Nonisotropic attractive Bose-Einstein condensates are investigated numerically with Newton and inverse Arnoldi methods. The stationary solutions of the Gross-Pitaevskii equation and their linear stability are computed. Bifurcation diagrams are calculated and used to find the condensate decay rates corresponding to macroscopic quantum tunneling, two-three-body inelastic collisions, and thermally induced collapse. Isotropic and nonisotropic condensates are compared. The effect of anisotropy on the bifurcation diagram and the decay rates is discussed. Spontaneous isotropization of the condensates is found to occur. The influence of isotropization on the decay rates is characterized near the critical point.

We consider momentum transfer using frequency-chirped standing-wave fields. Atom-beam splitter and mirror schemes based on Bragg scattering are presented. It is shown that a predetermined number of photon momenta can be transferred to the atoms in a single interaction zone.

The stability of doubly quantized vortices in dilute Bose-Einstein condensates of ${}^{23}\mathrm{Na}$ is examined at zero temperature. The eigenmode spectrum of the Bogoliubov equations for a harmonically trapped cigar-shaped condensate is computed and it is found that the doubly quantized vortex is spectrally unstable towards division into two singly quantized vortices. By numerically solving the full three-dimensional time-dependent Gross-Pitaevskii equation, it is found that the two singly quantized vortices intertwine before decaying. This work provides an interpretation of recent experiments [A. E. Leanhardt et al., Phys. Rev. Lett. 89, 190403 (2002)].

We investigate quantum dynamical properties of a trapped three-level ion interacting with two laser beams in $\Lambda$ configuration. A unitary transformation method is developed to study the interaction of the ion with its vibrational phonons, quanta of ion’s own center-of-mass motion. Under certain conditions on laser parameters, this interaction is shown to be unitarily equivalent to two-phonon cascade transitions. Complicated temporal behaviors of level populations and mean number of phonons are described clearly by identifying dynamical variables of the cascade model as building blocks. Furthermore, analyzing quantum states of vibrational phonons by Husimi-$Q$ function, we find that at times, determined by the underlying cascade dynamics, two- and three-component macroscopic quantum superposition states can be obtained depending on the Lamb-Dicke parameter and the initial conditions of the system. A wide range of initial conditions and experimental parameters are discussed using both exact and analytical solutions. Alternative routes to reach the target states are found.

By using the Hartree-Fock-Bogoliubov equations within the Popov approximation, we investigate the thermodynamic properties of a dilute binary Bose-Fermi mixture confined in an isotropic harmonic trap. For mixtures with an attractive Bose-Fermi interaction, we find a sizable enhancement of the condensate fraction and of the critical temperature of Bose-Einstein condensation with respect to the predictions for a pure interacting Bose gas. Conversely, the influence of the repulsive Bose-Fermi interaction is less pronounced. The possible relevance of our results in current experiments on trapped ${}^{87}\mathrm{Rb}{-}^{40}\mathrm{K}$ mixtures is discussed.

Doubly differential electron velocity spectra induced by 95-MeV/u ${}^{36}{\mathrm{Ar}}^{18+}$ from thin carbon foils were measured at GANIL (Caen, France) by means of the ARGOS multidetector and the time-of-flight technique. The spectra allow us to determine absolute singly differential cross sections as a function of the emission angle. Absolute doubly differential cross sections for binary encounter electron ejection from C targets are compared to a transport theory, which is based on the relativistic electron impact approximation for electron production and which accounts for angular deflection, energy loss, and also energy straggling of the transmitted electrons. For the thinnest targets, the measured peak width is in good agreement with experimental data obtained with a different detection technique. The theory underestimates the peak width but provides (within a factor of 2) the correct peak intensity. For the thickest target, even the peak shape is well reproduced by theory.

The formal theory of atomic ionization by electron impact relates the breakup amplitude to an integral expression involving the exact wave function and an unperturbed final state that contains two Coulomb functions with effective, noninteger charges. This integral expression has an associated phase factor that diverges logarithmically on an infinite volume unless the effective charges are chosen to satisfy a kinematic relationship, the so-called “Peterkop condition.” We derive the explicit form of the Peterkop phase for two commonly used models of electron-hydrogen ionization, the Temkin-Poet model and the collinear model. We show that the formal theory can be used to identify and remove this physically insignificant, volume-dependent phase from amplitudes computed using numerically stable integral expressions that do not satisfy the Peterkop condition.

