Session H6: Poster Session II

Control and Manipulation of Atomic Wavepackets By Dynamical Stabilization

For a quasi-one-dimensional (quasi-1D) atom subject to a train of kicks directed toward the origin, i.e., the ``nucleus'', the classical phase space contains large stable islands embedded in a chaotic sea. Atoms whose initial phase points lie within a stable island remain trapped through dynamical stabilization leading to creation of a non-dispersive wavepacket that undergoes strong transient phase-space localization. The positions of the stable islands depend on the frequency and strength of the kicks. Thus, once a wavepacket is localized, it can be steered toward different regions of phase space by ``chirping'' the frequency and/or amplitude of the HCPs. Strong transient phase space localization can also be obtained in quasi-1D atoms by application of a single HCP. We demonstrate that this transient localization can be maintained for extended periods by taking advantage of dynamical stabilization if, at the time of initial optimal localization, the wavepacket is placed at the center of a stable island associated with a subsequently-applied HCP train. This technique allows a larger fraction of the initial atoms to be trapped within an island.   

Chemical Properties of Dipole-Bound Negative Ions

In dipole bound negative ions the extra electron is weakly bound by the dipole potential of the neutral molecule in a diffuse orbital localized near the positive end of the dipole. In consequence, it is reasonable to expect that such species will be highly reactive and possess chemical properties similar to those of Rydberg atoms, which also contain a weakly-bound electron in a diffuse orbital. These properties are being examined using a negative ion Penning trap. Data for electron transfer in collisions with attaching targets such as SF$_6$ show that the rate constants for this process are large, $\sim$ 10$^{-7}$ cm$^3$ s$^{-1}$, and similar to those for free electron attachment. This suggests that collisions can be described in terms of an essentially-free electron model. This is further reinforced by the observation that rotational energy transfer in collisions with polar molecules can lead to rapid electron detachment, again with large rate constants of $\sim$ 10 $^{-7}$ cm$^3$ s$^{-1}$. Results for several target species will be presented and discussed in light of a free electron model.   

Selective Removal of Electrons from a Penning Trap for Negative Ion Autodetachment Studies

It is shown that free electrons can be selectively removed from a Penning trap used to store heavy autodetaching negative ions by application of a series of small positive extraction pulses to one of the end electrodes of sufficient amplitude to extract the electrons yet not significantly perturb the heavy ion motion. This precludes electron reattachment processes in the trap, allowing accurate measurement of negative ion lifetimes. This has been used to determine the lifetimes of SF$_6^-$ and C$_2$Cl$_4^-$ ions produced by electron transfer in collisions with K(np) Rydberg atoms. The data for C$_2$Cl$_4^-$ point to ion lifetimes in the range 3 to 500 $\mu$s. Those for SF$_6^-$ range from 1 to 10 ms. The measurements for SF$_6^-$ also provide evidence of radiative stabilization. For both targets the effects of post-attachment interactions involving the K$^+$ core ion become increasingly important for values of n $\leq$ 20, leading to a sizable increase in the product ion lifetimes.   

Recurrence Spectroscopy of Autoionizing Rydberg Argon in an Electric Field

Previously, we have performed single uv-photon excitation of metastable argon to spin-orbit autoionizing states between the first and second fine structure ionization limits. [1] A pulsed frequency-doubled dye laser excites the valence electron to a Rydberg state and excites the ionic core from j=1/2 to j=3/2. The core then relaxes and ejects the Rydberg electron. We have developed a new apparatus that allows us to measure these autoionizing states in an electric field using a fast beam. Using this apparatus we have extended the field-free measurements to probe the semi-classical dynamics of this system in an electric field using the method of recurrence spectroscopy [2]. Recurrence spectra for the autoionizing states in an electric will be compared to the corresponding spectra in the bound state region. Work supported by National Science Foundation. [1] J.D. Wright, P.A. Walker, J.H. Gurian, M. van Lier-Walqui, J.M. Lambert, H. Flores-Rueda, and T.J. Morgan; Bulletin of the American Physical Society (2004) [2] M L Keeler, H Flores-Rueda, J D Wright, and T J Morgan; J. Phys. B. 37, 809-815 (2004)   

Interpreting Orbit Profiles Obtained from Quantum Mechanically Derived Recurrence Spectra

The application of scaled energy spectroscopy (SES) to quantum spectra is used to obtain orbit profiles that are composed of the classical stability, launching angle probability, and quantum mechanical effects. To extract classical orbit stability requires consideration of all of these components. Orbit profiles generated using SES on quantum spectra are compared with profiles generated from classical calculations. The SES calculation shows interference between the main orbit and primitive repetitions. A simple analytical formula has been derived to predict the number of oscillation nodes in any given orbit below the ionization threshold. In addition, the quantum mechanically derived profiles show an asymmetry in orbit probability that is not apparent in the classical calculation. The uphill to downhill strength ratio can be predicted with an analytical formula based on the calculated dipole moment of the primitive uphill and downhill trajectories. Classical and quantum orbit profile calculations demonstrating the dependency of the derived analytical formulas will be presented.   

A Systematic Study of Quantum Defect Influences on Classical Orbit Probability

A collection of experimentally obtained spectra as a function of scaled energy can be used to generate a recurrence map, a map of orbit probability with scaled action and scaled energy being the independent variables. One promise of recurrence spectroscopy is to be able to interpret recurrence maps classically, with the recurrence strength being proportional to the classical orbit stability. A simple classical interpretation of such non-hydrogenic maps has thus far been limited because the orbit probability obtained in this manner also contains some quantum mechanical effects. Highly excited Stark spectra for the alkali metals and atoms with fictionalized quantum defects were calculated using standard matrix diagonalization techniques. From these, Stark maps were produced and orbit profiles were obtained. In this systematic numerical study, the effects of quantum defect on classical orbit probability and classical orbit stability are presented with careful consideration of initial launching angle distribution, oscillator strength and interference.   

Two Photon Excitation of Rydberg States in a MOT

We observe the generation of Rydberg atoms in a MOT via trap loss. In the course of this work two different excitation schemes were used: A two step resonant excitation and an off-resonant two photon excitation - detuned by 1.2 GHz from the 5P$_{3/2}$ state - both through the use of 780 nm 5S-5P$_{3/2}$ light and 480 nm 5P$_{3/2}$-ns,d$_{J}$ light. Final states of n=30, 50, and 70 were reached and for each state the trap loss as a function of the 480 nm laser power was measured. The lineshape of the transition was measured by slowly scanning the frequency of the excitation laser. This method reveals the significant difference in the lineshapes for off-resonant two-photon excitation as opposed to the two step process. The two-photon Rabi frequency is sufficient to power broaden the line profiles, which at low power have widths less than 5 MHz. This work was supported by the NSF and NASA.   

Application of the Polar R-Matrix Theory to Electron-Hydrogen Atom Scattering

The time-independent Schroedinger operator for electron-hydrogen atom scattering will be written in polar form (product of a positive definite hermitian operator times a unitary operator) and then used to calculate the R-matrix with arbitrary boundary conditions on a finite sphere. In the process, an approximate inverse of the Schroedinger operator will be constructed by projection onto the eigenstates of the positive definite hermitian component of the Schroedinger operator. This allows for an effective variational minimum principle by determination of the most rapidly converging expression for the operator inverse. The R-matrix will then be projected to infinity where the scattering matrix will be extracted.   

Excited State Quantum-Classical Molecular Dynamics

The development of a new theoretical, algorithmic, and computational framework is reported describing the corresponding excited state many-body dynamics by applying multiphysics described by classical equations of motion for nuclei and Hartree-Fock/Multi-Configuration Hartree-Fock and multiresolution techniques for solving the quantum part of the problem (i.e. the motion of the electrons). We primarily have in mind reactive and electron-transition dynamics which involves molecular clusters, containing hundreds of atoms, perturbed by a slow ionic/atomic/molecular projectile, with possible applications in plasma-surface interactions, cluster physics, chemistry and biotechnology. The validation of the developed technique is performed at three-body systems. Application to the transition dynamics in small carbon clusters and hydrocarbons perturbed by slow carbon ions resolves some long-standing issues in the ion-surface interactions in fusion tokamaks.   

Mapped Slow Variable Representation for three-body bound states

The adiabatic hyperspherical approximation is often used to calculate bound states of quantum three-body systems in atomic, molecular and nuclear physics. However, in many situations the accuracy of the energies and wavefunctions obtained in the approximation is not satisfactory. The widely used solution is to include non-adiabatic couplings represented by first and second derivatives with respect to the hyper-radius. However, because of many avoided crossings in adiabatic hyperspherical curves, it is difficult to include the coulings accurately. Another possible solution is to use the Slow Variable Representation (SVD). Using this method, we explore bound states of several three-body systems: The four isotopomers of the H$_3^+$ ion, the He$_3$ cluster, and a benchmark few-body problem of three bosons. For all the systems, the bound energies obtained using SVD are in good agreement with previous accurate calculations. To represent properly vibration of the He$_3$ cluster, we use the mapped Fourier grid method. The mapping is made only in the hyper-radial coordinate. It allows us to reduce significantly the number of sampling points and the calculation time.   

Classical calculation of the lifetimes and branching ratios for radiative decays of hydrogenic atoms

The correspondence principle for atomic radiation is extended to all hydrogenic states $n$ and $l >$ 0. Lifetimes and branching ratios are obtained using analytic calculations of the classical radiated spectrum for the elliptical orbit corresponding to a particular quantum state. The polarization of the radiation is used to separate out the angular momentum decreasing and increasing transitions. The lifetimes show excellent agreement with quantum mechanics for all principal quantum numbers $n$ and $l$ $\ge $ 1 (e.g. $<$ 100 ppm for $l \quad \ge $ 30, $<$ 0.1{\%} for $l \quad \ge $ 9, $<$ 1{\%} for $l \quad \ge $ 3). The calculated branching ratios are in reasonable agreement with quantum mechanics for all $n$', $l$', $n$ and $l \ge $ 1.   

A universal formula for the accurate calculation of hydrogenic lifetimes

The quantum mechanical lifetimes of atomic hydrogenic states are shown to follow a universal curve when plotted against a simple function of their quantum numbers $n$ and $l$. This universal curve is found to agree with a result derived from the correspondence principle. A simple formula which approximates the universal curve can be used to easily calculate lifetimes for all states $n$, $l \quad \ge $ 1 to an accuracy of 400 parts per million or better. The formula is especially useful for high-n states, where the full quantum calculation is extremely difficult or even impossible to perform.   

Quantum dynamics of H + LiF and Li + HF collisions at ultracold temperatures

The rapid progress in experimental methods such as photoassociation and Feshbach resonance methods led recently to the creation of Bose-Einstein condensates of molecules. This technical breakthrough opens new perspectives in the study of intermolecular interactions and offers new opportunites for the study of rovibrational relaxation and chemical reactivity in ultracold gases. In this work, we present quantum scattering calculations of H + LiF and Li + HF collisions at cold and ultracold temperatures for which the reactions proceed by quantum tunneling of the relatively heavy F atom through a barrier along the reaction path. Particular effort is made here to assign resonances due to the decay of metastable states of the Li$\cdots$FH and H$\cdots$LiF van der Waals complexes. The unusually deep van der Waals wells give rise to long-lived collision complexes and narrow scattering resonances in the energy dependence of reaction cross sections. The effect of vibrational excitation on the reactivity is also explored.   

Interactions of Rubidium and Metastable Argon at Ultracold Temperatures

We are investigating the interaction between ultracold rubidium (Rb) and ultracold metastable argon (Ar*) simultaneously confined in a dual species magneto-optical trap (MOT). We will report on recent quantitative measurements of the inter-species trap loss coefficients and present our preliminary results on photoassociative spectra of the Rb-Ar* complex. We will also report on studies of Penning and associative ionization in the MOT using a modified residual gas analyzer (RGA) as a detector. Finally, we will discuss the prospects for producing and spatially confining ultracold ground state RbAr, a weakly-bound van der Waals molecule. Support provided by the National Science Foundation and the Office of Naval Research.   

