The transverse mode of an atom laser beam that is outcoupled from a Bose–Einstein condensate is investigated and is found to be strongly determined by the mean-field interaction of the laser beam with the condensate. For repulsive interactions, the condensate acts as a diverging lens for the outcoupled atoms, and transverse interference fringes in the atomic beam are predicted due to the coherent addition of amplitudes for atoms emitted from different regions in the condensate. This effect can be used to investigate the transverse coherence of an atom laser beam.

In diffraction catastrophes such as the rainbow, the wave nature of light resolves ray singularities and draws delicate interference patterns. In quantum catastrophes such as the black hole, the quantum nature of light resolves wave singularities and creates characteristic quantum effects related to Hawking radiation. This paper describes the theory behind a recent proposal [U. Leonhardt, Nature (London) 415, 406 (2002)] to generate a quantum catastrophe of slow light.

Control of amplitude and phase of the driving field in an atom-field interaction leads towards the strong line narrowing and quenching in the spontaneous emission spectrum. We exploit this fact for the atom localization scheme and achieve a much better spatial resolution in the conditional position probability distribution of the atom. Most importantly the quenching in the spontaneous emission manifests itself in reducing the periodicity in the conditional position probability distribution and hence the uncertainty in a particular position measurement of the single atom by a factor of 2.

Four-phase spiral waves are predicted to exist in a nonlinear optical cavity with competing quadratic (i.e., ${\chi }^{\mathrm{}\left(2\right)\mathrm{}})$ and cubic (i.e., ${\chi }^{\mathrm{}\left(3\right)\mathrm{}})$ nonlinearities. These spatial structures are found in the mean-field model of a doubly resonant type-II frequency-degenerate optical parametric oscillator with an intracavity ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ isotropic medium. Degenerate four-wave mixing of signal and idler fields induced by the ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ medium breaks the phase invariance of the down-conversion process, producing nonlinear phase locking with four possible phase states. A parametrically forced Ginzburg-Landau equation is derived to explain the existence of multiphase spiral waves.

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? We provide an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling n-qubit Hamiltonian and local unitary operations. It follows that universal quantum computation can be performed using any entangling interaction and local unitary operations.

We analyze the bifurcation mechanism responsible for the experimentally observed polarization self-modulation (PSM) in a vertical-cavity surface-emitting laser subject to optical feedback. We show that closed branches of time-periodic intensity solutions connecting distinct external-cavity modes (ECMs) exhibit PSM. Along these bridges, the linearly polarized components of the optical field oscillate in antiphase and with a frequency close to the difference between two ECM frequencies. A beating mechanism between stable ECMs then explains the PSM phenomenon. Our results also substantiate recent theoretical studies of edge-emitting lasers subject to optical feedback.

The equivalence of the covariant renormalization and the partial-wave renormalization (PWR) approaches is proven explicitly for the one-loop self-energy (SE) correction of a bound electron state in the presence of external perturbation potentials. No “spurious” correction terms to the noncovariant PWR scheme are generated for Coulomb-type screening potentials and for external magnetic fields. It is shown that in numerical calculations of the SE with Coulombic perturbation potential spurious terms result from an improper treatment of the unphysical high-energy contribution. A method for performing PWR utilizing the relativistic B-spline approach for construction of the Dirac spectrum in external magnetic fields is proposed. This method is applied for calculating QED corrections to the bound-electron g factor in H-like ions. Within a level of accuracy of about 0.1% no spurious terms are generated in numerical calculations of the SE in magnetic fields.

Moshinsky’s work on diffraction in time is recognized as a particular case of monoenergetic, quantum dispersion process. Diffraction in time is extended to include new initial conditions, which under free evolution exhibit temporal quantum interference patterns in close analogy to spatial diffraction patterns found in optics. We show that free propagation of states, which initially are stationary states of infinite potential wells, diffract in time similarly as a plane wave by a double slit. We introduce the concepts of mass transport by transient Fraunhofer and Fresnel dispersion currents.

