Spatial and temporal self-imaging phenomena in atomic waveguides are studied. Planar, rectangular, and cylindrical guides with constant or graded refraction indexes are considered. Waveguide-internal beam splitters and interferometers are proposed. The influence of gravity is discussed.

It is shown that in the $|\Delta l|=2,$ resonant Raman migration of the population between Rydberg states of comparable principal quantum numbers $n\gg 1,$ the coupling of the resonant intermediate state to a lower-lying one acts as a suppressor of the migration due to the shift splitting of the resonant state.

We examine the spin-squeezing phenomena in a collection of interacting spins in the presence of an external field. We show that the combination of the external field and the nonlinear atom-atom interaction leads to a strong reduction of spin fluctuations that can be maintained in an extended period of time. Our results can be applied to achieve spin squeezing in a spinor Bose condensate.

The conditions of quantum-classical correspondence for a system of two interacting spins are investigated. Differences between quantum expectation values and classical Liouville averages are examined for both regular and chaotic dynamics well beyond the short-time regime of narrow states. We find that quantum-classical differences initially grow exponentially with a characteristic exponent consistently larger than the largest Lyapunov exponent. We provide numerical evidence that the time of the break between the quantum and classical predictions scales as $\log (\mathcal{J}/ħ),$ where $\mathcal{J}$ is a characteristic system action. However, this logarithmic break-time rule applies only while the quantum-classical deviations are smaller than $O\left(ħ\right).\mathrm{}$ We find that the quantum observables remain well approximated by classical Liouville averages over long times even for the chaotic motions of a few degree-of-freedom system. To obtain this correspondence it is not necessary to introduce the decoherence effects of a many degree-of-freedom environment.

We analyzed the effect of frequent measurements on the quantum systems that are chaotic in the classical limit. It is shown that the delta-kicked rotator, a well-known example of quantum chaos, is too special to be used as a testing ground for the effects of the repeated measurements. The abrupt change of state vectors by the δ-function kick singular interruptions causes a quantum anti-Zeno effect. However, in more realistic rotators with interaction potentials of continuous time dependence, the quantum Zeno effect prevails.

Consider a ring of N qubits in a translationally invariant quantum state. We ask to what extent each pair of nearest neighbors can be entangled. Under certain assumptions about the form of the state, we find a formula for the maximum possible nearest-neighbor entanglement. We then compare this maximum with the entanglement achieved by the ground state of an antiferromagnetic ring consisting of an even number of spin-1/2 particles. We find that, though the antiferromagnetic ground state typically does not maximize the nearest-neighbor entanglement relative to all other states, it does so relative to other states having zero z component of spin.

We present a scheme for information storage or retrieval through a quantum phase with a single operation, which generalizes the Ahn-Weinacht-Bucksbaum (AWB) scheme proposed and demonstrated in a recent experiment on N-state Rydberg atoms by Ahn, Weinacht, and Bucksbaum [Science 287, 463 (2000)]. Our scheme elaborates the AWB scheme through removing its original constraint on the smallness of the product of time and atom-light interactions by exactly evaluating the involved unitary transformations, and it is proved to have several pronounced advantages over the original one.

Entanglement between a particle and a detector is known to be inherent in the measurement process. Gurvitz recently analyzed the coupling of an electron in a double dot (DD) to a quantum point contact (QPC) detector. In this paper we examine the dynamics of entanglement that result between the DD and QPC. The rate of entanglement is optimized as a function of coupling when the electron is initially in one of the dots. It decreases asymptotically towards zero with increased coupling. The opposite behavior is observed when the DD is initially in a superposition: the rate of entanglement increases unboundedly as the coupling is increased. The possibility that there are conditions for which measurement occurs versus entanglement is considered.

Scattering of orthopositronium off helium target has been investigated using close-coupling method in the energy range 0–110 eV. Two basis sets, (a) $\mathrm{Ps}\mathrm{}\left(1s\right)+\mathrm{He}{(1s}^2,{1s2}^{1}s,{1s2}^{1}p)$ and (b) $\mathrm{Ps}\mathrm{}(1s,2p)+\mathrm{He}{(1s}^2,{1s2}^{1}s,{1s2}^{1}p),$ have been employed to find the scattering parameters. Low-order phase shifts, scattering length, and elastic and excitation cross section up to $n=2\mathrm{}$ are reported using close-coupling approximation. Total cross section is also given by adding other partial cross section and compared with available measured data and existing theoretical predictions. Our total cross section at zero energy is very close to the theoretical prediction of Drachman and Houston [J. Phys B 3, 1657 (1970)] and measured data of Canter et al. [Phys. Rev. A 12, 375 (1975)]. Present total cross section is in qualitative agreement with measured data of the University College London group in the energy range considered. In particular, present predictions are in good agreement with the UCL group in the energy range 20–30 eV. It has been found that elastic cross section is dramatically reduced, at zero or near zero energies, with the inclusion of target excitation in the expansion scheme. Moreover, ionization cross section of the Ps atom is found to be a major contributor to the total cross section above the ionization threshold.

