Nearly degenerate four-wave mixing (NDFWM) within a closed degenerate two-level atomic transition is theoretically and experimentally examined. Using the model presented by Lezama et al. [Phys. Rev. A 61, 013801 (2000)] the NDFWM spectra corresponding to different pump and probe polarization cases are calculated and discussed. The calculated spectra are compared to the observation of NDFWM within the ${6S}_{1/2}\mathrm{}(F=4\mathrm{})\mathrm{}\to {6P}_{3/2}\mathrm{}(F=5\mathrm{})\mathrm{}$ transition of cesium in a phase conjugation experiment using magneto-optically cooled atoms.

We show that the Bloch vectors lying on any great circle comprise the largest set $S_L$ for which the parallel states $|\overrightarrow{n},\overrightarrow{n}〉$ can always be exactly transformed into the antiparallel states $|\overrightarrow{n},-\overrightarrow{n}〉.$ Thus more information about $\overrightarrow{n}$ is not extractable from $|\overrightarrow{n},-\overrightarrow{n}〉$ than from $|\overrightarrow{n},\overrightarrow{n}〉$ by any measuring strategy, for $\overrightarrow{n}\in S_L.$ Surprisingly this most general transformation reduces to just a flip operation on the second particle. We also show here that a probabilistic exact parallel to antiparallel transformation is not possible if the corresponding antiparallel states span the whole Hilbert space of the two qubits. These considerations allow us to generalize a conjecture of Gisin and Popescu [Phys. Rev. Lett. $83,$ 432 (1999)].

The time evolution of quantum tunneling is studied when the tunneling system is immersed in a thermal medium. We analyze in detail the behavior of the system after integrating out the environment. An exact result for the inverted harmonic oscillator of the tunneling potential is derived and the barrier penetration factor is explicitly worked out as a function of time. The quantum mechanical formula for the case without environment is modified both by the potential renormalization effect and by a dynamical factor which may differ appreciably from the one previously obtained in the time range of 1/(curvature at the top of potential barrier).

A scheme to possibly implement the quantum computer is proposed based on the idea to build up the single qubit from two coupled quantum dots. The spatial separation of the two logic states of the qubit can greatly reduce the decoherence time, which allows one to perform the coherent quantum logic operations at a fairly high ratio. Together with the realization of the universal quantum logic gates, and the proper scheme of quantum measurement, the present proposal can satisfy all the essential criteria for quantum computing.

When a charged particle interacts with an atom it may induce double electronic transitions. The complete information on such a reaction is encompassed in the Green function of the interacting four-particle system (the external charged particle, the two electrons, and the residual ion). In this work we employ a perturbation expansion of the Green operator and derive from that a multiple-scattering series for the scattering operator. As pointed out here, each term in this series corresponds to a particular sequence of binary potential collisions. From a simple analytical analysis we identify the regions of the four-body spectrum where the effects of the multiple-scattering terms become prevalent. We uncover the existence of a left-right asymmetry in a two-particle collision. This dichroic feature occurs because the symmetry of space is broken by the presence of the particles not participating in the two-body encounter. We study the ionization-ionization–transfer reaction when the external charged particle is heavy. The present formal, exact analysis predicts, in addition to the Thomas peaks, a triple-star peak structure in the spectrum when considered as a function of the momenta of the ionized electron, the residual ion and the scattered projectile. It is shown that the star is two dimensional and that its shape is dependent on the velocity of the continuum electron. In addition we consider the ionization and positronium formation following the scattering of a positron from an atom. We point out that certain terms in the multiple-scattering series coincide due to the equal masses of the electron and the positron which open the way for interference effects.

Fixed-energy inverse scattering theory has been used to define central and spin-orbit Schrödinger potentials for the scattering of 5-eV polarized electrons from Xe atoms. The results are typical for a range of such data; including energies above threshold when the potentials become complex. The phase shifts obtained from an analysis of the measured differential cross section and analyzing power were used as input data. Both semiclassical (WKB) and fully quantal inversion methods were used to extract central and spin-orbit interactions. The analysis shows that information additional to the set of input phase shifts extracted from these (and similar) data may be needed to ascertain physical potentials.