Suppression of molecular cold collisions in a field

We have found that state-changing collisions of heteronuclear polar molecules in $\Sigma$ ground states can be suppressed by orders of magnitude in the presence of strong electric fields. The fields required to initiate this suppression are determined by introducing Stark shifts that are comparable to rotational intervals in the molecules. Under these circumstances, the field can induce qualitative changes in the structure of adiabatic curve-crossings, dramatically altering the collision physics. This result has implications for trapping and cooling polar $\Sigma$-state molecules in electrostatic traps.   

Pseudopotential treatment of atoms under two-dimensional confinement

The behaviors of atomic gases at cold temperatures are to a very good approximation described by a single atomic physics parameter. Consequently, low-energy observables can be reproduced quite well by replacing the shape-dependent atom-atom potential with a zero-range potential with a properly chosen coupling strength. Following the approach by Stock et al. [Phys. Rev. Lett. 94, 023202 (2005)], we derive pseudopotentials that properly describe the scattering between two atoms in two-dimensional space. The treatment can, e.g., describe the scattering between two spin-polarized fermions in two dimensions. The applicability of the proposed pseudopotentials is tested by performing numerical calculations. *This work is supported by the NSF.   

Photoassociation in a Bose-Einstein condensate: Many-body treatments with realistic molecular potentials

Photoassociation is a process creating an excited diatomic molecule from a pair of colliding cold atoms by use of a laser field. Photoassociation in a Bose-Einstein condensate is often well described by the standard Gross-Pitaevskii equation (GP) with a complex scattering length. However, for situations where the pair dynamics plays a significant role, one must go beyond this picture. We have considered two many-body models: one is based on the cumulant method [1] and the other is inspired by the pair wave function approach [2]. Both models are used with realistic molecular potentials, so that we can address the nonperturbative regimes. For continuous lasers of moderate intensities ($<$kW/cm$^{2})$, both models agree with the GP description. For higher intensities, the models predict the formation of noncondensed atoms instead of molecules, depending on the experimental conditions. \newline \newline \underline {References} \newline [1] T. K\"{o}hler, T. Gasenzer and K. Burnett, Phys. Rev. A 67, 013601 (2003) \newline [2] P. Naidon and F. Masnou-Seeuws, Phys. Rev. A 68, 033612 (2003)   

Convergent Atomic and Molecular Asymptotics

A technique is described for calculating the asymptotic phases and amplitudes of coupled channel wavefunctions through analytic continuation in the complex plane of a reaction coordinate. A non-perturbative analysis incorporates interactions associated with high-order multipole moments of fragment charge distributions, without the necessity of integrating Schrodinger's equation to asymptotic distances. The method should be particularly useful for the description of near-threshold and/or ultracold processes. Initial applications to two-channel model problems demonstrate the utility of the method.   

Siegert pseudostate treatment of ultracold collisions

The previously developed [1,2] formalism of Siegert pseudostates is applied to a two-channel model of ultracold collisions between fermions. The dependence of the real part of the energy of a low-lying Feshbach resonance on magnetic field is considered. The accuracy of a wave packet expanded in the basis of Siegert pseudostates is investigated before and after the real part of the Feshbach resonance has been tuned to negative energy. We observe the wave packet evolving in time [3]. Financial support by the U.S. Department of Energy, Office of Science is gratefully acknowledged. [1] O. I. Tolstikhin, V. N. Ostrovsky, and H. Nakamura, Phys. Rev. A {\bf 58}, 2077 (1998). [2] G. V. Sitnikov. I. Tolstikhin, Phys. Rev. A {\bf 67}, 2077 (2003). [3] R. Santra, J. M. Shainline, C. H. Greene, Accepted for publication in Phys. Rev. A.   

Vortex-Lattice Dynamics in Rotating Spinor Bose-Einstein Condensates

We report the observation of square vortex lattices in rotating dilute-gas spinor Bose-Einstein condensates (BEC). By coherently transferring a fraction of a rotating condensate in one internal atomic state to another internal state, we produce a pseudo-spin-1/2 spinor condensate. Following a macroscopic phase separation and vortex turbulence phase, the vortex lattice in each component of the BEC undergoes a transition from an overlapped hexagonal lattice to interlaced square lattices. The stability of the square structure is proved by its response to the applied shear perturbations. An interference technique also has been used in the experiment to verify that the vortex lattices in both components are interlaced, and form a skyrmion lattice. We also report recent progress towards loading rotating BECs into optical lattice.   

Experimental Studies of a Kicked BEC

In this poster we will present results of an experiment in which a pulsed off resonant standing light wave is incident upon an all optical BEC of Rb-87 atoms. This is related to experiments on the quantum delta kicked rotor (QDKR) that have been performed with cold atoms. These experiments have observed dynamical localization [1] and quantum accelerator modes [2]. In our experiments we use an all optical BEC which is exposed to a standing wave generated by a YAG laser. Importantly, because we can control the motion of the standing wave, it is possible to create a variety of different atomic dynamics. By using BEC instead of cold atoms we take advantage of an initial well defined state and the inter-atomic interactions. [1] F. L. Moore, J. C. Robinson, C. Bharucha, P. E. Williams, and M. G. Raizen, Phys. Rev. Lett. \textbf{73}, 2974 (1994) [2] M. K. Oberthaler, R. M. Godun, M. B. d'Arcy, G. S. Summy, and K. Burnett Phys. Rev. Lett. \textbf{83}, 4447 (1999).   

Hydrodynamic cooling of Rb87 thermal clouds in a time dependent potential

There has been much theoretical work done on investigating the behavior of an atomic cloud in presence of a time dependent potential [1, 2]. We study new experimental methods to realize such potentials and explore the atomic cloud's behavior in their presence. We load Rb87 atoms, with densities within the hydrodynamic regime, into an optical trap consisting of two far-off-resonant CO$_{2}$ laser beams propagating perpendicularly. The vertical beam is abruptly turned off causing momentum and space oscillations of the atomic cloud in the horizontal beam. In a second experiment, the cross section of the two beams is displaced from their foci. The spatial width of the cloud is now significantly increased at specific positions inside the trap. Releasing the optical trap at such positions leads to the clouds expansion in the axial direction, and a more efficient cooling. In this poster we describe the details of our optical set up and report our latest results. [1] P.W.H. Pinske et al., Phys. Rev. Lett. \textbf{78}, 990 (1997) [2] I. Shvarchuck et al., Phys. Rev A \textbf{68, }063603 (2003)   

Loading cold atoms into a time averaged optical dipole trap

We describe our investigations of optical dipole traps for neutral atoms using a high power CO$_2$ laser beams (FORT). Studies of these quasi-electrostatic traps lead us to the creation of a Bose-Einstein condensate (BEC) by all optical means. We have developed a new technique to increase the optical trap population, improving spatial and phase space densities of the atomic cloud. This enhances the evaporative cooling efficiency to realize a BEC. This technique is based on a fast sweeping of the CO$_2$ beam while loading the atoms from a Magneto optical trap. We have found that the FORT population (N$_{FORT})$, being proportional to the FORT volume, also saturates once a certain potential depth is reached. The goal would be to engineer the sweeping amplitude and frequency to increase the effective volume and keep the potential depth at its saturation limit. A considerable increase in the N$_{FORT }$is observed for a proper choice of the amplitude and frequency of the sweeping. A detailed study of these time averaged optical traps will be presented.   

Measurement of the effects of the Casimir-Polder force using dipole oscillations of a magnetically trapped Bose-Einstein condensate

In this experiment a Rb-87 Bose-Einstein condensate is used to measure the effects of the Casimir-Polder force in a region 1-5 microns from a dielectric surface. A nearly pure condensate ($>$80{\%} number fraction) placed at a fixed distance from the surface is given a small excitation resulting in a mechanical dipole oscillation. Effects from the Casimir-Polder force manifest themselves as small deviations to the natural dipole oscillation frequency ($\sim $10\^{-4} fractional change). Measurements have been made showing an unambiguous distinction between the Casimir-Polder force and the van der Waals force, showing good agreement with recent theory [1]. Future work includes making similar measurements in a high-temperature environment to demonstrate the predicted thermal dependence of the Casimir-Polder force. [1] Antezza M., Pitaevskii L.P., Stringari S., Phys. Rev. A 70, 053619 (2004).   

Progress on a Portable BEC System

Small and portable BEC vacuum systems can simplify atom-chip experiments and allow for more rapid development of cold atom applications such as inertial sensing. This work describes our experimental progress on small ($<$$30\times30\times15\,\textrm{cm}^{3}$) self-contained BEC vacuum cells. In the system an atom-chip seals the top of the vacuum cell, such that the cold atoms are $<$1mm from ambient atmosphere. This makes it possible to generate a significant field inside the vacuum using wires outside the vacuum envelope. Additionally, feed-throughs for on-chip electrical connections are made directly on or through the chip, which is much simpler than in standard vacuum systems. In order to allow for higher bakeout temperatures, and thus higher vacuum, we have attached a chip to a glass cell without epoxy. Because conventional alkali metal rubidium dispensers also emit hydrogen, we are developing a new means to dispense rubidium into the cell that will also allow rapid modulation of the rubidium pressure as required in single-chamber ultracold atom-chip experiments.   

The Gross-Pitaevskii Equation for Bose Particles in a Double Well Potential: Two-Mode Models and Beyond

Recent experiments (notably by the Oberthaler group in Heidelberg) have obtained quantitative information on tunneling oscillations and self-trapping of Bose ensembles in a double well potential. To develop a more versatile theoretical model to deal with varying conditions of atom number and potential shape, we have used the lowest symmetric and antisymmetric wavefunctions obtained from the Gross-Pitaevskii equation (GPE) for a double well potential, and solved coupled equations for two modes exactly. This yields effective tunneling parameters that depend on the number and phase of atoms in each well, hence is time-dependent, unlike previous models. We find that this ``variable tunneling model'' (VTM) yields results that agree more closely with numerical solutions of the time-dependent GPE, even for relatively large atom-atom interactions, for which two-mode models with localized wavefunctions fail. Our 3D solutions with the time-dependent GPE reproduce the above experimental results well, while the 3D two-mode model is not far off. Improved parameters for second quantization are also obtained. We will present extensive comparisons of results from the VTM and other approaches.   

Multiscale quantum defect theory for two atoms in a trap

We present a multiscale quantum defect theory (QDT) for two atoms in a trap that combines the quantum defect theory for the Van der Waals interaction\footnote{B. Gao, Phys. Rev. A \textbf{64}, 010701 (R) (2001).} at short distances with a QDT for the harmonic trapping potential at large distances. The theory provides a systematic understanding of not only how the trap states are effected by atomic interaction, but also how the molecular states are effected by trapping. The theory is applicable to arbitrary scattering lengths, and gives a simultaneous understanding of different angular momentum states by taking advantage of the angular-momentum insensitivities of short-range QDT parameters. In one sample application, we show that two atoms in a trap have a shape-dependent long-range correlation that becomes important for large scattering lengths.   

Beyond-mean-field calculation of atomic BEC energies in an anisotropic trap with tunable interaction

We report progress in extending our beyond-mean-field calculations to a larger number of atoms by pushing our perturbation series to next order. In our many-body approach, we use a dimensional perturbation theory treatment of N atoms with hard-sphere interactions. Our treatment of a condensate in a cylindrical trap depends on the high degree of symmetry of the condensate at zeroth order to include every two-body interaction. We are able to use symmetry to obtain analytic results for the ground state energy and excitation frequencies through first order for a few thousand atoms. Motivated by the substantial improvement of the ground state energy in going from zeroth to first order, we expect to obtain second order results valid for a larger number of atoms. We can also use the lowest and higher-order wave functions to obtain the density profile of the condensate. Because the number of atoms and the scattering length are simply parameters in this treatment, this method is well-suited to treat condensates over a wide range of N and interaction strengths, for example in the presence of a Feshbach resonance. This work was supported by ONR and ARO.   

