulations presented here.

In this paper, properties of a homogeneous Bose gas with a Feshbach resonance are studied in the dilute region at zero temperature. The stationary state contains condensations of atoms and molecules. The ratio of the molecule density to the atom density is $\pi {\mathrm{na}}^3.$ There are two types of excitations, molecular excitations and atomic excitations. Atomic excitations are gapless, consistent with the traditional theory of a dilute Bose gas. The molecular excitation energy is finite in the long-wavelength limit as observed in recent experiments on ${}^{85}\mathrm{Rb}.$ In addition, the decay process of the condensate is studied. The coefficient of the three-body recombination rate is about 140 times larger than that of a Bose gas without a Feshbach resonance, in reasonably good agreement with the experiment on ${}^{23}\mathrm{Na}.$

We consider dynamics of boson condensates in finite optical lattices under a slow external perturbation which brings the system to the unstable equilibrium. It is shown that quantum fluctuations drive the condensate into the maximally entangled state. We argue that the truncated Wigner approximation being a natural generalization of the Gross-Pitaevskii classical equations of motion is adequate to correctly describe the time evolution including both collapse and revival of the condensate.

We investigate a gas of superfluid fermionic atoms trapped in two hyperfine states by a spherical harmonic potential. We propose a regularization method to remove the ultraviolet divergence in the Hartree-Fock-Bogoliubov equations caused by the use of a zero-range atom-atom interaction. Compared with a method used in the literature, our method is simpler and has improved convergence properties. Then we compare Hartree-Fock-Bogoliubov calculations with the semiclassical local-density approximation. We observe that for systems containing a small number of atoms shell effects, which cannot be reproduced by the semiclassical calculation, are very important. For systems with a large number of atoms at zero temperature, the two calculations are in quite good agreement, which, however, is deteriorated at nonzero temperature, especially near the critical temperature. In this case, the different behavior can be explained within the Ginzburg-Landau theory.

We describe a very simple physical model that allows the analysis of high-order harmonic generation in gases when the pumping laser beam has an intensity profile that is not Gaussian but truncated Bessel. This is the typical experimental condition when sub-10-fs pump-laser pulses, generated by the hollow fiber compression technique, are used. This model is based on the analysis of the phase-matching conditions for the harmonic generation process revisited in view of the new spatial mode of the fundamental beam. In particular, the role of the atomic dipole phase and the geometric phase terms are evidenced both for harmonics generated in the plateau and in the cutoff spectral regions. The influence of dispersion introduced by free electrons produced by laser ionization has also been discussed in some detail. Spatial patterns of far-field harmonics are then obtained by means of a simplified algorithm which allows one to avoid the numerical integration of the harmonic beam propagation equation. Experimental spatial distributions and divergence angles of high-order harmonics generated in Ne with 7-fs titanium-sapphire pulses are compared with numerical simulations in various experimental conditions. The agreement between measurements and calculated results is found to be very satisfactory.

The fundamental principles of complementarity and uncertainty are shown to be related to the possibility of joint unsharp measurements of pairs of noncommuting quantum observables. A joint measurement scheme for complementary observables is proposed. The measured observables are represented as positive operator valued measures (POVMs), whose intrinsic fuzziness parameters are found to satisfy an intriguing pay-off relation reflecting the complementarity. At the same time, this relation represents an instance of a Heisenberg uncertainty relation for measurement imprecisions. A model-independent consideration shows that this uncertainty relation is logically connected with the joint measurability of the POVMs in question.

The van der Waals coefficients for positronium interactions with a number of rare gases (He, Ne, Ar, Kr, and Xe) and alkali-metal atoms (Li, Na, K, and Rb) are estimated using a variety of ab initio and semiempirical methods. Dispersion coefficients are also presented for atomic hydrogen and a number of rare-gas and alkali-metal atoms for validation purposes.

We investigate the stability of dark solitons (DSs) in an effectively one-dimensional Bose-Einstein condensate in the presence of the magnetic parabolic trap and an optical lattice (OL). The analysis is based on both the full Gross-Pitaevskii equation and its tight-binding approximation counterpart (discrete nonlinear Schrödinger equation). We find that DSs are subject to weak instabilities with an onset of instability mainly governed by the period and amplitude of the OL. The instability, if present, sets in at large times and it is characterized by quasiperiodic oscillations of the DS about the minimum of the parabolic trap.

