Session W1: Poster Session III

Boundary Solutions of the Two-electron Schr\"{o}dinger Equation at Two-particle Coalescences of the Atomic Systems

The limit relations for the partial derivatives of the two-electron atomic wave functions at the two-particle coalescence lines have been obtained numerically using accurate CFHHM wave functions. The asymptotic solutions of the proper two-electron Schr\"{o}dinger equation have been derived for both electron-nucleus and electron-electron coalescence. It is shown that the solutions for the electron-nucleus coalescence correspond to the ground and singly excited bound states, including triplet ones. The proper solutions at small distances $R$ from the triple coalescence point were presented as the second order expansion on $R$ and $\ln R$. The vanishing of the Fock's logarithmic terms at the electron-nucleus coalescence line was revealed in the frame of this expansion, unlike the case of electron-electron coalescence. On the basis of the obtained boundary solutions the approximate wave function corresponding to both coalescence lines have been proposed in the two-exponential form with no variational parameters.   

Temperature dependence of argon excimer emission from pulsed discharge excited argon clusters

Argon second continuum excimer emission is observed from a pulsed discharge excited pulsed supersonic argon expansion. The expansion nozzle consists of a temperature controlled, 15 cm long slit with a variable width (35 $\mu $m to 250 $\mu $m). The intensity of the argon excimer emission near 126 nm is investigated as a function of the width of the expansion nozzle slit, temperature of the expansion nozzle and position within the cathode-anode gap. The pressure within the nozzle has been measured as 2--4 bar and the excitation consists of a 50 ns negative current pulse of about 15kV and 700A. The observation of the emission depends directly on the size and quantity of clusters formed in the expansion. To determine the dependence of the emission upon clusters and the cluster size distribution, the mean cluster size is diminished by increasing the expansion nozzle and gas temperature. The temporal evolution of the second continuum emission and the observed spectra are presented as a function of nozzle temperature and slit width.   

Mixing of ro-vibrational levels of the $3\,^3\Pi$ and $4\,^3\Pi$ states of NaK due to nonadiabatic coupling

We report further results of our investigation of the excited $3\,^3\Pi$ and $4\,^3\Pi$ electronic states of NaK. These electronic states exhibit an avoided crossing, and many ro-vibrational levels are mixtures of both electronic components. The hyperfine structure and energies of numerous ro-vibrational levels were determined using the Doppler-free, perturbation-facilitated optical-optical double resonance (PFOODR) technique [J.~Chem.~Phys.\ {\bfseries 122}, 144313 (2005)]. However, the hyperfine spectra of the $3\,^3\Pi$ and $4\,^3\Pi$ levels are very similar, and excitation spectra to the two states are difficult to distinguish. Further work has shown that bound-free spectroscopy provides a means of differentiating the two electronic states and even estimating the mixing fractions for pairs of ro-vibrational levels. The nonadiabatic coupling between the $3\,^3\Pi$ and $4\,^3\Pi$ states has been exactly formulated in terms of the diabatic potential curves, and the diabatic curves have been determined that best fit the experimental data. Comparison between experimental and theoretical mixing fractions will be presented.   

Fine and hyperfine structure of ro-vibrational levels of the NaK $1\,^3\!\Delta$ states from $v=3$ to near the dissociation limit

Our previous high-resolution spectroscopic studies of the fine and hyperfine structure of ro-vibrational levels of the $1\,^3\!\Delta$ state of NaK have been extended to include vibrational levels up to $v = 59$, the highest of which are within $4~\mathrm{cm}^{-1}$ of the dissociation limit. Using the IPA method, a potential curve was determined that reproduces all measured levels ($3 \le v \le 59$) to an accuracy of $\sim 0.026\,\mathrm{cm}^{-1}$, and $C_6$ and $C_8$ coefficients have also been determined from the long range potential. The fine and hyperfine structure of the $1\,^3\!\Delta$ ro-vibrational levels were analyzed to determine the values $A_v$ and $b_{\mathrm{F}}$ of the spin-orbit coupling constant and the hyperfine Fermi contact constant. The measured fine and hyperfine structure for $v$ in the range $44 \le v \le 48$ exhibits anomalous behavior due to the mixing between the $1\,^3\!\Delta$ and $1\,^1\!\Delta$ states. The theoretical method has been extended to treat this interaction, and the results provide an accurate representation of the complicated patterns that arise. {\it Ab initio} calculations of the spin-orbit coupling constants $A_v$ are also underway.   

Spin-orbit coupling of the NaK $3^{3}\Pi$ and $3^{1}\Pi$ states: Determination of the coupling constant and observation of quantum interference effects