Many-body multipartitioning perturbation theory (MPPT) was applied to calculate the potential energy of 11 lowest electronic states of the NaRb molecule, $A,C{}^1{\Sigma }^{+}-X{}^1{\Sigma }^{+},$ $B,D{}^1\Pi –X^1{\Sigma }^{+},$ $D{}^1\Pi –A{}^1{\Sigma }^{+}$ and $D{}^1\Pi –B{}^1\Pi$ transition dipole moments, as well as nonadiabatic L-uncoupling matrix elements between the examined ${}^1\Pi$ and four lowest ${}^1{\Sigma }^{+}$ states for both ${}^{23}{\mathrm{Na}}^{85}\mathrm{Rb}$ and ${}^{23}{\mathrm{Na}}^{87}\mathrm{Rb}$ isotopomers. The relevant MPPT ab initio matrix elements and energy curves were converted by means of the approximate sum rule to radiative lifetimes and $\Lambda$-doubling constants $(q$ factors) for the particular rovibronic levels of the $B{}^1\Pi$ and $D{}^1\Pi$ states. The theoretical lifetimes agree well with their experimental counterparts for both $B{}^1\Pi$ and $D{}^1\Pi$ states. The q factor estimates obtained in the singlet-singlet approximation are in good agreement with the experimental ones for the $D{}^1\Pi (1\mathrm{}<~v^{\prime }<~12;7<~J^{\prime }<~50)$ levels, exhibiting a pronounced difference for the $B{}^1\Pi$ state. Considerably better agreement was achieved by accounting for the spin-orbit perturbation effect caused by the near-lying $c^3{\Sigma }^{+}$ state. Relative intensity distributions in the $D{}^1\overrightarrow{\Pi }X{}^1{\Sigma }^{+}$ dispersed fluorescence spectra excited by fixed ${\mathrm{Ar}}^{+}$ laser lines were measured for $v^{\prime }{(J}^{\prime })=0\mathrm{}(44),$ $1\left(104\right),$ $4\left(25\right),$ $6(44,120),$ $10\left(36\right),$ and $12\left(50\right)\mathrm{}$ $D{}^1\Pi$ levels. The experimental intensities and term values were simultaneously embedded in the nonlinear least-square fitting procedure to refine the $D{}^1\Pi$ potential.

The local-spin-density functional method, with an optimized effective potential and self-interaction correction, is used to study the energy structure of hollow atoms and ions in the bulk of metallic materials. The energy structure of conduction electrons in the bulk of metallic material is treated by the jellium model. Based on this method, we have studied the x-ray spectra and Auger spectra of ${\mathrm{N}}^{q+}$ hollow atoms and ions in the bulk of Al, as well as in the vacuum. The experimental Auger spectra in the collision of ${\mathrm{N}}^{6+}$ with an insulating surface and conducting surface can be well understood based on our studies. Our calculated x-ray and Auger spectra of hollow atoms or ions in the vacuum and in the bulk of material suggest the need for further systematic experimental investigation.

We have calculated annihilation probability densities in positron collisions against the He atom. Our scattering wave functions were obtained with the Schwinger multichannel method [J. S. E. Germano and M. A. P. Lima, Phys. Rev. A $47,$ 3976 (1993)]. It has been found that direct annihilation, in which electronic cloud deformation shields the nuclear repulsive potential effectively attracting the positron to a binary encounter, dominates the annihilation process at low impact energies. Closer to the real positronium formation threshold, the signature of virtual positronium has been noticed. At room temperature, significant annihilation probability has been observed over a somewhat extended region.

Time connection between electrons in dynamic atomic systems is considered. We describe time correlation in terms of the Dyson time ordering operator T. In this paper we decompose T into an uncorrelated term $T_{\mathrm{unc}},$ plus a correlated term $T_{\mathrm{cor}}=T-T_{\mathrm{unc}},$ which interconnects the time-dependent external interactions. We show that time correlation between electrons requires both $T_{\mathrm{cor}}$ and spatial electron-electron correlation. Two examples are analyzed. In transfer ionization the time correlation operator incoherently changes the shape of an electron-electron Thomas peak. In double excitation the influence of $T_{\mathrm{cor}}$ in amplitudes for coherently interfering pathways changes resonance intensities and profiles.