Magnetism, squeezing, and entanglement in dipolar spin-1 condensates

We investigate the magnetic response of a $F=1$ spinor condensate with magnetic dipole-dipole interactions. The interplay of the collisional and dipolar interactions between atoms, and the magnetic Zeeman effect induces a rich variety of quantum phases in the ground state structure. Under a magnetic field sweep, the dipolar interaction gives rise to a stepwise magnetization curve. We also study the effects of the magnetic field on the spin squeezing and show that the behavior of the squeezing parameter clearly characterizes the quantum phases of our system. Finally, we propose a scheme to create the maximally entangled state between $|m_F=\pm1\rangle$ atoms with a time varying transverse magnetic field. Our scheme involves only the ground state of the system, and is thus robust against spontaneous-emission-induced decoherence and is also independent of the atom number.   

Velocity-Selective Optical Hyperfine Pumping in (87)Rb Vapor

The absorption spectra of a probe laser in the presence of a saturating, uni-directional, linearly-polarized pump laser have been measured for the $^{87}$Rb $D_2$ transition in a room-temperature vapor cell. Using two independently tunable, copropagating, narrow-line lasers for pump and probe, the Doppler-broadened ground state velocity distributions of atoms in the pump beam are directly observed. Strong velocity-selective optical hyperfine pumping is observed due to the non-degenerate level structure of the excited and ground states. It is found that the pump beam may be tuned within the multi-level $F=2\rightarrow F'$ transition to create peaked, highly non-thermal velocity distributions for the two ground state hyperfine levels. The widths and heights of these features in the absorption spectra are examined.   

Bichromatic Local Oscillator for Detection of Two-Mode Squeezing

\\ In recent years two-mode squeezing has become an active area of research as a source of continuous variable entanglement and EPR correlations; however, the experimental characterization of two- mode squeezed sources still remains a problem. The usual detection scheme, based on heterodyne measurements, requires the use of a local oscillator with a frequency equal to the mean of the frequencies of the two-mode squeezed fields. The squeezing information is then located around the frequency of the beat note between the local oscillator and the squeezed fields. Such frequencies are usually in the GHz range for squeezing from alkali atoms and can in principle be arbitrarily large. The combined requirements of high bandwidth and low noise place difficult constraints on the detection system, since the electronic noise of the system usually increases as the bandwidth of the detection system increases. \\ We propose the use of a bichromatic field as the local oscillator in the heterodyne measurements. By the proper selection of frequencies of the bichromatic field it is possible to arbitrarily select the frequency around which the squeezing information is located, thus making it possible to use a low bandwidth detection system to characterize a two-mode squeezed source. Since the measurement frequency can be arbitrarily selected, it is also possible to move away from any excess noise present in the system. Experimental implementation of this detection scheme is presented.   

Stationary pulses of light: three-dimensional confinement and nonlinear optics

We show that the method of stationary pulses of light [1] can be extended to confine pulses of light in all three spatial dimensions. This is achieved through a waveguiding effect due to the transverse dependence of the index of refraction in an Electromagnetically Induced Transparency (EIT) medium. We experimentally demonstrate this effect and show how it can be used to confine pulses of light in all three spatial dimensions. This method could be used to strongly enhance nonlinear interactions between weak pulses of light [2]. Specifically, we show that an efficient Kerr-like interaction between two pulses can be implemented by exploiting the steep atomic dispersion associated with narrow EIT resonances. [1] M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Nature {\bf 426}, 638 (2003). [2] A. Andr\'{e}, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Phys. Rev. Lett. (in press).   

Progress towards realization of quantum networks using atomic ensembles

We report on our progress towards generation, storage and communication of single photon states using atomic memory. Specifically, we describe proof-of principle experiments demonstrating generation of single photon pulses of light with controllable propagation direction, timing, and pulse shapes [1]. The approach is based on preparation of an atomic ensemble in a state with a desired number of atomic spin excitations, which is later converted into a photon pulse by exploiting long-lived coherent memory for photon states and electromagnetically induced transparency (EIT). We describe our efforts to optimize the performance of such a novel single photon source. Specifically we propose and demonstrate a novel propagation geometry that optimizes mode matching and signal to noise ratio. We discuss our progress towards transmitting single photon states between two atomic memory nodes connected by photonic channels and outline the prospects for long-distance quantum communication using these techniques. [1] M. D. Eisaman, L. Childress, A. Andr\'{e}, F. Massou, A. S. Zibrov, and M. D. Lukin, Phys. Rev. Lett. {\bf 93}, 233602 (2004).   

Chirping and superradiance

The role of dipole-dipole interactions is studied for Dicke-like superradiant decay. Whereas the incoherent part of the interaction, leading to speed-up and line-broadening, is qualitatively well-known, we introduce the coherent part that leads to a chirp accompanying the decay. Studies or more realistic and/or more complicated setups are included.   

Quantum optics in impurity bound excitons

Group theoretical techniques are used to deduce he selection rules and energy splitting of electric dipole lines of a donor or acceptor exciton in a group-IV semiconductor. We propose to realize electromagnetically induced transparency and slow light by identifying a suitable lambda system. Parameters for achieving EIT and light storage are estimated.   

Raman superradiance in atomic gases

A mean field theory for Raman superradiance with recoil is presented to analyze recent Raman superradiant experiments [Phys.Rev. A 69, 041603(R) and Phys. Rev. A 69, 041601(R)]. Recoil is found to induce the decay of Raman coherence. Instability analysis shows that the Raman transition may have a collective instability when the decay of the optical field is small. Comparison with Rayleigh superradiance is also included.   

Cavity QED with Quantized Center of Mass: Correlation Functions, Tunneling, and Entanglement

For an atom in a driven cavity with an external potential, we examine nonclassical correlations and entanglement. The effects of center of mass motion including tunneling are included. We find a very sensitive dependence of various correlation functions on center of mass motion. We obtain analytic results in the case of a harmonic potential, or that of a lattice potential that has half the wavelength of the driving field. It may be possible to use the sensitivity of these correlation functions to yield information about atomic motion, such as Levy flights for example. Further we find that two cross correlations between transmitted and fluorescent light yield information about the entanglement in the system. Also, we discuss inequalities between intensity-intensity and intensity-field correlations in this system, and find nonclassical behavior of a new type.   

Quantum State Transfer Between Matter and Light

We report on the coherent quantum state transfer from a two-level atomic system to a single photon. Entanglement between a single photon (signal) and a two-component ensemble of cold rubidium atoms is used to project the atomic ensemble onto any desired state by measuring the signal photon in a suitable basis. The atomic qubit is read out by stimulating directional emission of a single photon (idler) from the collective state of the ensemble. Faithful preparation and readout of atomic state are verified by the observed correlations between the signal and the idler photons. These results enable implementation of distributed quantum networking.   

Investigation of Electromagnetically Induced Transparency in Open V, $\Lambda$ and Cascade Doppler-Broadened Molecular Systems

We have demonstrated electromagnetically induced transparency (EIT) for two-color transitions in inhomogeneously broadened lithium and sodium dimer vapors. EIT has been observed via fluorescence detection in three systems of different energy level configurations (V, $\Lambda $, $\Xi )$ by employing two continuous-wave single frequency lasers. The dependence of the transparency profile on the beam geometry (V-system), coupling laser intensity ($\Lambda $-system) and wavelength ratio of the applied fields (cascade system) has been investigated. The openness of the molecular V-type system is accountable for rendering the medium transparent even for residual Doppler line widths greater than the induced Autler-Townes splitting. Our findings have been complemented by theoretical studies that trace the presence of EIT at the density matrix level. These theoretical predictions agree well with the experimental results.   

Diffusion of atomic coherence in atomic vapor cells

Diffusion plays an important role in establishing the equilibrium ground state coherence in rubidium vapor cells, of relevance to Coherent Population Trapping (CPT) as used in small atomic clocks, as well as Electromagnetically Induced Transparency (EIT), and slow and and stored light. Here, we present experimental studies of the effects of coherence diffusion utilizing several techniques including the application of magnetic field gradients to destroy coherence that diffuses away from the laser beam; as well as the retrieval of multiple pulses from stored light, in which coherence returns to the volume of the laser beam due to diffusion.   

Bond coordinates as an alternative: Low energy reactive collisions of He2+ with He; comparison of TD and TI quantum calculations

``Reactive'' and ``inelastic'' processes in the ionic $He_{3}^{+}$ system[1] have been separated and analyzed through the simulation of the $^{3}He + ^{4}He_ {2}$ collision. The combined use of TD and TI techniques allowed the study for both high and very low kinetic energies; the agreement between the corresponding results in the medium energy range is very good. Influence of the internal excitation of the reagents and implications on the dynamics of evaporation in He clusters will be discussed[2,3]. Emphasis will be made on the TD wavepacket propagation methodology used for the calculation of state-to-state transition probabilies, based bond coordinates: This method[4] was suggested recently by one of the authors, and is applied for the first time to a process with three open channels. Bond coordinates can have several advantages over the use of standard Jacobi ones [1] E. Scifoni, E. Bodo and F. A. Gianturco, Eur. Phys. J. D, 30, 363 (2004) [2] E. Bodo, F. A. Gianturco, A. Dalgarno, J. Phys. B 35 (2002) 2391. [3] E. Bodo and F. A. Gianturco, Eur. Phys. J. D, 31 (2004) 423 [4] M. Lara, A. Aguado, O. Roncero,and M. Paniagua. J. Chem. Phys., 113, 1781 (2000)   

Fully Differential Measurements on Single Ionization of He by 75 keV Proton Impact

Fully momentum analyzed scattered projectiles and recoil ions in 75 keV p + He collisions were measured in coincidence. The momentum of the ionized electrons was deduced from momentum conservation. We obtained fully differential three-dimensional angular distributions of electrons with an energy of 5.5 eV. Through the use of position sensitive detectors, data were recorded for a broad range of scattering angles simultaneously. According to the first Born approximation, peak structures in the direction of the momentum transfer q (difference between initial and final projectile momentum) and --q were expected (binary and recoil peak). Instead, we observe a peak which is shifted backwards at small scattering angles and forward at large scattering angles relative to q and no significant recoil peak. These observations as well as unexpected features outside the scattering plane are a manifestation of a surprisingly important role of the projectile -- target nucleus interaction.   

A Improved Version of ISICS

The C++ program, ISICS, which calculates K, L, M sub-shell ionization and x-ray production cross sections from the PWBA and ECPSSR theories, has found much use in basic and applied research. The following improvements have been added to the original version: united-atom option for the binding energy correction, easy inputting of new atomic parameters, along with corrections of minor bugs in the original version. Sample results will be demonstrated.   

Electron Transfer, Ionization, and Excitation in Collisions between $\alpha$ Particles and H($1s$) Atoms

Following earlier coupled-Sturmian calculations by Shakeshaft\footnote{R. Shakeshaft, Phys. Rev. A {\bf 14}, 1626 (1976).} on p-H collisions, the author reported Sturmian calculations on electron transfer in 20-200 keV $\alpha$-H collisions.\footnote{T. G. Winter, Phys. Rev. A {\bf 25}, 697 (1982).} These calculations, carried out 24 years ago on Penn State's IBM 3033 mainframe computer, took 2-4 cpu hours per total cross section per $\alpha$ energy. Now, using a very similar Fortran program, they have been repeated with the same 19- to 24-state bases and numerical parameters on a 3.32 GHz IBM ThinkPad in about 1/300th the cpu time, reproducing the transition probabilities at each impact parameter to at least five digits and the integrated capture cross sections to the full published three digits. The cross sections have also now been confirmed stable to three digits with respect to the choice of the numerical parameters. These calculations can now much more readily be extended to larger bases and a wider range of energies. Direct excitation and ionization will also be considered.   