We study the quantum computational power of a generic class of anisotropic solid-state Hamiltonians. A universal set of encoded logic operations are found, which do away with difficult-to-implement single-qubit gates in a number of quantum-computer proposals, e.g., quantum dots and donor atom spins with anisotropic exchange coupling, quantum Hall systems, and electrons floating on helium. We show how to make the corresponding Hamiltonians universal by encoding one qubit into two physical qubits, and by controlling nearest-neighbor interactions.

The ultimate goal of the classicality program is to quantify the amount of quantumness of certain processes. Here, classicality is studied for a restricted type of process: quantum information processing (QIP). Under special conditions, one can force some qubits of a quantum computer into a classical state without affecting the outcome of the computation. The minimal set of conditions is described and its structure is studied. Some implications of this formalism are the increase of noise robustness, a proof of the quantumness of mixed state quantum computing, and a step forward in understanding the very foundation of QIP.

We introduce generalized cat states for d-level systems and obtain concise formulas for their entanglement swapping with generalized Bell states. We then use this to provide both a generalization to the d-level case and a transparent proof of validity for an already proposed protocol of secret sharing based on entanglement swapping.

The formulation of the time-dependent close-coupling method is extended to allow the calculation of electron-impact triple-differential cross sections for atoms. The fully quantal method is applied to the electron-impact ionization of hydrogen at an incident energy of 54.4 eV for various scattering geometries. The time-dependent close-coupling results are found to be in very good agreement with those obtained by a time-independent exterior complex-scaling method. On the other hand, even though the incident energy is relatively large, significant differences are found between the two nonperturbative cross-section results and those obtained using perturbative distorted-wave methods. Large differences are found for those geometries that require an accurate knowledge of the correlation between two outgoing continuum electrons in the presence of a Coulomb nuclear field.

We have constructed the $X{}^1{\Sigma }_g^{+}$ potential for the collision between two ground-state Mg atoms and analyzed the effect of uncertainties in the shape of the potential on scattering properties at ultracold temperatures. This potential reproduces the experimental term values to $0.2\hspace{0.5em}{\mathrm{cm}}^{-1}$ and has a scattering length of $+1.4\mathrm{}\left(5\right)\mathrm{}\hspace{0.5em}\mathrm{nm}$ where the error is predominantly due to the uncertainty in the dissociation energy and the $C_6$ dispersion coefficient. A positive sign of the scattering length suggests that a Bose-Einstein condensate of ground-state Mg atoms is stable.

Absolute total electron-ion recombination rate coefficients of argonlike ${\mathrm{Sc}}^{3+}{(3s}^2{3p}^6)$ ions have been measured for relative energies between electrons and ions ranging from 0 to 45 eV. This energy range comprises all dielectronic recombination resonances attached to $3\overrightarrow{p}3d$ and $3\overrightarrow{p}4s$ excitations. A broad resonance with an experimental width of $0.89\pm 0.07\hspace{0.5em}\mathrm{eV}$ due to the ${3p}^5{3d}^2{}^{2}F$ intermediate state is found at $12.31\pm 0.03\hspace{0.5em}\mathrm{eV}$ with a small experimental evidence for an asymmetric line shape. From R-matrix and perturbative calculations we infer that the asymmetric line shape may not only be due to quantum-mechanical interference between direct and resonant recombination channels as predicted by Gorczyca et al. [Phys. Rev. A 56, 4742 (1997)], but may be partly also due to the interaction with an adjacent overlapping dielectronic recombination resonance of the same symmetry. The overall agreement between theory and experiment is poor. Differences between our experimental and our theoretical resonance positions are as large as 1.4 eV. This illustrates the difficulty to accurately describe the structure of an atomic system with an open $3d$ shell with state-of-the-art theoretical methods. Furthermore, we find that a relativistic theoretical treatment of the system under study is mandatory since the existence of experimentally observed strong ${3p}^5{3d}^{2}2D$ and ${3p}^{5}3d4s{}^{2}D$ resonances can only be explained when calculations beyond $\mathrm{LS}$ coupling are carried out.

