A study is made of low-energy electron-impact single ionization of ground-state helium. The time-dependent close-coupling method is used to calculate total integral, single differential, double differential, and triple differential ionization cross sections for impact electron energies ranging from 32 to $45\mathrm{eV}$. For all quantities, the calculated cross sections are found to be in very good agreement with experiment, and for the triple differential cross sections, good agreement is also found with calculations made using the convergent close-coupling technique.

We describe several routes to quantum degenerate gases based on simple schemes to efficiently load atoms into and evaporate them from a “dimple” crossed dipolar trap. The dimple is loaded nonadiabatically by collisions between atoms which are trapped in a reservoir which can be provided either by a dark spontaneous-force magneto-optical trap (MOT), the (aberrated) laser beam itself, or by a quadrupolar or quadratic magnetic trap. Optimal loading parameters for the dimple, relatively high temperature, and tight optical trap are derived from thermodynamic equations including possible inelastic and Majorana losses. Evaporative cooling is described by a set of simple equations, taking into account gravity, the possible occurrence of the hydrodynamical regime, Feshbach resonances, and three body recombination. The solution implies that to have efficient evaporation the elastic collisional rate (in ${\mathrm{s}}^{-1}$) must be on the order of the trap frequency and lower than 100 times the temperature in microkelvins. Following this approach Bose-Einstein condensates with more than ${10}^7$ atoms should be obtained in much less than $1\mathrm{s}$ starting from an ordinary MOT setup.

Recent developments in the field of ultracold gases has led to the production of degenerate samples of polar molecules. These have large static electric-dipole moments, which in turn causes the molecules to interact strongly. We investigate the interaction of polar particles in waveguide geometries subject to an applied polarizing field. For circular waveguides, tilting the direction of the polarizing field creates a periodic inhomogeneity of the interparticle interaction. We explore the consequences of geometry and interaction for stability of the ground state within the Thomas-Fermi model. Certain combinations of tilt angles and interaction strengths are found to preclude the existence of a stable Thomas-Fermi ground state. The system is shown to exhibit different behavior for quasi-one-dimensional and three-dimensional trapping geometries.

In this paper we formulate the time-dependent many-body theory of photoassociation in an atomic Bose-Einstein condensate with realistic interatomic interactions, using and comparing two approximations: the first-order cumulant approximation [Phys. Rev. A 65, 033601 (2002)], and the reduced pair wave approximation [Phys. Rev. A 68, 033612 (2003)]. The two approximations differ only by the way a pair of condensate atoms is influenced by the mean field at short interatomic separations. In both cases we identify two different regimes of photoassociation: the adiabatic regime and the coherent regime. The threshold for the so-called “rogue dissociation” [Phys. Rev. Lett. 88, 090403 (2002)] (where the Gross-Pitaevskiĭ model breaks down) is found to be different in each regime, shedding new light on the experiment of McKenzie et al. [Phys. Rev. Lett. 88, 120403 (2002)]. Comparing numerical solutions for the two approximations with the Gross-Pitaevskiĭ predictions, we find two different effects: reduction of the photoassociation rate at short times, and creation of correlated pairs of atoms when the laser intensity is switched on rapidly. We also observe effects on the symmetry of the photoassociation line shapes, giving the possibility to experimentally distinguish between the two approximations.

An analytical study of optically driven laser diodes (LDs) has been undertaken to meet the requirement for a theoretical treatment for chaotic drive and synchronization occurring in the injection-locked LDs with strong injection. A small-signal analysis is performed for the sets of rate equations for the injection-locked LDs driven by a sinusoidal optical signal. In particular, as a model of chaotic driving signals from LD dynamics, an optical signal caused by direct modulation to the master LD is assumed, oscillating both in field amplitude and phase as is the case with chaotic driving signals. Consequently, we find conditions that allow reduction in the degrees of freedom of the driven LD. Under these conditions, the driven response is approximated to a simple form which is found to be equivalent to driven damped linear oscillators. The validity of the application of this theory to previous work on the synchronization of chaos and related phenomena occurring in the injection-locked LDs is demonstrated.

We systematically study the interaction between two quantized optical fields and a cyclic atomic ensemble driven by a classic optical field. This so-called atomic cyclic ensemble consists of three-level atoms with $\Delta$-type transitions due to the symmetry breaking, which can also be implemented in the superconducting quantum circuit by Yu-xi Liu et al. [Phys. Rev. Lett. 95, 087001 (2005)]. We explore the dynamic mechanisms to creating the quantum entanglements among photon states, and between photons and atomic collective excitations by the coherent manipulation of the atom-photon system. It is shown that the quantum information can be completely transferred from one quantized optical mode to another, and the quantum information carried by the two quantized optical fields can be stored in the collective modes of this atomic ensemble by adiabatically controlling the classic field Rabi frequencies.