According to quantum collision theory, scattering amplitudes are complex numbers, which are completely defined by their magnitude and phase. Although the phase information is generally not determined entirely in collision experiments, the phases are well defined and can be used to check computational models. We use four state-of-the-art approaches to calculate the magnitude and phase of the electron-hydrogen ionization amplitude in the Temkin-Poet S-wave model. We demonstrate that the correct phase can be extracted for each method by using the appropriate final-state continuum functions.

The interaction between matter and fields is a classical problem. Still there are difficulties. Time symmetry is broken. So the radiation damping belongs to a class of phenomena, which includes transport properties. We propose a radically different approach based on the extension of the dynamics of integrable systems. We consider a simple model, a harmonic oscillator interacting with a field. For integrable systems, it is well known that there exists a unitary transformation U. However, in the radiation damping we have resonances between the action of the particle and the actions of the field. This makes the system an example of Poincaré nonintegrable systems. We extend the unitary operator to a new star-unitary operator $\Lambda .$ This changes the dynamical description of radiation damping. Once we know the Hamiltonian, we can of course write the Hamilton equations. But we have the possibility to go to new descriptions. The invertible $\Lambda$ transformation gives many new aspects, which are hidden in the initial description. For example, we show that there are fluctuations, and that there exists an irreducible probability description. The transformation to $\Lambda$ representation corresponds to a transformation to Markovian probability equations. We can always come back to the initial representation by the inverse transformation. We have verified this remarkable prediction by detailed numerical calculations. We need the $\Lambda$ transformation to obtain the definition of a dressed unstable mode, which has a well-defined lifetime. In the initial representation there are various time scales and there is no strictly exponential lifetime. The situation is the same as the one we have studied in the quantum case in recent papers.

The entanglement between the spins of a pair of particles may change because the spin and momentum become mixed when viewed by a moving observer [R. M. Gingrich and C. Adami, Phys. Rev. Lett. 89, 270402 (2002)]. In this paper, it is shown that, if the momenta are appropriately entangled, the entanglement between the spins of the Bell states can remain maximal when viewed by any moving observer. Based on this observation, a relativistic invariant protocol for quantum communication is suggested, with which the nonrelativistic quantum information theory could be invariantly applied to relativistic situations.

The problem of entanglement produced by an arbitrary operator is formulated and a related measure of entanglement production is introduced. This measure of entanglement production satisfies all properties natural for such a characteristic. A particular case is the entanglement produced by a density operator or a density matrix. The suggested measure is valid for operations over pure states as well as over mixed states, for equilibrium as well as nonequilibrium processes. Systems of arbitrary nature can be treated, described by field operators, spin operators, or any other kind of operator that is realized by constructing generalized density matrices. The interplay between entanglement production and phase transitions in statistical systems is analyzed using the examples of Bose-Einstein condensation, the superconducting transition, and magnetic transitions. The relation between the measure of entanglement production and order indices is analyzed.

We give a detailed account of the one-way quantum computer, a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states. We prove its universality, describe why its underlying computational model is different from the network model of quantum computation, and relate quantum algorithms to mathematical graphs. Further we investigate the scaling of required resources and give a number of examples for circuits of practical interest such as the circuit for quantum Fourier transformation and for the quantum adder. Finally, we describe computation with clusters of finite size.

We compare three proposals for nondeterministic control-sign gates implemented using linear optics and conditional measurements with nonideal ancilla mode production and detection. The simplified Knill-Laflamme-Milburn gate [Ralph et al., Phys. Rev. A 65, 012314 (2001)] appears to be the most resilient under these conditions. We also find that the operation of this gate can be improved by adjusting the beam splitter ratios to compensate to some extent for the effects of the imperfect ancilla.

We use linearly polarized 45 fs pulses to create rotational wave packets in ${\mathrm{N}}_2$ and ${\mathrm{O}}_2.$ We Coulomb explode molecules with a high-intensity circularly polarized pulse and use an ion imaging detector to measure a series of two-dimensional projections of the wave packet’s angular distribution in 27 fs increments. We highlight the evolving wave packet near the first, second, sixth, and tenth full revival times and also near the one-eighth, one-quarter, one-half, and three-quarter fractional revivals.