In secret sharing protocols, a secret is to be distributed among several partners such that leaving out any number of them, the rest do not have the complete information. Strong multiqubit correlations in the state by which secret sharing is carried out had been proposed as a criterion for security of such protocols against individual attacks by an eavesdropper. However we show that states with weak multiqubit correlations can also be used for secure secret sharing. That our state has weak multiqubit correlations is shown from the perspective of violation of local realism, and also by showing that its higher-order correlations are described by lower ones. We then present a unified criterion for security of secret sharing in terms of violation of local realism, which works when the secret sharing state is the Greenberger-Horne-Zeilinger state (with strong multiqubit correlations), as well as states of a different class (with weak multiqubit correlations).

Structural isomerization dynamics of three- and four-atom clusters of vanishing total angular momentum is studied in terms of internal coordinates of n-body systems on the basis of a gauge theory. The so-called principal-axis hyperspherical coordinates are employed effectively as collective variables for the study of isomerization reactions. It turns out that the non-Euclidean metric on the internal space gives rise to a force, which works in response to internal motions called the democratic (kinematic) rotations in the internal space. This metric force generally tends to induce an asymmetry in mass balance of a system, and is coupled with the usual potential force to give rise to trapped motions in the vicinity of the transition states of the cluster. This observation provides a different perspective for the so-called recrossing problem in chemical reaction dynamics.

Absolute total cross sections (TCSs) for 0.6–370 eV electrons scattered by tetrafluoroethylene $\left({\mathrm{C}}_2{\mathrm{F}}_4\right)$ molecules have been measured using a linear transmission method. The TCS energy function for ${\mathrm{C}}_2{\mathrm{F}}_4$ shows one very broad enhancement with the maximum value of $30\times {10}^{-20}{\mathrm{m}}^2$ located around 30 eV. On the low-energy slope of the TCS curve some weak features near 2.8, 9.5, and 16 eV are discernible. Above 50 eV the present TCS agrees well with theoretical predictions. Absolute TCS for ethylene $\left({\mathrm{C}}_2{\mathrm{H}}_4\right)$ has also been measured and compared with the TCS for ${\mathrm{C}}_2{\mathrm{F}}_4.$ Effect of substitution of fluorine atoms for hydrogen (perfluorination effect) was indicated and discussed. The reported TCS for ${\mathrm{C}}_2{\mathrm{H}}_4$ is distinctly higher than experimental data existing so far.

We present a scheme to generate arbitrary superpositions of Dicke states of excitons in optically driven quantum dots. The proposal is based on a sequence of laser pulses to control transitions between the nearest-neighbor Dicke states appropriately. It is shown that only N laser pulses are needed to generate arbitrary superpositions of Dicke states of N quantum dots.

Unentangled pure states on a bipartite system are exactly the coherent states with respect to the group of local transformations. What aspects of the study of entanglement are applicable to generalized coherent states? Conversely, what can be learned about entanglement from the well-studied theory of coherent states? With these questions in mind, we characterize unentangled pure states as extremal states when considered as linear functionals on the local Lie algebra. As a result, a relativized notion of purity emerges, showing that there is a close relationship between purity, coherence, and (non)entanglement. To a large extent, these concepts can be defined and studied in the even more general setting of convex cones of states. Based on the idea that entanglement is relative, we suggest considering these notions in the context of partially ordered families of Lie algebras or convex cones, such as those that arise naturally for multipartite systems. The study of entanglement includes notions of local operations and, for information-theoretic purposes, entanglement measures and ways of scaling systems to enable asymptotic developments. We propose ways in which these may be generalized to the Lie-algebraic setting and, to a lesser extent, to the convex-cones setting. One of our motivations for this program is to understand the role of entanglementlike concepts in condensed matter. We discuss how our work provides tools for analyzing the correlations involved in quantum phase transitions and other aspects of condensed-matter systems.

The $K{\beta }_2$ x-ray spectra of zirconium, niobium, molybdenum, and palladium targets bombarded with 20.8-MeV/amu ${}^{12}\mathrm{C}$ ions were measured with a high-resolution transmission-type bent crystal spectrometer. Well resolved $M^1$ and $M^2$ satellite lines were observed. Average M-shell and $3s,p-$ and $3d$-subshell ionization probabilities for nearly central collisions were deduced. These values are compared with theoretical predictions from the semiclassical approximation using hydrogenlike and Dirac-Hartree-Fock wave functions. The experimental energy shifts of the $K{\beta }_2{M}^{m=1,2\mathrm{}}$ satellite lines are compared with values obtained from extensive multiconfiguration Dirac-Fock calculations.