\textbf{Absolute Charge Exchange Cross Sections for O}$^{5+}$\textbf{, O}$^{6+}$\textbf{, and O}$^{7+ }$\textbf{Collisions with CO and CO}$_{2}$

Motivated by ongoing EUV and X-ray studies of comets, we have continued our experimental investigations of absolute charge exchange cross sections for highly-charged ions present in the solar wind incident on cometary gases. These are the first measurements on the JPL charge exchange beam-line using a new LabView data acquisition system combined with a larger gas cell exit aperture. Data for O$^{5+}$ {\&} O$^{7+ }$on CO$_{2}$ agree with earlier measurements [1], and are included in these new results for O$^{5+}$, O$^{6+}$, and O$^{7+ }$on CO and CO$_{2}$. The ion beam accelerating potential was 7 kV, which yields ion velocities consistent with the fast component of the solar wind. Agreement with earlier, smaller exit aperture measurements is also significant in demonstrating an independence from angular collection issues for these fast, heavy ions and targets. This was verified by studying collection angle-cross section effects for slow $^{3}$He$^{2+}$ ions on He and H$_{2}$. This work was carried out at JPL/Caltech, and was supported through contract with NASA. N.Djuric also acknowledges support through the NASA-NRC program. [1] J.B. Greenwood, et al., Phys. Rev A \textbf{63}, 062707 (2001).   

Reaction Microscope for Ion-Atom and Ion-Molecule Interactions at Auburn University

We have designed and built a new end station at the Auburn University accelerator to perform COLTRIMS style measurements of the interactions between fast ions and atomic or molecular targets. The newly completed apparatus incorporates large multi-hit position sensitive detectors, a supersonic atomic/molecular beam and uniform electric and magnetic fields for performing momentum imaging spectroscopy. Planned collision investigations include measurement of fundamental processes such as ionization, capture and transfer ionization of both atomic and molecular targets. Preliminary results for orientation effects on the double ionization of molecular hydrogen will be presented.   

Numerical study of charge transfer processes in collisions of Be$^{4+}$ and He$^{2+}$ with atomic hydrogen

We have calculated state-selective charge-transfer cross sections in collisions of Be$^(4+}$ with H(1s) and of He$^{2+}$ with H(1s). We have used the lattice time-dependent Schr\"odinger equation (LTDSE) approach, the atomic orbital coupled channel (AOCC) method, and the classical trajectory Monte Carlo (CTMC) method. The calculations are performed with impact energy ranging between 1keV/u and 1MeV/u. With a well chosen basis-function set, we have found that AOCC gives good agreement with LTDSE. Also, with regard to Wigner's $n^{-3}$ law, we have found that CTMC gives good extrapolations to the cross sections calculated by LTDSE and AOCC toward high $n$ levels such as for those greater than 6. Thus, in our presentation, we will propose theoretical values of the total charge-transfer cross sections for these collision systems based on a combination of the most reliable results of the various method. This research used resources of the Center for Computational Sciences at Oak Ridge National Laboratory, which is supported by the Office of Science of the Department of Energy under Contract DE-AC05-00OR22725, and also of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098.   

Three-body dynamics in single ionization ion-atom collisions

Kinematically complete differential cross sections are presented for single ionization of sodium by H$^{+}$ and C$^{6+}$ at energies between 0.1 and 1.0 MeV/u. The momentum distributions for electron emission are studied as a function of the recoil momenta of the sodium ion. Calculations are made using the Classical Trajectory Monte Carlo model and the Continuum-Distorted-Wave (CDW) quantum method. Both models include the three-body interactions between the projectile, ionized electron, and Na$^{+}$ recoil ion. It is shown that the double collision dynamics between the active electron and both the projectile and recoil ion can be easily distinguished if the recoil ion momenta are measured in coincidence with that of the electron.   

Autoionization of He by partially stripped ion impact

The autoionization of He by ion impact can be considered a two step process in which the atom is first excited to an autoionizing state and afterwards decays emitting one electron to the continuum. Several theoretical methods have been developed in order to predict the position of the autoionization peak and the profile of the ``Coulomb focusing peak.'' For the latter, the enhancement in the impinging ion direction arises by the postcollisional interaction between the emitted electron and the receding projectile. Previous studies have considered He$^{+}$ projectiles with a pure Coulomb potential. In this work, we present the new features that partially stripped ions will leave on the main visible structures of the doubly differential cross sections (i.e. the autoionization and binary rings). These energy and angular profiles are also compared with those obtained with pure Coulombic ions.   

Singularity Structure of the Free-Free Radiative Transition Matrix Element.

Using the Lippman-Schwinger formalism we analyze the origin and derive general expressions for delta-function, pole-type and log-type singularities of 3D and radial free-free radiative transition matrix elements. We demonstrate how discrepancies between acceleration, velocity and length forms at singularities can arise due to non-commutation of some limiting procedures inherent in scattering theory. Using the phase-amplitude method, we obtain analytic properties of soft-photon free-free matrix elements and derive expressions for the general case of (fully, partially, and un-) screened Coulomb potentials.Results are used to analyze the structure of trajectories of zeroes of matrix elements in the plane of incident and final energies) in the soft-photon regime.   

Charge Transfer Cross Section Measurement in Na+ + Rb(4d)

Single charge transfer measurements at in the few keV collision energy range are fairly well known, both experimentally and theoretically. The exception to this is the case of charge transfer from excited-state targets. Here, we present experimental charge transfer cross sections, differential in scattering angle, for 7 keV Na$^{+}$ + Rb(4d). The measurements were made using the MOTRIMS methodology, and the Rb is prepared using resonant, 2-photon, 2-color, laser-excitation.   

The Effect of Image States on Resonant Neutralization of Hydrogen Anions near Metal Surfaces

We scrutinize the role of electronic image states on the ion--survival by comparing the resonant charge transfer dynamics of hydrogen anions near Pd(111), Pd(100), and Ag(111) surfaces~[1,2]. It is found that image states that are degenerate with the metal conduction band favor the recapture of electrons by outgoing ions. In sharp contrast, localized image states that occur inside the band gap hinder the recapture process and thus enhance the ion--neutralization probability.\newline [1]~Chakraborty et~al., Nucl. Instr. Meth.~B, in print,\newline [2]~Chakraborty et~al., Phys. Rev.~A~69, 052901   

Measurement of alignment dependence in single ionization of hydrogen molecules by fast protons

Relative cross sections for the 4 MeV H$^{+}$ + D$_{2}$ ($^{1}\Sigma _{g}^{+})^{ }\to $ D$_{2}^{+}$(1$s\sigma )$ + e$^{-}$ process are measured as a function of the molecular alignment during the interaction. The angle between the molecular axis and the projectile is obtained by using a momentum imagining technique and isolating the events in which the D$_{2}^{+}$(1$s\sigma )$ ions are excited to the vibrational continuum of the electronic ground state and subsequently dissociate. While several theoretical models suggest different angular distributions, and anisotropic distributions have been observed for double ionization of D$_{2}$, our preliminary results do not show significant anisotropies.   

Studying angular and radial correlation in atomic systems by means of the transfer-ionization process

We report a joint theoretical-experimental study of the transfer ionization process p + He $\rightarrow$ H$^0$ + He$^ {2+}$ + e$^-$ for different collision geometries, where the collision fragments were detected in coincidence. We demonstrated that the fully differential cross section was sensitive to both radial and angular correlation in the target. We have, we believe, demonstrated conclusively that the mechanism proposed by Schmidt-B\"ocking does indeed give the dominant contribution to the transfer-ionization process. Both theory and experiment are now in good accord and indicate that transfer ionization in fast collisions at small scattering angles is very sensitive to high-level target correlation effects. \\1. A.L. Godunov, Colm T. Whelan and H.R.J. Walters, {\it J. Phys. B:} {\bf 37}, L201 (2004); 2. A.L. Godunov, Colm T. Whelan and H.R.J. Walters et al, {\it Phys. Rev.} A (2005) (submitted; 3. M. Sch\"offler, A.L. Godunov, Colm T. Whelan, et al {\it J. Phys. B:} (2005) (submitted)   

Elastic and transport cross sections for inert gases in a hydrogen plasma

Accurate elastic differential and integral scattering and transport cross sections have been computed using a fully quantum-mechanical approach for hydrogen ions (H$^{+}$, D$^{+}$ and T$^{+})$ colliding with Neon, Krypton and Xenon, in the center of mass energy range 0.1 to 200 eV. The momentum transfer and viscosity cross sections have been extended to higher keV collision energies using a classical, three-body scattering method. The results were compared with previously calculated values for Argon and Helium, as well as with simple analytical models. The cross sections, tabulated and available through the world wide web (www-cfadc.phy.ornl.gov) are of significance in fusion plasma modeling, gaseous electronics and other plasma applications.   

Electron Impact Dissociation of CH2+ Producing CH+ and C+ Fragments

Absolute total cross sections have been separately measured for electron-impact dissociation of CH$_{2}^{+}$ molecular ions resulting in CH$^{+}$ and C$^{+}$ fragments for 3-100 eV collisions using a crossed electron-ion beams technique. Magnetic analysis was used to selectively separate and detect the product CH$^{+}$ and C$^{+}$ ions, which were generated through a combination of dissociative excitation (DE) and dissociative ionization (DI) channels. DE yields neutral light fragments, while DI yields charged light fragments in addition to the CH$^{+}$ or C$^{+}$. In these measurements coincident light H, H$_{2}$ and/or H$^{+}$, H$_{2}^{+}$ fragments were not detected. The relatively `hot' (internal state) 10 keV CH$_{2}^{+}$ ions were provided by the ORNL CAPRICE ECR ion source. For both CH$^{+}$ and C$^{+}$ the measured total cross sections above 20 eV are approximately equal and energy independent at $\sim $ 5 x 10$^{-17}$ cm$^{2}$. The total uncertainties of the present results are about 10{\%} at 40 eV. A broad peaked structure is observed in the CH$^{+}$ cross section rising to $\sim $ 1 x 10$^{-16}$ cm$^{2}$ at 10 eV. These heavy fragment data are being combined with previous measurements of light fragments from dissociation of CH$_{2}^{+}$ in an attempt to develop a coherent picture of the total electron-impact dissociation process. Research was sponsored by the OBES and OFES, U.S. DOE, under Contract No. DE-AC05-00OR22725 with UT-Battelle, LLC.   

Electron Impact Ionization of Helium

Recently completed measurements of the absolute doubly-differential cross sections for the electron impact ionization of helium at low incident energies will be presented. The measurements were taken using the moveable nozzle technique.\footnote{M.\ Hughes, K.\ E.\ James, Jr., J.G.Childers, and M.A.\ Khakoo, {\it Meas. Sci. Technol.} {\bf 14}, 841 (2003)} Data were taken at incident energies of 26~eV, 28~eV, 30~eV, 32~eV, 34~eV, 36~eV, and 40~eV. The results are compared to the theoretical convergent close-coupling calculations of Bray {\it et al.}\footnote{Igor Bray, Dmitry V.\ Fursa, and Andris T.Stelbovics {\it J.\ Phys.\ B} {\bf 36}, 2211 (2003)}, and good agreement is observed. This work is funded by the National Science Foundation under grant \# NSF-RUI-PHY-0096808.   

Excitation of ground state of Oxygen to a metastable state by electron impact

We have made preliminary calculation for the excitation of oxygen atom from the ground $2p^4 (^3P)$ to the mtastable $2p^33s (^5S)$ state. We have used the recently extended MCHF method for multi-open channels to calculate the excitation cross sections. The important electron correlation and polarization effects have been taken into account completely ab-initio by the extended MCHF method. We have also used the R-matrix method to calculate the same to compare with the MCHF results. We will present the comparison of both MCHF and R-matrix results with the available experimental and other theoretical calculations. These results will be useful for astrophysical applications.   

Excitation of Atomic Nitrogen by Electron Impact

The B-spline R-matrix method with a pseudostates approach has been used to calculate electron collision excitation cross sections for the resonance $2p^3$ $^4S^o$ - $2p^23s$ $^4P$, $2s2p^4~^4P$, $2p^24s~^4P$, $2p^23d~^4P$ and forbidden $2p^3~^4S^o$ - $2p^3$ $^2D^o$, $^2P^o$ transitions for incident electron energies from threshold to 100 eV. The effect of coupling to the continuum is included through the use of pseudostates. The close-coupling expansion contains 21 spectroscopic bound states and 18 pseudostates. The pseudostates are chosen to account for most of the dipole polarizabilities of initial and final states. The non- orthogonal orbitals are used to describe the term dependence of radial functions for an accurate representation of target states. Measured absolute direct excitation cross sections of nitrogen are reported by Doering and coworkers from Johns Hopkins University. Our results will be compared with the measured cross sections.   