The Bogoliubov theory of weakly interacting bosons is generalized to Bose-Einstein condensates with internal degrees of freedom so that a single effective Hamiltonian produces various many-body ground states or metastable spin domains and the corresponding collective modes on an equal footing.

Correspondence between frequency and energy spectra and biorthogonality conditions for the excitations of Bose-Einstein condensates described by the Gross-Pitaevskii model have been derived self-consistently using general properties arising from the Hamiltonian structure of the model. It has been demonstrated that frequency resonances of the excitations with positive and negative energies can lead to their mutual annihilation and appearance of the collective modes with complex frequencies and zero energies. Conditions for the avoided crossing of energy levels have also been discussed. General theory has been verified both numerically and analytically in the weak interaction limit considering an example of vortices in a binary mixture of condensates. Growth of excitations with complex frequencies leads to spiraling of the unit and double vortices out of the condensate center to its periphery and to splitting of the double- and higher order vortices to the unit-order vortices.

We derive an equation of motion for the velocity fluctuations of a two-dimensional deformed trapped Bose gas just above the critical temperature in the hydrodynamical regime. From this equation, we calculate the eigenfrequencies and the corresponding density fluctuations for a few low-lying excitation modes. Using the method of averages, we derive a dispersion relation in a deformed trap at very high temperature that interpolates between the collisionless and hydrodynamic regimes. We make use of this dispersion relation to calculate the frequencies and the damping rates for monopole and quadrupole mode in both the regimes. We also discuss the time evolution of the wave-packet width of a Bose gas in a time-independent trap as well as a time-dependent trap.

We propose a scheme of a one-atom laser which produces a cavity-field virtually in a stationary Fock state. It is based upon the unexpectedly simple dynamics of the Jaynes-Cummings system at multiphoton resonances at far-off resonance. We find that an anomalously high cavity mode excitation occurs at a particular set of atomic, cavity, and driving-field frequencies.

A two-photon transition in cold Rb atoms will be probed with a phase-coherent wide bandwidth femtosecond laser comb. Frequency domain analysis yields a high-resolution picture where phase coherence among various transition pathways through different intermediate states produces interference effects on the resonantly enhanced transition probability. This result is supported by the time domain Ramsey interference effect. The two-photon transition spectrum is analyzed in terms of the pulse repetition rate and carrier frequency offset, leading to a cold-atom-based frequency stabilization scheme for both degrees of freedom of the femtosecond laser.

The amplitude-phase formulation of the one-dimensional Schrödinger equation is investigated within the context of Ermakov systems. The boundary conditions for amplitude functions corresponding to bound states are given in terms of the Ermakov invariant and a related constant, which also monitors the behavior of the accumulated phase function. A procedure leading to the numerical construction of smooth, nonoscillating amplitude and phase functions is proposed, and illustrated in the case of the harmonic oscillator and the centrifugal Coulomb potential. The use of this procedure as a tool to define radial basis functions for bound channels within the framework of scattering theory is discussed.

The carbon $1s$ photoelectron spectra of HCCH and DCCD have been measured at a photon energy of 330 eV and an instrumental resolution about half the natural linewidth. The vibrational structure in the spectra has been analyzed in terms of a model in which the parameters are the force constants for carbon-carbon and carbon-hydrogen stretching in the core-ionized molecules and the changes in bond lengths between the core-ionized and neutral molecules. Within this model, three different approaches to core-hole localization have been considered. Treating the core hole as completely localized, with the molecular motion following the diabatic energy surfaces, does not describe the data correctly. Treating the core hole as completely delocalized, with the molecular motion following the adiabatic surfaces, gives a good fit to the spectra but leads to zero-point energies that are completely unreasonable. A fit that takes into account vibronic coupling between the vibrational manifolds of the ${}^2{\Sigma }_u^{+}$ and ${}^2{\Sigma }_g^{+}$ electronic states of the ion gives good agreement with the data and leads to reasonable molecular parameters. Ab initio calculations of the molecular properties of the core-ionized molecule give results that are in excellent agreement with those obtained from this fit. The lifetime width for the carbon $1s$ hole state is $106\pm 2\mathrm{meV},$ significantly higher than for ${\mathrm{CH}}_4\hspace{0.5em}(95\mathrm{}\pm 2\mathrm{meV}).\mathrm{}$ This result is not in accord with predictions based on a one-center model of Auger decay.