A semiclassical, multimode model of a continuously pumped atom laser is presented. For a spatially independent coupling process it is found that the system is unstable below a critical scattering length. As large atomic interactions will increase the phase diffusion of the lasing mode, it is desirable to obtain a stable atom laser with low nonlinearity. It is shown that spatially dependent pumping stabilizes the atom laser to a finite number of modes, and can induce single-mode operation.

We study collective spontaneous emission from a linear array of N two-state atoms using quantum trajectory theory and without an a priori single-mode assumption. Assuming a fully excited initial state, we calculate the angular distribution of the $k\mathrm{th}$ emitted photon, $k=1,\dots ,N.\mathrm{}$ We investigate the evolution of the distribution from a dipole radiation pattern for the first photon emission to a distribution characteristic of directional superradiance. The formalism is developed around an unravelling of the master equation in terms of source-mode quantum jumps. Exact calculations for 11 and fewer atoms do not show directional superradiance, but are characterized by delayed (subradiant) photon emissions directed along the axis of the linear array. A modified boson approximation is made to treat the many-atom case, where it is found that strong directional superradiance occurs for a few hundred atoms; the decay of subradiant excitations is preserved in the tail of the superradiant pulse.

Holland and Burnett [Phys. Rev. Lett. 71, 1355 (1993)] have argued that twin Fock states of equal photon number $N$ injected at both input ports of a Mach-Zehnder interferometer lead to phase measurements with accuracies approaching the Heisenberg limit $\Delta {\phi }_{\mathrm{HL}}=1/\left(2N\right).$ However, the method of phase detection suggested by those authors, obtaining the difference of the photocurrents at the output ports of the interferometer, is not sensitive to the phase difference between the two interferometer paths; in fact, the photocurrent vanishes. In this paper we show that the use of parity measurements on just one of the output modes not only is sensitive to the phase difference but that the sensitivity approaches the Heisenberg limit for large $N.\mathrm{}$

We report a detailed study of the longitudinal relaxation of several coherent states on the nuclear-magnetic-resonance (NMR) two-qubit quadrupole system, ${}^{23}\mathrm{Na}$ (spin 3/2) in a lyotropic liquid-crystal system at room temperature. Relaxation of pseudopure states, simulated pseudo-Bell states and Hadamard states were investigated. The coherence of superposition states was verified by applying the respective quantum “reading” operators and comparing the recovered state with the original one. The degree of recovery varies between $\approx 70\%$ and $\approx 100\%,$ depending on the time length of the gate, as compared to relaxation times. Spin-lattice relaxation results follow a recently proposed multiexponential model that includes mixed magnetic dipolar and electric quadrupolar interactions. Relaxation curves are governed by initial conditions, and from the experimental curves individual transition rates are derived. The transverse relaxation time constant $T_2$ is found not to depend on the initial distribution of populations. This is a systematic study of relaxation in the context of NMR quantum computing.

Dissociative recombination of ${\mathrm{CO}}_2$ ions has been studied at the heavy-ion storage ring ASTRID. Electrons were scattered on both singly and doubly charged positive ions of the molecule, and the absolute cross sections were measured in the energy range of ${10}^{-3}–{10}^1\mathrm{eV}.$ Thermal rate coefficients of $\alpha$$\left({\mathrm{CO}}_2^{+}\right)$ $=(6.5\mathrm{}\pm 1.9)\times {10}^{-7}\times (300/T[\mathrm{K}]{)}^{0.8}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ and $\alpha$$\left({\mathrm{CO}}_2^{2+}\right)$ $=(6.2\mathrm{}\pm 2.1)\times {10}^{-7}\times (300/T[\mathrm{K}]{)}^{0.5}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ were extracted. Furthermore, branching ratios for molecular breakup into neutral product channels have been measured using a grid technique. The branching ratios were measured at $\sim 0\mathrm{eV}$ for ${\mathrm{CO}}_2^{+},$ and in the entire energy range from ${10}^{-3}\mathrm{eV}$ to 50 eV for ${\mathrm{CO}}_2^{2+}.$ This measurement reveals pronounced structure in the ${\mathrm{CO}}_2^{2+}$ branching ratios.

We report measurements of positronium (Ps) formation cross sections for 0.1–60 eV positrons scattered by Mg atoms. There is reasonable agreement between the measured cross sections and recent calculations of those values, both of which indicate an unusually steep increase of the Ps formation cross section from zero to a large peak value as the positron energy is increased from the Ps formation threshold to less than 1 eV above that threshold.