Electron Impact Excitation of $O^{3+}$

The Breit-Pauli R-matrix with pseudostates approach has been used to calculate electron impact excitation cross sections between fine-structure levels of the $2s^22p$, $2s2p^2$, $2p^3 $, $2s^23s$, $2s^23p$, $2s^23d$, 2s2p3s, 2s2p3p, 2s2p3d, $2s^24s$, and $2s^24p$ configurations of $O^{3+}$. The effect of coupling to the highly excited bound and contonuum target states have been simulated by using a set of pseudostates in the R-matrix expansion. The target states are represented by configuration-interaction wave functions that yield excitation energies and oscillator strengths which are in close agreement with experiment and other accurate calculations. Rydberg series of resonances converging to the excited level thresholds are found to make substantial contributions to the cross sections. Significant differences with earlier calculations indicate the importance of coupling to the continuum.   

Electron Impact Excitation of Molecular Nitrogen.

New electron impact differential cross-sections for excitation of the lowest eight electronic states of molecular nitrogen will be presented. The data were obtained by unfolding high resolution electron energy loss spectra of molecular nitrogen using well-known Franck-Condon factors and normalized using our moveable source system\footnote{Hughes et al., Meas. Sci. Technol. \underline {14}, 841 (2003).} to the Time-of-Flight measurements of LeClair and Trajmar.\footnote{L. R. LeClair and S. Trajmar, J. Phys. B \underline {29}, 5543 (1996).} The data were taken at a large range of incident electron energies from near-threshold to 100eV and for scattering angles up to 130 degrees. Comparison to available experiments and theory is made. \\ ~ \\ This work is supported by a grant from the NASA Planetary Atmospheres Program office.   

Cross sections for excitation of the metastable levels of Kr

The heavy rare gases (Kr,Xe) differs from the lighter ones (Ne,Ar) in that the energy levels for each excited configuration are split into two separate tiers. This energy difference is due to the large spin-orbit splitting of the $^2P_{3/2}$ and $^2P_ {1/2}$ ion cores. We have measured excitation cross sections out of the two metastable levels of the Kr $4p^55s$ configuration and into the levels of the $4p^55p$ configuration by detecting the radiation from these levels induced by electron collisions. The atomic beam effusing through a hole in a hollow cathode discharge contains Kr atoms in both the $J$=2 and $J$=0 metastable levels as well as atoms in the ground level. The electron energy is low enough so that excitation into the $4p^55p$ levels can occur only from the metastable levels. The $J$=2 and $J$=0 metastable levels are each associated with a different ion core. To determine the cross sections out of the two metastable levels separately we utilize laser quenching. Cross sections from the $J$=2 metastable level ($^2P_{3/2}$ ion core) are largest into $4p^55p$ levels with the same ion core. Likewise, values for the $J$=0 metastable level ($^2P_{1/2}$ ion core) are largest into excited levels with the same ion core. This is true even for the $J=2$ level of the $4p^55p$ ($^2P_{1/2} $) configuration, which is a dipole-forbidden transition from the $J$=0 metastable level but dipole-allowed from the $J$=2 metastable level.   

Electron-impact excitation of carbon

The $B$-spline $R$-matrix method [1,2] is used to investigate electron-impact excitation of carbon from threshold to 60$\,$eV. An MCHF method with non-orthogonal orbitals is employed to generate an accurate representation of the target. Our close-coupling expansion includes the bound and autoionizing states of carbon derived from the $1s^22s^22p^2$, $1s^22s^22p3\ell~(\ell\!=\!0,1,2)$, $1s^22s^ 22p4s$, $1s^22s2p^3$, and $1s^22p^4$ configurations, plus pseudo-states to fully account for the polarizability of the ground state. Cross sections and effective collision strengths are presented for important transitions from the ground state $2p^2$ $^3P$ and the metastable $2p^2$ $^1D$ and $^1S$ states. Our predictions for the cross sections show significant discrepancies from those of previous calculations carried out with the standard $R$-matrix approach in a similar scattering model~[3]. These discrepancies are due to the different target descriptions, with the present one giving overall superior agreement with experiment for energy levels and oscillator strengths. The cross sections show prominent resonance structures in the low-energy region. The energy positions, widths, and classifications for the detected resonances are presented. \par\noindent [1] O. Zatsarinny and C. Froese Fischer, J. Phys. B~{\bf 33}, 313 (2000). \par\noindent [2] O. Zatsarinny and C. Froese Fischer, J. Phys. B~{\bf 37}, 2173 (2004). \par\noindent [3] K.M. Dunseath {\it et al.}, J. Phys. B \bf{30}, 277 (1997).   

Electron Impact Ionization of H$_2$

Relative doubly-differential cross sections for the low energy electron impact ionization of H$_2$ have been measured. Measurements have been completed at 30~eV incident energy and scattering angles of $60^\circ$ and $90^\circ$, and at 40~eV incident energy and scattering angles of $50^\circ$ and $90^\circ$. The calibration of the electron analyzer during these measurements employed the recent doubly-differential cross section measurements of atomic hydrogen.\footnote{J.\ G.\ Childers, K.E.James, Jr., Igor Bray, M.\ Baertschy, and M.\ A.\ Khakoo, {\em Phys.Rev.\ A} {\bf 69}, 022709 (2004).} These measurements represent a new calibration standard useful in the determination of the transmission function of electron analyzers. This work is funded by the National Science Foundation under grant \# NSF-RUI-PHY-0096808.   

$R$-matrix with pseudo-states calculation for electron scattering from rubidium

We have applied an $R$-matrix with pseudo-states model to calculate electron scattering from rubidium atoms. Using a semi-empirical model potential to describe the Rb$^+$core~[1], we obtain a highly accurate description of the target valence spectrum. Results will be presented for total and angle-differential cross sections, spin-polarization and asymmetry functions, and various electron-impact coherence parameters. The convergence of the theoretical predictions with the number of states in the close-coupling expansion is analyzed. Comparison of the results with recent experimental data [2,3] shows satisfactory though by no means perfect agreement. \par\noindent [1] K. Bartschat, {\it Computational Atomic Physics} (Springer, 1996), Ch.~2. \par\noindent [2] B.V. Hall {\it et al.}, J. Phys. B {\bf 37} (2004), 1113. \par\noindent [3] W.E. Guinea {\it et al.}, J. Phys. B {\bf 38} (2005), in press.   

Electron scattering from large molecules: a 3d finite element R-matrix approach

To solve the Schr\"{o}dinger equation for scattering of a low energy electron from a molecule, we present a three-dimensional finite element R-matrix method [S. Tonzani and C. H. Greene, { J. Chem. Phys.} {\bf 122} 01411, (2005)]. Using the static exchange and local density approximations, we can use directly the molecular potentials extracted from ab initio codes (GAUSSIAN 98 in the work described here). A local polarization potential based on density functional theory [F. A. Gianturco and A. Rodriguez-Ruiz, { Phys. Rev. A} {\bf 47}, 1075 (1993)] approximately describes the long range attraction to the molecular target induced by the scattering electron without adjustable parameters. We have used this approach successfully in calculations of cross sections for small and medium sized molecules (like SF6, XeF6, C60 and Uracil). This method will be useful to treat the electron-induced dynamics of extended molecular systems, possibly of biological interest, where oth er more complex ab initio methods are difficult to apply.   

Very high-order harmonic generation from Ar atoms and Ar$^{+}$ ions in super intense pulsed laser fields

We present an \textit{ab initio} nonpertubative investigation of the mechanisms responsible for the production of very high-order harmonic generation (HHG) from Ar atoms and Ar$^{+}$ ions by means of the self-interaction-free time dependent density functional theory recently developed [1]. Further, by introducing an effective charge concept, we can study at which laser intensity the contribution to the high-energy HHG from Ar$^{+}$ ions precede over the Ar atoms. Comparing the HHG behavior from Ar atoms and Ar$^{+}$ ions in super intense laser field, we conclude that the high energy HHG observed in the recent experiment [2] originated from the ionized Ar atoms. [1] J.J. Carrera, S.I.Chu and X.M.Tong, Phys. Rev. A (submitted) [2] Gibson, et. al., PRL 92, 033001 (2004)   

Sixth-Order Dynamic Hyperpolarizability of Hydrogen Rydberg Levels

The sixth-order dynamic hyperpolarizability, $\gamma^{(6)}(\omega)$, determines the third-order laser intensity $I$ corrections, $\Delta E_n^{(6)}\sim \gamma^{(6)}I^3$, to the usual Stark-effect, $\Delta E_n^{(2)}\sim \alpha I$, of an atomic level $|E_n\rangle$. The corrections $\Delta E_n^{(2)}$, $\Delta E_n^{(4)}$, and $\Delta E_n^{(6)}$ can be used to estimate the behavior of perturbation theory (PT) series with increasing intensity, and their imaginary parts allow one to estimate the threshold intensity of atomic level stabilization. For numerical calculations of 6th order PT matrix elements for $\gamma^{(6)}$, we generalize the method of Sturmian expansions of the Coulomb Green's function having two arbitrary parameters (suggested in [1] for calculations of $\Delta E_n^{(4)}\sim \gamma^{(4)}I^2$). Numerical calculations of $\gamma^{(6)}$ for $n \leq 10$ and linear laser polarization were carried out over a wide interval of frequencies, from $\hbar\omega \sim 0.1|E_n|$ up to $\hbar\omega \sim 10|E_n|$. In the high-frequency limit, all circular states (with $l = |m|= n-1$) clearly show the onset of stabilization. Our result for the $5g$-state is in reasonable agreement with experiments [2] for Ne. [1] N. L. Manakov et al., Sov. Phys. JETP {\bf 98}, 254 (2004). [2] N. J. van Drutten et al., PRA {\bf 55}, 622 (1997).   

Alternative Representations for H in an Intense Laser Field

We will present calculations of hydrogen in an intense laser field. In particular, we will focus on alternative representations to examine their effectiveness for computing and understanding ionization. We solved the time-dependent Schrodinger equation using methods like finite differences and b-splines for the spatial degrees of freedom utilizing various coordinate systems. The prospects for application to multielectron atoms will be explored.   

Electron Capture and Ionization in Laser--Assisted Collisions

We study laser-assisted ion--atom collisions in a strong laser field (above $10^{12}~\mathrm{W/cm^2}$) by solving the time dependent Schrödinger--equation on a 3-dimensional numerical grid. This way we obtain benchmark results for electron capture and ionization probabilities that are compared with other theoretical approaches, such as the non--perturbative basis-generator method (Kirchner, Phys. Rev. Lett.~89-093203), time--dependent scattering theory (Li et al., J.~Phys.~B~35-557) or grid-models of reduced dimensionality (Niederhausen et al., Phys. Rev.~A~70-023408). Our results for impact-parameter dependent ionization and capture probabilities for a colliding proton with a hydrogen atom in the presence of circularly polarized light show a strong dependence on both, the absolute laser phase and the laser helicity. In particular, we find an interesting strong dependence of the ionization probability on the impact parameter and laser phase that might enable the measurement of the absolute laser phase.   

X-ray probes of strong field processes in atoms

Ultrafast laser-X-ray pump-probe experiments will be a major thrust area for the next generation light sources. The shorter pulselength of the X-rays, 200 fs compared to the current 100 ps at APS, will enable probing of ultrafast transient phenomena initiated by, for example, a high power, ultrafast laser. At zero time delay, there will be substantial modification of the spectrum of the sample due to the presence of the laser. We are measuring this modification in the near threshold spectrum of a well-characterized sample (in our case, gas phase krypton atoms) in the presence of the laser over field strengths of 10$^{10}$ - 10$^{14}$ W/cm$^{2}$. Technical developments have made it possible to place 40{\%} of the available x-ray flux ($\sim $1 million x rays/pulse) within a 10 micron spot contained within a $\sim $100 micron laser focus. At an intensity of $\sim $2 x 10$^{14}$ W/cm$^{2}$, krypton ionization is saturated and we have obtained a complete near-edge spectrum of singly-ionized Kr. Coulomb expansion of the laser-produced ion assembly has been studied both with x-ray in/x-ray out techniques and charged particle detection. X-ray in/x-ray out techniques offer a distinct advantage when probing primary processes since charged particle detectors are sensitive to secondary collisions whereas x-ray emission occurs on the femtosecond timescale.   