The fidelity for cloning coherent states is improved over that provided by optimal Gaussian and non-Gaussian cloners for the subset of coherent states that are prepared with known phases. Gaussian quantum cloning duplicates all coherent states with an optimal fidelity of $2∕3$. Non-Gaussian cloners give optimal single-clone fidelity for a symmetric 1-to-2 cloner of 0.6826. Coherent states that have known phases can be cloned with a fidelity of $4∕5$. The latter is realized by a combination of two beam splitters and a four-wave mixer operated in the nonlinear regime, all of which are realized by interaction Hamiltonians that are quadratic in the photon operators. Therefore, the known Gaussian devices for cloning coherent states are extended when cloning coherent states with known phases by considering a nonbalanced beam splitter at the input side of the amplifier.

It is shown that the Raabe and Welsch [Phys. Rev. A 71, 013814 (2005)] criticism of the Dzyaloshinskii-Lifshitz-Pitaevskii theory of the van der Waals–Casimir forces inside a medium is based on misunderstandings. It is explained why and at which conditions one can use the “Minkowski-like” stress tensor for calculations of the forces. The reason why, in my opinion, the approach of Raabe and Welsch is incorrect is discussed.

In this Reply to the preceding Comment [Phys. Rev. A 73, 047801 (2006)], we summarize and maintain our position that the Casimir force should be calculated on the basis of the Lorentz force.

It is shown that the kinetic-energy distribution of ions emerging from a cluster target irradiated by an intense laser pulse arises from three main effects: (1) the spatial profile of the laser beam, (2) the cluster size distribution in the experiment, and (3) possible saturation effects in the cluster ionization. Our model reveals that each of these effects leaves a characteristic fingerprint in the ion kinetic-energy spectrum. Moreover, it provides a quantitative link between observable ion spectra under experimental conditions and the ideal single-cluster result of a typical calculation.

We theoretically investigate the interaction of polar molecules with optical lattices and microwave fields. We demonstrate the existence of frequency windows in the optical domain where the complex internal structure of the molecule does not influence the trapping potential of the lattice. In such frequency windows the Franck-Condon factors are so small that near-resonant interaction of vibrational levels of the molecule with the lattice fields have a negligible contribution to the polarizability, and light-induced decoherences are kept to a minimum. In addition, we show that microwave fields can induce a tunable dipole-dipole interaction between ground-state rotationally symmetric $(J=0)$ molecules. A combination of a carefully chosen lattice frequency and microwave-controlled interaction between molecules will enable trapping of polar molecules in a lattice and possibly realize molecular quantum logic gates. Our results are based on ab initio relativistic electronic structure calculations of the polar KRb and RbCs molecules combined with calculations of their rovibrational motion.

We have measured the velocity field of a vortex lattice within a sodium Bose-Einstein condensate using Bragg scattering. The phase gradient of the macroscopic wave function was mapped into the spatial structure of the diffracted atom cloud, allowing for the single shot measurement of the rotation parameters. A combination of spectral and spatial information yields a complete description of the superfluid flow, coarse grained over the lattice structure, including direct and independent measurements of the rate and sense of rotation. Signatures of the microscopic quantum rotation have also been observed.

Breakup and recombination processes for loosely bound molecules composed of atoms with a large scattering length $a$ necessarily involve interactions that are nonperturbative in the exact two-body interaction. If these processes involve atoms with relative momenta much larger than $\hslash ∕\mid a\mid$, the leading contributions to their rates can be separated into short-distance factors that are insensitive to $a$ and long-distance factors that are insensitive to the range of the interaction. These factorization contributions can be obtained from the leading term in a perturbation expansion in the exact atom-atom scattering amplitude. The short-distance factors are atom-atom cross sections at a lower collision energy. In the special case of inclusive breakup cross sections for atom-molecule scattering, the long-distance factors simply count the number of atoms in the molecule.

The collision-induced (CI) first hyperpolarizability tensor for the $\mathrm{He}\text{−}\mathrm{Ne}$ pair composed of the lightest noble gas elements has been obtained on the grounds of an ab initio method as a function of the interatomic distance $R$. Collision-induced hyper-Rayleigh (CIHR) spectra scattered in mixtures of such atoms at temperatures of 95 and $295\mathrm{K}$ are computed in absolute units both quantum mechanically and classically for the frequency shifts up to $1000{\mathrm{cm}}^{-1}$. The spectral features of the CIHR profiles due to the vector $b_1$ and septor $b_3$ parts of the hyperpolarizability tensor are discussed. The quantum character of computed spectra, especially significant at lower temperatures, has been found out. The integrated intensities of the spectra have been evaluated and used as a criterion of the reliability of the computed profiles. The frequency-dependent depolarization ratio of the CIHR spectra was evaluated and discussed. The properties of the resulting HR profiles have been compared with the depolarized CI Rayleigh spectrum of the $\mathrm{He}\text{−}\mathrm{Ne}$ pair.