We present a contribution to the discussion of how best to minimize time-evolving wave functions near the edge of a space-time grid. Our suggestion builds on the work of several groups and adopts an optical potential with real and imaginary parts separated in space (though not necessarily in time) to bring about an artificial acceleration and subsequent suppression of the wave-function amplitude as it approaches the boundary of discretized space-time. The emphasis of the proposal is on the absorption of incident wave functions characterized by low kinetic energy (long de Broglie wavelength) and/or a broad spread of momenta. The action of the optical potential is quantified by calculations of transmission and reflection as a function of incident wave-function kinetic energy, relative bandwidth, and de Broglie wavelength. Numerical constraints on the maximum by which a wave packet may be accelerated and the time and space over which the accelerating potential may act are discussed within the terms of the split-operator method for wave-function propagation. The perceived advantages of spatially overlapping real and imaginary potentials with respect to the minimization of broad-bandwidth wave functions are investigated. It is found that the addition of a simple, though not totally arbitrary, energy shift applied in space prior to absorption by a negative imaginary potential greatly enhances the absorption of wave packets constructed from multiple momentum components.

We elicit the ability of monocentric close-coupling expansions to describe ionization in $\overline{p}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collisions. We show that expansions in terms of exponentially decaying basis functions are definitively unable to provide reliable ionizing distributions in the outgoing part of the collision, since they cannot be enlarged enough to suitably reproduce the outer part of the continuum wave functions. We review the construction of a monocentric expansion in terms of spherical Bessel functions confined in a box that has recently been proposed to better describe the ionizing wave functions and hence overcome the failure of the usual expansions [B. Pons, Phys. Rev. Lett. 84, 4569 (2000)]. We ascertain the reliability of the method and enlarge our previous study of ionizing $\overline{p}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collisions from low to high impact velocities.

Positronium formation in the transfer-excitation reaction of positrons impacting on singlet and triplet metastable $\mathrm{He}\mathrm{}\left(1s2s\right)\mathrm{}$ is studied at intermediate and high impact energies within the framework of a four-body version of the continuum distorted wave-final state model. Cross sections for selective final states of the residual target as well as total cross sections and polarization fraction of the $2p-1s$ multiplet line of ${\mathrm{He}}^{+}$ are computed by using a partial-wave technique. For $2p$ final states of ${\mathrm{He}}^{+}$ cross sections exhibit interference patterns.

We find the lateral projection of the Casimir force for a configuration of a sphere above a corrugated plate. This force tends to change the sphere position in the direction of the nearest corrugation maximum. The probability distribution describing different positions of a sphere above a corrugated plate, which is fitted well with experimental data demonstrating the nontrivial boundary dependence of the Casimir force, is suggested.

We present a detailed experimental and theoretical study of electron-impact single ionization of ${\mathrm{Ne}}^{7+}.$ High-resolution and high-precision energy-scan measurements of the K-shell excitation threshold region have been performed with statistical uncertainties as low as 0.036% and an energy stepwidth of 0.39 eV. Resonance features in the cross section of ${\mathrm{Ne}}^{7+}$ arising from indirect ionization processes have been observed. A new unified R-matrix calculation of the ionization cross section very well reproduces most of the features observed in the experiment.