Nondipole interactions in outer-shell photoionization

New aspects of photoionization are being investigated through measurements and theoretical calculations of nondipole interactions. Interference of electric-dipole amplitudes with electric-quadrupole and magnetic-dipole amplitudes give rise to asymmetries between the intensities of photoelectrons emitted in the forward- and backward-hemispheres with respect to the photon propagation direction. Nondipole asymmetries are sensitive to variations in the magnitudes and phases of photoionization amplitudes such as due to discrete-continuum and continuum-continuum channel coupling. We have developed an electron spectrometer system designed to efficiently measure nondipole asymmetries in photoelectron angular distributions. Using 10-160 eV radiation at Wisconsin's Synchrotron Radiation Center, we are studying nondipole interactions in direct- and resonant-photoionization of the outer shells of atomic rare gases and small molecules. Recent results will be presented.   

Non-Dipole Effects in Spin Polarization of Photoelectrons from $3d$ Subshells of Xe, Cs and Ba

The non-dipole contribution to spin polarization of photoelectrons from Xe, Cs and Ba $3d_{5/2}$ and $3d_{3/2}$ levels is calculated. The calculation is carried out within the framework of a modified version of the Spin-Polarized Random Phase Approximation with Exchange. The effects of relaxation of excited electrons due to the $3d$-vacancy creation are also accounted for. It is demonstrated that the parameters that characterize the photoelectron angular distribution as functions of the incoming photon energy, although being predictably small, acquire additional peculiarities when the interaction between electrons that belong to the $3d_{5/2}$ and $3d_{3/2}$ components of the spin-orbit doublet is taken into account.   

Correlation Effects in the Photoionization of Confined Calcium and Zinc

Studies of atoms confined in an endohedral environment have aroused significant recent interest [1]. In this work, the photoionization @Ca and @Zn have been studied using the Relativistic-Random-Phase Approximation, modified to include the confinement potential. Photoionization of the 4$s$ and 3$p$ subshells of free and confined atomic calcium, along with the 4$s$, 3$d$, 3$p$ and 3$s$ subshells of free and confined atomic zinc, have been studied. The photoionization parameters of confined atoms differ significantly from those of their ``free'' counterparts. The dipole cross sections and angular distribution asymmetry parameters exhibit oscillations with energy arising from the back scattering of the escaping electron by the confining potential, i.e., ``confinement resonances'' [2]. These oscillations persist when nondipole matrix elements are also included as is reflected in the nondipole cross section and angular distribution asymmetry parameters [3]; the relative strengths of the oscillations due to back-scattering in the E1 and E2 photoionization parameters have qualitatively different profiles as a function of photon energy. [1] V. K. Dolmatov, A. S. Baltenkov, J.-P. Connerade and S. T. Manson, Radiation Phys. Chem. \textbf{70}, 417 (2004). [2] M. Ya. Amusia, A. S. Baltenkov, V. K. Dolmatov, S. T. Manson and A. Z. Msezane, Phys. Rev. A \textbf{70}, 023201 (2004). [3] P.C. Deshmukh, Tanima Banerjee, K. P. Sunanda and R. Hari Varma, Radiation Phys. and Chem (submitted).   

MCHF Studies of Partial Photoionization Cross section of Atomic Fluorine

We will present results of theoretical investigation on the partial and total photoionization cross sections between the $^1D$ and $^1S$ thresholds of atomic fluorine using the multiconfiguration Hartree-Fock method of bound and continuum wave functions. The $2p^4(^1S)ns,md $ series observed by experiment through their decay into the allowed $2p^4(^3P)kl$ and $2p^4(^1D)kl$ ionization channels are carefully identified. The $2s2p^6 \ ^{2}S $ resonance is seen to interact strongly with the nearby $2p^4(^1S)4s \ ^{2}S $ resonance. The results are compared with the available experimental and theoretical data. The energy positions of the resonance series $2p^4(^1S) ns,md $ as well as $2s2p^6 \ ^{2}S$ are found to be in very good agreement with experimental observations.   

Satellite Lines in High-Energy Atomic Photoionization

The recent discovery that interchannel coupling persists to high energy [1] has altered the viewpoint that the non-relativistic photoionization cross section for an \textit{nl} atomic subshell at asymptotically high energies was essentially a single-electron process and depends upon energy E as E$^{-(l+7/2)}$ [2]. It was shown [3] that, owing to interchannel coupling, that this is correct only for photoionization \textit{ns} and \textit{np} states; for all \textit{nl} states with greater $l$, the asymptotic energy dependence is E$^{-9/2}$, just as it is for \textit{np} states. In the present work, implications of initial state correlation are explored. It is found that including initial state configuration interaction can have a profound effect upon the high-energy photoionization. For the photoionization of most \textit{nl} subshells ($l\ne $ 0) throughout the periodic system, the dominant transition is not the single-particle transition from the \textit{nl} subshell but a satellite transition of \textit{ns}$\to $\textit{kp} character. The cross section for the satellite transition exhibits the high-energy dependence characteristic of an $s$-state of E$^{-7/2}$, while the single-particle (main line) transition behaves as E$^{-9/2}$. Thus, in the nonrelativistic high-energy limit, most photoionization cross sections behave as E$^{-7/2}$, and satellite transitions dominate. Several examples are presented. This work was supported by DOE, NSF, and BSF. [1] E. W. B. Dias, \textit{et al}, Phys. Rev. Lett. \textbf{78}, 4553 (1997). [2] U. Fano and A. R. P. Rau, Phys. Rev. \textbf{162}, 68 (1967). [3] M. Ya. Amusia, \textit{et al}, Phys. Rev. Lett. \textbf{85}, 4703 (2000).   

Photoionization of Atoms and Ions Confined by Negatively-Charged C$_{60}$

Recent studies of the photoionization of atoms and ions endohedrally confined in C$_{60}$ have uncovered a wealth of new physics concerning how the atomic properties are modified by the confinement [1]. In a continuation of these investigations, the effects of a negatively-charged C$_{60}^{-q}$ cage on the photoionization of confined N 2$p$ and Li$^{+}$ 1$s$ have been investigated using Hartree-Fock and Spin-Polarized Random-Phase Approximation with Exchange methodologies. Our results for N 2$p$ with q=2 show that the lowest energy ``confinement resonance'' [2] at about 20 eV is increased by about a factor of five and narrowed somewhat by the charge on the cage. For Li$^{+}$ 1$s$, calculations with q=1 to 3 show a modest increase with q in the lowest resonance at about 90 eV, plus an entirely new and unexpected series of much narrower resonances that increase in amplitude with q. In addition, the threshold behavior is altered dramatically in going from q=0 to 3. Since each initial state is smaller than the C$_{60}$ radius, i.e., unaltered by the confinement, this phenomenology is due to the final state wave function, the emerging photoelectron interacting with the combined ionic and confinement potential. This work was supported by NSF and CRDF. [1] V. K. Dolmatov, A. S. Baltenkov, J.-P. Connerade and S. T. Manson, Radiation Phys. Chem. \textbf{70}, 417 (2004). [2] M. Ya. Amusia, A. S. Baltenkov, V. K. Dolmatov, S. T. Manson and A. Z. Msezane, Phys. Rev. A \textbf{70}, 023201 (2004).   

Nondipole Photoionization Parameters of Atomic Mercury

Over the past few years, photoionization parameters have been found to be affected by nondipole terms at much lower energies than was known earlier [1,2]. The primary motivation for the present investigation is to study the effect of interchannel coupling involving E1 and E2 photoionization channels from subshells with large orbital angular momentum ($l>$2). In an extension of earlier work [3], the nondipole photoelectron angular distribution asymmetry parameters $\gamma $and$\delta $ from the 6$s$ and 5$d$ subshells of atomic mercury have been obtained in the energy range from the respective thresholds up to 45 au. Relativistic-Random-Phase Approximation (RRPA) theory at various levels of truncation of the RRPA was used which allowed us to pinpoint the effects of interchannel coupling. The role of interchannel coupling between the 6$s$ and 5$d$ photoionization channels and the 4$f$ channels in both the dipole (E1) and the quadrupole (E2) manifolds has been detailed and has been found to be of considerable significance. This work was supported by DST and NSF. [1] A. Derevianko, W. R. Johnson and K. T. Cheng , At. Data Nucl. Data Tables \textbf{73}, 153 (1999). [2] O. Hemmers, \textit{et al}, Phys. Rev. Lett. \textbf{91}, 053002 (2003); \textbf{93}, 11301 (2004). [3] P. C. Deshmukh, Radiation Phys. and Chem. \textbf{70}, 515 (2004) and references therein.   

The Iron Project and the Rmax Project: New Computational Methods and Atomic Processes in Heavy Elements

We describe recent progress in two sets of codes designed to study collisiional and radiative processes in heavy elements: (I) The R-Matrix II method, and (II) The Full Breit-Pauli R-Matrix method. New calculations are in progress for the Iron group and heavier elements. Results will be presented for Fe and Ni ions in several ionization stages. In addition, the application of the Iron Project and the RmaX Project data to laboratory and astrophysical sources will be demonstrated, in particular for time-resolved spectroscopy of X-ray lines of He-like ions, and for the analysis of optical and near-infrared spectra of Fe~I-II-III in active galactic nuclei including exact radiative transfer.   

Calculation of He photoionization with excitation and de-excitation cross section

We present calculation results for photo-ionization with de- excitation of excited He and helium-like ions at high but non- relativistic photon energies $\omega$. The cross-section of this process is expressed in fact via integrals similar to that used already in description of two-electron ionization and ionization with excitation. In principle, the considered process can be separated pure experimentally from other two- electron processes, namely double ionization and ionization with excitation, if the photoelectrons's energy for a given incoming photon frequency $\omega$ is detected. Very accurate non-variation wave functions are used. As excited several lower $^{1}S$ and $^{3}S$ states are considered. We present the ratios $R^{+*}_{d}$ of the cross sections ``photo-ionization with de-excitation'' $\sigma ^{+*}_{(d)}(\omega )$ and ``photo- ionization with excitation'' $\sigma ^{+*}(\omega )$. It is shown how $R^{+*}_{d}$ depends upon the excitation of the target object and the charge of its nucleus.   

Are Electron Partial Waves Real

Experiments determining the partial wave content of electrons are uncommon. The standard approach to partial wave expansion of the wavefunction of electrons often ignores their spin. In this non-relativistic approximation the partial waves are labeled by their orbital angular momentum quantum number, e.g. d-waves. As our previous work has shown, this non-relativistic approximation usually fails for photoelectrons. Partial waves should be further specified by their total angular momentum. With d-waves for example, one would need to distinguish between d$_{3/2}$ and d$_{5/2}$ partial waves. Although energetically degenerate, fully relativistic d$_{3/2}$ and d$_{5/2}$ partial waves of photoelectrons have fundamentally different angular distributions. Using experimental and theoretical methods we have developed, we obtain partial wave probabilities of photoelectrons from polarization measurements of ionic fluorescence. We found that for selected states of the residual ion, there are energy regions where the photoelectron is in a single partial wave with predictable angular distributions.   