The coupled-channel optical method has been applied to study positron scattering by atomic sodium at intermediate energies. The optical potential that accounts only for the continuum has been implemented into the close-coupling framework and includes positron–sodium-atom and the positronium–sodium-ion channels. Elastic, excitation, ionization, positronium formation, and total cross sections are reported and are compared with other theoretical and experimental data, where available.

We calculate the frequency profile of the rate for breakup of ${\mathrm{H}}_2^{+}$ by one photon in the presence of a strong dc field. After photoexcitation of the molecular ion from its ground $1s\sigma$ electronic state to the $2p\sigma$ electronic state, the nuclei are temporarily trapped by a dc field-induced barrier with turning point $R_{\max }.$ However, the nuclei are released through either rotation of the internuclear axis (which, for the sake of tractability, we ignore) or dc-field ionization involving resonant transfer from the $2p\sigma$ state to a more highly excited state. The most prominent resonance occurs at an internuclear separation that is less than $R_{\max }$ and, in a.u., is approximately ${3/(8F}_{\mathrm{dc}})+3,$ where $F_{\mathrm{dc}}$ is the dc field strength. We interpret the change in the frequency profile, as $F_{\mathrm{dc}}$ varies, in terms of different aspects of the dynamics of the breakup process, in particular the dispersion of the probability distribution of the nuclei due to over-the-barrier dissociation from the $1s\sigma$ state.

Videotape with a sinusoidal magnetization of $31\hspace{0.5em}\mu \mathrm{m}$ wavelength is used to reflect Cs atoms with unit reflectivity in a 75 m/s atomic beam. The atoms serve as a probe, allowing us to measure the magnetic field at the surface. A technique is presented for mounting the videotape so that its surface can be curved to a specific shape or made flexible. We show that such a reflector provides high-quality grazing-incidence atom optics and we demonstrate deflections as large as $23°$ in a whispering-gallery geometry.

Accurate potential-energy curves are used consistently instead of Coulombic curves to determine the internuclear separation at ionization, $R_{\mathrm{ion}},$ in a strong laser field, for charge states of ${\mathrm{N}}_2$ up to ${\mathrm{N}}_2^{5+}.$ Furthermore, we exlude the kinetic energy gained from previous ionization steps in determining $R_{\mathrm{ion}}.$ With these improvements, we analyze various dissociation pathways from ${\mathrm{N}}_2^{2+}$ to ${\mathrm{N}}_2^{5+}$ and find that the charge symmetric pathways do not give physical results. In fact, it appears that all ionization up to ${\mathrm{N}}_2^{5+}$ involves the charge asymmetric channel ${\mathrm{N}}_2^{4+}\to {\mathrm{N}}^{+}+{\mathrm{N}}^{3+}.$ By determining the time between each ionization step, we observe the competition between laser intensity and internuclear separation in determining the molecular ionization rate. Finally, our data are consistent with recent observations that short pulse (<130 fs) ionization leaves fragments in electronically excited states whereas long pulse (>600 fs) ionization leaves them in ground electronic states.

A strong blueshift of high-order harmonics was observed when intense femtosecond Ti:sapphire laser pulses were applied to Ar and Ne. The blueshift was systematically investigated for various experimental parameters, such as laser intensity, laser-pulse duration, and gas density. We observed the harmonic blueshifts of two times the laser frequency in the 39th harmonic from Ar and four times the laser frequency in the 85th harmonic from Ne. A semiclassical calculation predicted the inverse proportionality of the blueshift to the laser-pulse duration, which was confirmed in the experiment done with 30 fs and 80 fs pulses. The density dependence of blueshift showed that the self-phase modulation in an ionizing medium was not a major factor of the observed blueshift. The experimental results along with theoretical calculations confirmed that the observed blueshift resulted mainly from the nonadiabatic effect due to the rapid increase in the femtosecond laser electric field.

We consider a possible technique for mode locking an atom laser, based on the generation of a dark soliton in a ring-shaped Bose-Einstein condensate, with repulsive atomic interactions. The soliton is a kink, with angular momentum per particle equal to $ħ/2.\mathrm{}$ It emerges naturally when the condensate is stirred at the soliton velocity and cleansed with a periodic out coupler. The result is a replicating coherent field inside the atom laser, stabilized by topology. We give a numerical demonstration of the generation and stabilization of the soliton.

In this paper, we consider the conditions for the existence of autosolitons, in trapped Bose-Einstein condensates with attractive atomic interactions. First, the variational approach is employed to estimate the stationary solutions for the three-dimensional Gross-Pitaevskii equation with trap potential, linear atomic feeding from the thermal cloud, and two- and three-body inelastic processes. Next, by using exact numerical calculations, we show that the variational approach gives reliable analytical results. We also discuss the possible observation of autosolitons in experiments with ${}^7\mathrm{Li}.$