By using slave particle (slave boson and slave fermion) techniques on the Bose-Hubbard model, we study the finite temperature properties of ultracold Bose gases in optical lattices. The phase diagrams at finite temperature are depicted by including different types of slave particles and the effect of the finite types of slave particles is estimated. The superfluid density is evaluated using the Landau second order phase transition theory. The atom density, excitation spectrum, and dispersion curve are also computed at various temperatures, and how the Mott-insulator evolves as the temperature increases is demonstrated. For most quantities to be calculated, we find that there are no qualitative differences in using the slave boson or the slave fermion approaches. However, when studying the stability of the mean field state, we find that in contrast to the slave fermion approach, the slave boson mean field state is not stable. Although the slave boson mean field theory gives a qualitatively correct phase boundary, it corresponds to a local maximum of Landau free energy and cannot describe the second order phase transition because the coefficient $a_4$ of the fourth order term is always negative in the free energy expansion.

We study the ground-state properties of a trapped Bose-Einstein condensate with a neutral impurity. By varying the strength of the attractive atom-impurity interactions, the degree of localization of the impurity at the trap center can be controlled. As the impurity becomes more strongly localized, the peak condensate density, which can be monitored experimentally, grows markedly. For strong enough attraction, the impurity can make the condensate unstable by strongly deforming the atom density in the neighborhood of the impurity. This “collapse” can possibly be investigated in bosenova-type experiments.

A coupled-cluster approach for systems of $N$ bosons in external traps is developed. In the coupled-cluster approach the exact many-body wave function is obtained by applying an exponential operator $\exp \left\{T\right\}$ to the ground configuration $\mid {\varphi }_0⟩$. The natural ground configuration for bosons is, of course, when all reside in a single orbital. Because of this simple structure of $\mid {\varphi }_0⟩$, the appearance of excitation operators $T={\sum }_{n=1}^N{T}_n$ for bosons is much simpler than for fermions. We can treat very large numbers of bosons with coupled-cluster expansions. In a substantial part of this work, we address the issue of size consistency for bosons and enquire whether truncated coupled-cluster expansions are size consistent. We show that, in contrast to the familiar situation for fermions for which coupled-cluster expansions are size consistent, for bosons the answer to this question depends on the choice of ground configuration. Utilizing the natural ground configuration, working equations for the truncated coupled-cluster with $T=T_1+T_2$, i.e., coupled-cluster singles doubles are explicitly derived. Finally, an illustrative numerical example for a condensate with up to $N=10000$ bosons in an harmonic trap is provided and analyzed. The results are highly promising.

The electron impact dissociative double-ionization cross sections for ${\mathrm{H}}_2\mathrm{O}$ between 45 and $1500\mathrm{eV}$ have been measured using time of flight mass spectrometry. The energy dependence of the ${\mathrm{H}}^{+}+\mathrm{O}{\mathrm{H}}^{+}$ and ${\mathrm{H}}^{+}+{\mathrm{O}}^{+}$ ion pair production cross sections indicate that Auger-like autoionization following a vacancy in the $2a_1$ molecular orbital is the main double ionization channel at high velocities. In contrast to expectation, these findings show that dissociation through the ${\mathrm{H}}_2{\mathrm{O}}^{2+}$ precursor state is a significant process at high collision energies. Knowledge of this process is vital as it has a direct affect on the production of important molecular species, such as ${\mathrm{H}}_2$, during water radiolysis. Branching ratios of the various fragments produced following both autoionization and double ionization have also been obtained.

We perform extensive magnetic Feshbach spectroscopy of an ultracold mixture of fermionic ${}^{40}\mathrm{K}$ and bosonic ${}^{87}\mathrm{Rb}$ atoms. The magnetic-field locations of 13 interspecies resonances are used to construct a quantum collision model able to predict accurate collisional parameters for all $\mathrm{K}\text{−}\mathrm{Rb}$ isotopic pairs. In particular, we determine the interspecies $s$-wave singlet and triplet scattering lengths for the ${}^{40}\mathrm{K}\text{−}{}^{87}\mathrm{Rb}$ mixture as $(-108\pm 3)a_0$ and $(-205\pm 5)a_0$, respectively. We also predict accurate scattering lengths and the position of Feshbach resonances for the other $\mathrm{K}\text{−}\mathrm{Rb}$ isotopic pairs. We discuss the consequences of our results for current and future experiments with ultracold $\mathrm{K}\text{−}\mathrm{Rb}$ mixtures.