Photoionization of Kr$^{5+}$ Ions using Synchrotron Radiation

Absolute measurements of cross sections for photoionization of Kr$^{5+}$ are reported in the photon energy range 74 -- 175 eV at spectral resolutions of 50 meV and 100 meV. The experiments were performed using synchrotron radiation from an undulator beamline of the Advanced Light Source with an ion-photon merged-beams endstation. The Flexible Atomic Code (FAC) and Cowan atomic structure code were used to calculate energy levels, excitation energies and oscillator strengths for autoionizing transitions from the ground and metastable states of Kr$^{5+}$. The results show that the photoion yield spectrum in the photon energy range 88 -- 175 eV is dominated by excitation of an inner-shell $3d$ electron into \textit{np} and \textit{nf} orbitals, and in the energy range 74 -- 88 eV by excitation of a $4s$ electron into \textit{np} orbitals. Continuum photoionization is negligible by comparison. When their energy scales are shifted by several eV, the resonance energies and oscillator strengths calculated using both atomic structure codes agree well with the measurements.   

Photoelectron Recapture Investigation in Ar Using Two-Dimensional Photoelectron Spectroscopy

``Complete'' two-dimensional photoelectron spectra of Ar in the vicinity of the $2p$ ionization thresholds have been measured allowing several features in the spectra to be explained. The photoelectron recapture probability above the $2p_{1/2}$ threshold has been studied by measuring directly the kinetic energies of the reemitted photoelectrons as a function of the photon energy. We find a recapture maximum at about 120 meV above the threshold. Our experimental results are compared with semiclassical calculations as well as with the quantum-mechanical calculation of Tulkki \textit{et al.} [Phys. Rev. A 41, 181 (1990)] and are found to be in moderate agreement.   

A Complete Relativistic Determination of Photoelectron Partial Wave Probabilities by Polarization Analysis of the Fluorescence from an Excited Argon Photoion

Following atomic photoionization, the angular momentum of the photoelectron is coupled with that of the residual ion. For excited states, the angular momentum of this photoion can be directly assessed via fluorescence polarimetry, thereby allowing the photoelectron partial wave probabilities to be determined with high resolution and efficiency. This determination is not limited to the orbital angular momentum of the photoelectron but also allows a full relativistic partial wave analysis. Using circularly-polarized ionizing radiation from threshold to 2 eV above, we have measured the circularly-polarized fluorescence in the collision plane as well as the linearly-polarized fluorescence above this plane, thereby allowing the complete determination of all three partial wave probabilities for the Ar 3$p^{6}$ to Ar$^{+}$ 3$p^{4}$4$p \quad ^{2}$F$_{7/2}+\varepsilon ^{~}d_{5/2}$, $g_{7/2}$, $g_{9/2}$ photoionization process.   

Production and Decay of Ultracold Feshbach Molecules in Bosonic and Fermionic Species.

We investigate the production efficiency of weakly-bound, ultracold molecules in bosonic $^{85}$Rb and also fermionic $^{40}$K when the magnetic field is swept across a Feshbach resonance [1]. For adiabatic sweeps of the magnetic field, our novel model shows that the conversion efficiency of \textit{both} species is solely determined by the phase space density of the atomic cloud, in contrast to a number of theoretical predictions. In the non-adiabatic regime our measurements of the $^{85}$Rb molecule conversion efficiency follow a Landau-Zener model. The spontaneous dissociation of these $^{85}$Rb molecules has also been observed [2]. The molecular lifetime shows a strong dependence on magnetic field, varying by three orders of magnitude between 155.5 G and 162.2 G. Our measurements are in good agreement with theoretical predictions in which molecular dissociation is driven by inelastic spin relaxation [3]. Molecule lifetimes of tens of milliseconds can be achieved close to resonance. [1] Cond-mat/0411487 [2] Phys. Rev. Lett. \textbf{94}, 020401 (2005) [3] Phys. Rev. Lett. \textbf{94}, 020402 (2005)   

Signature of chaos in high-lying doubly-excited two-electron atoms

Recently proposed diabatization and truncation techniques are used in solving Schr\"{o}dinger equation for two-electron systems. Within this method, it is easy to obtain relatively high accurate energy levels for doubly-excited states of a given symmetry. Nearest-neighbor spacings (NNS) statistics of the energy levels are performed for real 3D helium atom below ionization threshold $I_{20}$. The ss model of helium-like ions are also used, which allows us to analyze NNS up to $I_{35}$. We show evidence of the transition towards Wigner distribution as the energy range gets closer to double-ionization threshold.   

Third-order many-body perturbation theory calculations for low-lying states in beryllium

A detailed breakdown of many-body perturbation theory (MBPT) contributions through third order is presented for energies of the ten $(2l \, 2l')$ states of beryllium. A total of 84 one-body and 578 two-body terms contribute to the third-order energy. Third-order MBPT calculations for monovalent atoms were carried out fifteen years ago by Blundell \textit{et al}.[1] Second-order calculations for ions of the berylliumlike isoelectronic sequence were also reported six years later[2]. In that paper, only 4 one-body and 20 two-body terms contribute to the second-order energy of neutral Be. The agreement with experimental energies was at $5\%$ level. Our study aims to present complete third-order MBPT formulas, and apply them to the simplest two-valence particles system beryllium to improve the agreement with experiment.\newline \newline $^1$ S.A. Blundell, W.R. Johnson and J. Sapirstein, Phys. Rev. A \textbf{42}, 3751 (1990).\newline $^2$ M.S. Safronova, W.R. Johnson and U.I. Safronova, Phys. Rev. A \textbf{53}, 4036 (1996).   

Collisional depolarization of the atomic Cs-$6s^{2}S_{1/2}\rightarrow10s^{2}S_{1/2}$ transition with argon buffer gas

We report an experimental investigation of collisional depolarization of the atomic cesium $6s^{2}S_{1/2}\rightarrow 10s^{2}S_{1/2}$ two-color two-photon polarization spectrum. The Ar pressure dependence of the spectrum revealed strong depolarization in the vicinity of the $6s^{2}S_{1/2}\rightarrow6p^{2}P_{3/2}\rightarrow10s^{2}S_{1/2}$ stepwise resonances using short pulse pump-probe technique. The linear polarization degree was measured with the first laser tuned to resonance and the second laser tuned within a \pm 11 $cm^{-1}$ range. In the absence of collisions, the measured polarization spectrum is in excellent agreement with calculations. The polarization measurement on the $6s^{2}S_{1/2}\rightarrow6p^{2}P_{3/2}\rightarrow10s^{2}S_{1/2}$ transition and an overview of the experimental techniques of our results are also presented.   

Spectral Modulation by Rotational Wave Packets

Periodic rephasing of molecular rotational wave packets can create rapid fluctuations in the optical properties of a molecular gas which can be used to manipulate the temporal phase and spectral content of ultrashort light pulses. We have demonstrated spectral control of a time-delayed ultrafast probe pulse propagating through the rotational wave packet prepared by a pump laser pulse. The spectrum of the probe pulse can be either broadened or compressed, depending on the relative sign of the temporal phase modulation and the initial chirp of the probe pulse. Adjustment of the spectral phase at the output of the interaction region allows controlled temporal pulse streching$^1$ and compression$^2$. The degree to which the spectrum of an ultrafast pulse can be modified depends on the strength and shape of the rotational wavepacket. We are studying the optimization of the rotational wave packet excitation with complex, shaped pump laser pulses for the purpose of optimizing probe pulse spectra modulation. $^1$ Klaus Hartinger and Randy A. Bartels, Opt. Lett., submitted (2005). $^2$ R.A. Bartels, T.C. Weinacht, N. Wagner, M. Baertschy, Chris H. Greene, M.M. Murnane, and H.C. Kapteyn , Phys. Rev. Lett., {\bf 88}, 013903 (2002). {\bf This work was supported by the NSF.}   

Pressure broadening of the sodium $3s$-$3p$ resonance lines by helium atoms.

Quantum mechanical calculations are performed of the emission and absorption profiles of the sodium $3s$-$3p$ resonance lines under the influence of a helium perturbing gas. We use carefully constructed potential energy surfaces and transition dipole moments to compute the emission and absorption coefficients at temperatures $T=158$, $240$, $403$, $500$, $1000$, $2000$ and $3000$~K at wavelengths between $500$ nm and $760$ nm. Contributions from quasi-bound states are included. The resulting red and blue wing profiles are compared with previous theoretical calculations and experimental measurements. Supported in part by NSF and NASA.   

Calculations of autodetachment lifetimes of metastable states of Ba$^-$ and Eu$^-$

The metastable $5d6s6p$ $J=9/2$ state of Ba$^-$, which decays by autodetachment to $6s^2\epsilon h$, has been found to be long lived with an estimated lifetime greater than 1 ms \footnote{ V. V. Petrunin $et~al.$, Phys. Rev. Lett. {\bf 75}, 1911 (1995).} \footnote{T. Andersen $et~al.$, J. Phys. B {\bf 30}, 3317 (1997).}. For the bound state, we have extended our basis set to include orbitals up to $l=6$ due to the importance of $\langle nlvl'|H|nl\epsilon h\rangle$ contributions to the energy width. We have also opened the $5p$ subshell to provide core-valence correlation to ensure proper mixing of the important $5d^2\epsilon h$ and $6p^2\epsilon h$ configurations in the continuum state. As we approach completion of this calculation, current results suggest an auto detachment lifetime greater than 10 ms. The analogous, and more computationally challenging, $4f^75d6s6p$ $J=8$ state in Eu$^-$, which decays by autodetachment to $4f^76s^2\epsilon h$, has been found to be similarly long lived.   

Infrared Transitions in Fe II

The spectral analysis of the star $\eta$ Carinae has been undertaken by Verner {\it et al.} [1]. This analysis requires, as input, oscillator strengths of a wide range of transitions. Many of the transitions in the ultraviolet region have recently been studied both experimentally and theoretically (e.g. Pickering {\it et al.} [2]). However, the required infrared transitions have received little attention. In this work, we have used configuration interaction methods to calculate oscillator strengths of Fe II transitions of the form $5s- 5p$. Both lower and upper states of these transitions are highly excited, so it is necessary also to include many other states in the calculation, partly because of strong configuration interaction mixing between states.\\[0.3cm] We will present results for these transitions and compare them with results by Raassen and Uylings [3].\\[0.5cm] \noindent [1] Verner E.M.\ {\it et al.}, {\it Astrophys. J.} {\bf 581} 1154 (2002) \\[0.0cm] [2] Pickering J.C.\ {\it et al.}, {\it Astron. Astrophys.} {\bf 396} 715 (2002) \\[0.0cm] [3] Raassen A. J. J., Uylings P. H. M., {\it Astron. Astrophys.} {\bf 340} 300 (1998) \\   

X-ray emission from collisions of O$^{7+}$ with atomic and molecular gases in the 35 to 50 KeV range.

The solar winds are mainly comprised of protons and helium ions; however, the energetic x rays emitted from ion-comet interactions originate from the smaller fraction of heavier highly charged solar-wind ions (e.g., C, N, O, Mg, Fe ions), which have large electron-capture cross sections. One of the goals of this work is to provide high-resolution spectroscopic information for modeling of soft x-ray emission observed from solar-wind ion interactions with cometary gases. Using the JPL ECR ion source in conjunction with a grazing incidence XUV spectrometer, equipped with a CCD camera, x rays in the wavelength range from 2 to 40 nm have been measured in collisions of O$^{7+}$ with CH$_{4}$, CO, He, H$_{2}$, and H$_{2} $O gases.   

Cl K$\beta$ and Cl K$\alpha$ resonant x-ray Raman

K$\beta$ and K$\alpha$ x-ray emission has been measured after core Cl 1{\it s} resonant excitation of gas phase HCl. Dispersive asymmetrical K$\alpha$ emission lines were observed. This new effect is described in terms of resonant x-ray Raman scattering. In the case of the K$\beta$, we observed a dynamical emission explained, thanks to theoretical calculations, by the nuclear dynamics on a sub-femtoseconde time scale. Work was partly supported by NSF grant PHY-01-40375.   