We present a method of direct estimation of important properties of a shared bipartite quantum state, within the “distant laboratories” paradigm, using only local operations and classical communication. We apply this procedure to spectrum estimation of shared states, and locally implementable structural physical approximations to incompletely positive maps. This procedure can also be applied to the estimation of channel capacity and measures of entanglement.

We discuss some systematic methods for implementing state manipulations in systems formally similar to chains of a few spins with nearest-neighbor interactions, arranged such that there are strong and weak scales of coupling links. States are permuted by means of bias potentials applied to a few selected sites. This generic structure is then related to an atoms-in-a-cavity model that has been proposed in the literature as a way of achieving a decoherence-free subspace. A method using adiabatically varying laser detuning to implement a controlled NOT gate in this model is proposed.

We here report on the optical pumping of both ${}^{14}\mathrm{NH}$ and ${}^{15}\mathrm{NH}$ radicals from the metastable $a{}^1\Delta$ state into the $X{}^3{\Sigma }^{-}$ ground state in a molecular beam experiment. By inducing the hitherto unobserved spin-forbidden $A{}^3\Pi \leftarrow a{}^1\Delta$ transition, followed by spontaneous emission to the $X{}^3{\Sigma }^{-}$ state, a unidirectional pathway for population transfer from the metastable state into the electronic ground state is obtained. The optical pumping scheme demonstrated here opens up the possibility to accumulate NH radicals in a magnetic or optical trap.

Efforts to provide accurate atomic collisional data for use in fusion plasma models have been extended to provide electron-impact ionization cross sections for all stages of beryllium. Ionization cross sections are presented from the ground and first excited states of Be, ${\mathrm{Be}}^{+},$ ${\mathrm{Be}}^{2+},$ and ${\mathrm{Be}}^{3+}.$ For all cases, two perturbative distorted-wave methods are used to calculate the ionization cross section. For Be, ${\mathrm{Be}}^{+},$ and ${\mathrm{Be}}^{2+},$ the nonperturbative time-dependent close-coupling and the R matrix with pseudostates methods are used to calculate the ionization cross sections. R matrix with pseudostates calculations are also presented for ${\mathrm{Be}}^{3+}.$ In general, the two nonperturbative methods are in good agreement with each other for electron-impact ionization of Be, ${\mathrm{Be}}^{+},$ and ${\mathrm{Be}}^{2+}.$ Furthermore, for ionization from the ground and the first excited states of Be and the first excited state of ${\mathrm{Be}}^{+},$ the perturbative distorted-wave calculations are significantly higher than the nonperturbative calculations. The atomic level resolved rate coefficients generated in this work have been archived and will be used to increase the accuracy of collisional-radiative modeling for beryllium.

The experimental three-atom recombination coefficients of the atomic states ${}^{23}\mathrm{Na}|{F=1,m}_F=-1〉,$ ${}^{87}\mathrm{Rb}|{F=1,m}_F=-1〉,$ and ${}^{85}\mathrm{Rb}|{F=2,m}_F=-2〉,$ together with the corresponding two-body scattering lengths, allow predictions of the trimer bound-state energies for such systems in a trap. The recombination parameter is given as a function of the weakly bound trimer energies, which are in the interval $1<m(a/ħ{)}^2{E}_3<6.9\mathrm{}$ for large positive scattering lengths $a.\mathrm{}$ The contribution of a deep-bound state to our prediction, in the case of ${}^{85}\mathrm{Rb}|{F=2,m}_F=-2〉,$ for a particular trap, is shown to be relatively small.

When a strong attosecond laser pulse acts simultaneously with a fast ionic projectile, the electronic response of an atom changes and leads to a drastic change in the final momenta, which may be observed in recoil-ion momentum experiments. The nonlinear response to the combined fields leads in certain cases to ionization probabilities more than three times larger than the probabilities by either of the two fields individually. The results are based on an algorithm for accurate solution of the time-dependent Schrödinger equation in three dimensions, which has the property that it requires CPU time comparable with that of two-dimensional methods.