A high kinetic energy beam of ${\mathrm{C}}_{60}^{-}$ ions produced by electrospray was collided with He and Ne targets, and the cross sections for production of positive and negative fragment ions were determined. In these experiments we observed both ${\mathrm{C}}_{59}^{+}$ and ${\mathrm{C}}_{59}^{-}$ fragment ions with He and Ne target gases. Since the initial internal energy of the ions is low, it is possible to knock out one carbon atom from the fullerene cage and thereby form ${\mathrm{C}}_{59}$ ions with lifetimes long enough to allow them to be detected (of the order of $10\hspace{0.5em}\mu \mathrm{s}).\mathrm{}$ Comparisons with molecular dynamic simulations show that the cross sections for formation of ${\mathrm{C}}_{59}^{-}$ and also ${\mathrm{C}}_{58}^{-}$ can be explained as the result of a “prompt” knock-out process.

In this paper we discuss the effect of phase noise upon the efficiency of population transfer produced by stimulated Raman adiabatic passage (STIRAP). To allow an adjustable cross-correlation of the two fields we consider the pump and Stokes pulses to be derived from a single phase-diffusing exponentially correlated laser, but we allow some time delay T between the noise signals. We present examples of Monte Carlo simulations, showing unexpected regularities in the dependence of efficiency upon pulse area for partially cross-correlated fields: efficiency does not monotonically increase with increasing pulse area, as would be expected. We explain these, and other properties, by using a simple model of pulse shapes to derive analytic expressions for efficiency. Although derived for a specific analytic form, the formulas also provide a useful description of transfer efficiency by other pulse shapes. We also obtain an estimate of the fundamental limit on the transfer efficiency with STIRAP, based on the Schawlow-Townes limit to laser bandwidths.

The spin dynamics and its reaction on the particle motion are investigated for free and bound electrons in intense linearly polarized laser fields. Employing both classical and quantum treatments we analytically evaluate the spin oscillation of free electrons in intense laser fields and indicate the effect of spin-orbit coupling on the motion of the electron. In Mott scattering an estimation for the spin oscillation is derived. In intense laser ion dynamics spin signatures are studied in detail with emphasis on high-order harmonic generation in the tunneling regime. First- and second-order calculations in the ratio of electron velocity and the speed of light show spin signatures in the radiation spectrum and spin-orbit effects in the electron polarization.

Integrated optical structures offer the intriguing potential of compact, reproducible waveguide arrays, rings, Y junctions, etc., that could be used to design evanescent field traps to transport, store, and interact atoms in networks as complicated as any integrated optical waveguide circuit. We theoretically investigate three approaches to trapping atoms above linear integrated optical waveguides. A two-color scheme balances the decaying evanescent fields of red- and blue-detuned light to produce a potential minimum above the guide. A one-color surface trap proposal uses blue-detuned light and the attractive surface interaction to provide a potential minimum. A third proposal uses blue-detuned light in two guides positioned above and below one another. The atoms are confined to the “dark” spot in the vacuum gap between the guides. We find that all three approaches can be used to trap atoms in two or three dimensions with approximately 100 mW of laser power. We show that the dark spot guide is robust to light scatter and provides the most viable approach for constructing integrated optical circuits that could be used to transport and manipulate atoms in a controlled manner.

Coherence properties of two down-converters continuously coupled via idler beams are analyzed. A formal equivalence between this device and two well-known experiments on quantum interference by Mandel’s group is developed. As in these experiments the signal coherence is shown to be induced by a principal indistinguishability of signal photons. We also show that the which-way information about a signal photon carried by the idler beams periodically attains its maximum and minimum values in the course of the evolution. The optimal which-way measurement for our setup is constructed.

The creation of a second-order nonlinear susceptibility ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ in thermally poled silica glasses is known to be related to positive charge migration. As opposed to currently used models, we herein propose a model that takes into account charge dissociation and charge recombination occurring during the poling process. This model, known as the Proctor and Sutton model, was used to determine the space-charge distribution within silica plates submitted to an electric field. In this paper, we perform theoretical calculations in order to adapt this model to the high values of the applied electric field during the poling process. Moreover, we prove that there is a voltage threshold below which no ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ can be induced. We also point out the existence of a nonzero electric field within the entire sample. To test the validity of this model, we poled 1 mm thick Infrasil™ silica slabs using voltages ranging from 0 to 4 kV. Maker fringe patterns have been recorded in order to estimate the magnitude of the induced nonlinear ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ coefficient. We report experimental evidence of a poling voltage threshold of 900 V in these samples.