Dielectronic recombination rate coefficients to excited states of O~III from O~IV and dielectronic satellite lines

Energy levels, radiative transition probabilities, and autoionization rates for C-like oxygen (O$^{2+}$) including $1s^22s^22pnl$, $1s^22s2p^2nl$, and $1s^22p^3nl$ ($n$=2-8, $l \le n-1$) states are calculated by relativistic Hartree-Fock method with configuration interaction (Cowan code). Autoionizing levels above the thresholds $1s^22s^22p\ ^2P$, $1s^22s2p^2\ ^4P,\ ^2D,\ ^2S,^2P$, and $1s^22p^3\ ^4S,\ ^2D$ are considered as well. The branching ratios relative to the first threshold and intensity factors are calculated for dielectronic satellite lines, and the dielectronic recombination rate coefficients are found for the excited 218 odd-parity and 218 even-parity states. The total dielectronic recombination rate coefficient is derived as a function of electron temperature, the contribution from the excited states with $n >$ 8 being estimated by extrapolation of all atomic characteristics. The state-selective dielectronic recombination rate coefficients to excited states of C-like oxygen are calculated as well, which makes the present results especially useful for modeling the O III spectral lines in a recombining plasma. This work was supported in part by DOE/NNSA under UNR grant DE-FC52-01NV14050.   

Optical clockwork for a precision measurement in hydrogen

Ultracold trapped hydrogen ($<$100 micro kelvin) provides an excellent environment for spectroscopy and an opportunity to extend the experimental precision of the Lamb shift and the Rydberg constant. We will describe a newly constructed array of stable laser systems (ring dye laser, prismless Ti:saph femtosecond comb, synchronized diode lasers) designed to measure the ratio of the frequency of the 2S-8S transition to the frequency of the 1S-2S transition in hydrogen.   

Creating Cold Molecules to Constrain the Evolution of the Fine Structure Constant

Theories that try to unify gravity with the other fundamental forces predict variations in the fundamental constants over time, including the fine structure constant. Comparing measurements of OH transition frequencies at cosmological distances with laboratory based measurements can give a limit of the time variation of the fine structure constant. We create cold OH molecules by using the phenomenon of supersonic expansion to cool the molecules and the Stark effect to slow the resulting molecules for precision spectroscopic measurements. We have made the most precise measurements of microwave transitions in the ground state of OH to complement the astronomical observations.   

Work on improving a high precision experiment in helium

Current work to improve an experimental setup for high precision laser spectroscopy of helium is presented. Included is ongoing work to construct a UHV apparatus for improved signal to noise, among other benefits. Also presented are efforts to design and implement a high brightness electron source using a lanthanum hexaboride cathode. This will provide the electron emission for initial state preparation of the helium atoms. Efforts to design and construct a cost effective laser source suitable for high precision spectroscopy and laser pumping applications are presented. Results with our custom designed Bragg gratings and ytterbium doped fiber in a Distributed Bragg Reflector configuration are discussed.   

Hamiltonian Symmetry in Special Relativity and the N-Body Dirac Equation: Progress Report

At recent DAMOP, ICPEAC and ICAP meetings I have reported on the new symmetric special relativity (SSR) needed to cure a flaw in relativistic quantum dynamics responsible for the absence of an n-body Dirac equation [1]. In SSR both position and velocity space are hyperbolic. The Hubble length $\rho(t)$ and light speed $c$ provide standards of length and velocity and share the cosmological time-dependence, $H(t)= c(t)/\rho(t)$. Their product is the new Hubble-Lorentz constant, $\sigma=c(t)\rho(t)= {c^2}{H_0}^{-1}=5\times10^{34}\mathrm{m}^2/\mathrm{s}$. The theory solves the center of mass problem and sustains an n-body Dirac equation, a fully relativistic Schrödinger equation, and a new, highly symmetrical hyperbolic Poincaré group. It provides a systematic dynamical derivation for algorithms used for center-of-mass effects like mass polarization, recoil and reduced mass in precision calculations in atomic spectroscopy. While not yet within range of detection, the idea of measuring the Hubble parameter $H_0$ in a local spectroscopic process can now be contemplated. The theory and its most recent results and implications will be reported. [1] F. T. Smith, Ann. Fond. L. de Broglie, to be published.   

N-resonances and atomic clocks

N-resonances are all-optical three-photon-absorption resonances with potential applications in small atomic clocks. We present a characterization of N-resonances in ${}^{87}$Rb in a vapor cell and detailed comparison with an analytical model.   

The United Field

First of all, the basic contradiction between the traditional electromagnetism principles and the assumption of the quantum theory is discovered. Then, the basic nature rule that everything including the electron, nuclear and so on is form of the energy, the energy and substance could be transferred from each other on certain conditions is put forward. And the characters of the force field are put forward. After that, the basic characters of the force field were discussed. It is also discussed that with the expansion of the universe, the element's physical and chemistry characters will change. The conclusion that the electromagnetic wave has same character along different directions was demonstrated. And the conclusion that the electron outside the atomic nucleus does not take any negative electric charge was drawn. By the end, it is discovered that both the electromagnetism field and the electric field are special forms of force fields. And it is discovered also that both the electromagnetism force and the electric force are special forms of the resultant force of the gravitation force and repulsion force. Later, an example how to realize the traditional electromagnetism theory was given out. Both the paper titled with the theory of modifying the law of gravity and the paper titled with the mistakes of the theory of relativity are the foundation of this theory.   

Mathematical Model for Fermions Using Orthogonal and Reciprocal Symmetries of Mat-Quantum Entities

Using the principles of ASR Alternative theory of special relativity, the reciprocity principle of construction elementary particles, association of points principle, and special distribution of mat-quantum in fermions a new mathematical model especially for electron is constructed and mass, angular momentum of electron are calculated theoretically, Coulomb felid interaction between two electrons are computed using MatLab program to sum extents.   

Three bosons in one dimension with short-range interactions

We solve the three-boson problem in one dimension for a variety of interactions. As a benchmark calculation, we follow a procedure outlined by McGuire to find exact results for the particle-dimer scattering phase shifts and three-body binding energies. These results are then compared to adiabatic hyperspherical calculations using the Eigenchannel R-matrix method, and to numerical solutions to the Faddeev equations. Excellent agreement is found between the various calculations. Next, we construct a low-momentum effective two-body interaction which we test in both the two and three-body sector. We show that cutoff-dependence and errors for two- body observables are removed order by order in our effective interaction. With the introduction of a single parameter three-body interaction, three-body observables are predicted to percent-level accuracy.   

Non-linear self-trapping of ultra cold atoms in two dimensions

We dynamically observe a non-linear self-trapping transition in a 2D optical lattice. Quantum degenerate atoms are confined by a dipole trap in the middle of a much larger 2D optical lattice. When the dipole trap is turned off, the atoms are self-trapped in a ring of 1D tubes when the difference in mean field energy between adjacent tubes is sufficiently larger than the tunneling energy. Because the atoms are free to expand ballistically perpendicular to the lattice plane, the density eventually drops below the critical self-trapping density. At that point the atoms can tunnel between the tubes, so they suddenly start to expand transversely in the lattice plane.   

Electron-Electron and Electron-Nuclear Interactions in Ionizing Atom-Atom Collisions

We report cross sections for ionization of He coincident with electron loss from He, Li, C, O, and Ne projectiles. For He, Li, C, and O projectiles, the cross sections were measured directly, while the Ne cross sections were obtained by transforming results for He projectiles colliding with Ne. We find that, at energies of about 100 keV/u, neutral projectiles can ionize a He target almost as effectively as a charged projectile. The contribution to ionization due to electron-electron interactions is found to scale with the number of available projectile electrons. Comparing ionization by the bound electrons on projectiles to ionization by free electrons, we find the cross sections for ionization by bound electrons are systematically smaller than those for free electrons.   

Loading and quantum state control of atoms in microscopic optical traps

As part of an experimental effort to demonstrate quantum logic gates using neutral atom hyperfine qubits we present experimental results showing loading of atoms into two micron sized optical dipole traps separated by $8~\mu\rm m.$ The trapping sites are optically resolved on a CCD camera using fluorescence imaging. We use the $F=2, m_F=0$ and $F=1, m_F=0$ clock states as the qubit basis. After optical pumping into the $F=2, m_F=0$ state tightly focused beams are used to perform two-photon stimulated Raman rotations between the qubit states. This approach provides the capability for performing qubit rotations on a site specific basis, by spatial scanning of the Raman beams. These steps, together with work in progress on dipole-dipole interaction of atoms excited to high lying Rydberg levels, will form the basis for demonstration of a neutral atom CNOT gate. This work is funded by the NSF and the Army Research Office.   

Period-doubling Instability of a Bose-Einstein Condensate in a Periodically Translated Optical Lattice

We observe dynamical instability of a Bose-Einstein condensate in a periodically translated optical lattice, which results in transient period-doubling of the zero momentum condensate wavefunction. The onset of instability is marked by the sudden growth of peaks at half the lattice recoil momentum in the atomic interference pattern of the released condensate. The effect is attributed to band shaping, introduced by modulation of the optical lattice potential, and breaking of translational symmetry by interparticle interaction. The threshold conditions for instability are successfully predicted by the Gross- Pitaevskii equation, in combination with simple arguments for the single-particle band shape. We connect this onset with the destructive interference of nearest-neighbor tunnelling amplitudes in the two lowest bands.   

Experimental Progress Toward a Quantum Hall Array of Bosonic Atoms

We describe progress toward the production of an array of small, isolated clusters of bosonic atoms, each held in an optical dipole potential which locally approximates a harmonic oscillator with a rotating anisotropy and/or minimum position. We show how this is accomplished by interfering ordinary gaussian beams, using only modulation of the beam phases, and present results demonstrating the ability to controllably impart angular momentum to atoms held in this potential. This demonstrates a promising method for producing strongly correlated few-body atomic states analogous to electrons in the fractional quantum hall effect\footnote{see e.g. Popp, M; Paredes, B; Cirac, JI; PHYSICAL REVIEW A; NOV 2004; v.70, no.5, p.053612}. We outline the experimental challenges in producing and observing such states.   

Single-beam all-optical $^{87}$Rb BEC

We report Bose-Einstein condensation of $^{87}$Rb using all-optical means. We observe a critical temperature of $\sim$125nK, $\sim$100,000 atoms at criticality, and pure condensates of $\sim$ 20,000 atoms. We have observed pure condensates in the m$_F$=0 state as well as condensates distributed among all Zeeman sublevels, as also observed by Barrett et al. and Cennini et al. Our apparatus consists of a quasistatic dipole trap generated by a single tightly-focused 40W CO$_2$ laser. Forced evaporative cooling is performed simply by temporal control of the laser intensity. Due to the dependence of trap frequency on intensity, particular attention has been paid to the choice of evaporative path using the scaling laws described by O'Hara et al.   

The effects of molecular vibration on the yield of high-order harmonic generation.

It is well-accepted that the high-order harmonic spectrum is the results of interference between many attosecond pulses. Each of the attosecond pulse is produced by a three-step process taking place within one laser cycle. For light molecules such as H$_{2}$, the first step is the ionization of one electron. When the freed electron returns to the H$_{2}^{+}$, the internuclear distance is changed. This may cause the electron to miss the ion during its revisit, thus reducing its probability to recombine with the parent ion. As a result, the high harmonic generation yield is lower for H$_{2}$ than D$_{2}$, since D$_{2}$ has a longer vibration period ($\sim $21 fs) than that of H$_{2}$ ($\sim $15 fs). Here we report, to the best of our knowledge, the first experimental observation of the effects of vibration on the yield of HHG in molecules. We compared the high-order harmonic spectra of H$_{2}$, HD and D$_{2}$. The shortest pulses were $\sim $8 fs, which is almost the same as one half of the vibration period of H$_{2}$. Using such short pulses assures that the internuclear distances of all three types of molecules are in the increasing phase of a cycle when the harmonics are generated. From the HHG spectra it is evident that the yield of D$_{2}$ is a factor of two higher than that of H$_{2}$, while that of HD is in between. This is consistent with the theoretical predictions.   

Optical and Electronic properties of some Interface Materials

The interface materials are of great importance in microelectronic device because of their role for the electrical, optical and electronic characteristics. This paper reports electronics and optical properties of some such materials used as interface like Aluminum Oxide etc. Ab-intio self-consistent studies are carried out using density functional theory methods. These studies include like band structure, Density of state, optical conductivity and dielectric coefficient etc. Results are compared with earlier available reported work and discussed in detail.