We have studied the mutually perturbing $3^{3}\Pi_{\Omega = 0}(v = 32, J = 19) \sim 3^{1}\Pi_{\Omega = 1}(v = 6, J = 19)$ levels of NaK that are coupled together by the spin-orbit interaction. This coupling is nominally forbidden by the $\Delta \Omega = 0$ selection rule for spin-orbit perturbations. However $3^{3}\Pi$ levels labeled by different values of $\Omega$ are mixed by rotational coupling; i.e. the $3^{3}\Pi _{\Omega }$ levels are best described by a coupling scheme intermediate between Hund's cases (a) and (b). Thus the $3^{1}\Pi_{\Omega = 1}$ level couples to the $3^{3}\Pi_{\Omega = 0}$ level via the small admixture of $3^{3}\Pi_{\Omega = 1}$ character in the latter. The $3^{3}\Pi_{\Omega = 0}(v = 32, J = 19) \sim 3^{1}\Pi_{\Omega = 1}(v = 6, J = 19)$ $f$ symmetry pair is of particular interest since it appears to be very close to a 50-50 mixture of triplet and singlet character, and the splitting between these levels provides a direct measure of the $3^{3}\Pi \sim 3^{1}\Pi$ spin-orbit coupling constant. Excitation spectra of the $3^{3}\Pi_{\Omega =0}(v = 32, J = 19) \sim 3^{1}\Pi_{\Omega = 1}(v = 6, J = 19)$ $e$ symmetry pair through the mixed ``window'' levels $1(b)^{3}\Pi_{\Omega = 0}(v = 17, J = 18, 20) \sim 2(A)^{1}\Sigma^{+}(v = 18, J = 18, 20)$ display dramatic quantum interference effects associated with ``singlet'' and ``triplet'' excitation channels. Complete cancellation for one or the other of the two upper states is observed for excitation from the predominantly triplet members of the window level pairs.   

Magnetism in Clusters of Cobalt and Chromium.

We report on measurements of magnetism in cobalt and chromium clusters of between 10 and 200 atoms. Both elements show magnetic order that exceeds that of the bulk. The low dimensionality of clusters allows them to retain much of their atomic magnetism. While cobalt is already ferromagnetic in the bulk, it shows increasing magnetization per atom as the cluster size decreases. Chromium, however, is antiferromagnetic in the bulk, so the observed magnetization in chromium clusters is more exotic.   

Tensor Polarizabilities of Sodium Rydberg States

We have used a time-domain spectroscopy technique to measure transitions between fine structure levels of Na Rydberg d and p states in a static electric field. Transitions are driven by delayed pairs of intense sub-nanosecond half-cycle electric field pulses. With these measurements we have determined the fine-structure splittings and tensor polarizabilities of the $n^*$d states for n = 15 to 24, and the $n^*$p states from n = 25 to 32. The results are more than an order of magnitude more accurate than earlier measurements of these quantities.   

Accurate treatment of doubly-excited Rydberg resonance states and dc-field ionization rates of two-electron systems

We present a complex-scaling (CS)-generalized pseudospectral (GPS) method in hyperspherical coordinates (HSC) for \emph{ab initio} and accurate treatment of the electron structure and quantum dynamics of two-electron systems [1]. The GPS method allows non-uniform and optimal spatial discretization of the two-electron Hamiltonian in HSC with the use of only a very modest number of grid points. The procedure is applied for the precision calculation of the energies and widths of doubly-excited Rydberg resonance states as well as the ionization rates of He atoms in intense dc fields. [1] J.~Heslar and S.~I.~Chu, Phys.\ Rev.\ A (submitted).   

Production and sensitive detection of PbF molecules for an e-EDM experiment.

The stationary states of a molecule in a pure electric field are degenerate in the sign of the projection of total angular momentum on the field axis. A lifting of this $\pm $M$_{F}$ degeneracy would be an indication of CP (time reversal) symmetry violation. For heavy paramagnetic molecules, this CP violation would be attributed to an electron electric dipole moment (e-EDM) and could at once separate Supersymmetric models from the Standard Model and explain why we are made of matter instead of antimatter. A major obstacle to observing CP violation in this way is that the background magnetic-field induced splitting of the $\pm $M$_{F}$ degeneracy normally dwarfs any possible electric-field induced splitting. Here we report how the physics of $^{2}\Pi _{1/2}$ PbF can be exploited to gain extraordinary sensitivity to the e-EDM while reducing the magnetic g factor to less than 10$^{-7}$. A new radical beam source and sensitive resonance enhanced multi-photon ionization (REMPI) detection of PbF are reported.   

Neutral Atom Lithography Using a Bright Metastable Helium Beam

We have performed neutral atom lithography using a beam of metastable 2$\,^3$S Helium (He*) that is brightened sequentially by the bichromatic force and then optical molasses\footnote{M. Partlow et al., Phys. Rev. Lett {\bf 93}, 213004 (2004).}. We have successfully demonstrated this technique using a physical mask of fine mesh covering a self assembled monolayer (SAM) of nonanethiol over a 20 nm evaporated film of Au on a Si wafer substrate\footnote{Younan Xia et al. Chem. Mater. {\bf 7}, 2332 (1995)}. The 20 eV internal energy of He* damages the SAM so that those damaged molecules and the underlying Au layer can be removed using a wet chemical etch$^5$. Samples created this way have an edge resolution of $\sim \,$63 nm that we measured with an atomic force microscope. This technique has promise for creating nano-structured meta-materials with unusual optical properties.   

Development of a high-flux Ca atom interferometer

We present progress towards a Ca atom interferometer. The device will utilize a thermal beam of atoms for simplicity and high signals. The atom waves will be split and recombined using a single-photon transition at a wavelength of 657 nm. A unique alignment scheme will be used to reduce systematic drifts due to Doppler shifts. We are currently working to improve the linewidth of the 657 nm laser and constructing a 423 nm blue laser to transversely cool the atoms and to detect the output of the interferometer. We are also characterizing a thermal Ca beam using laser absorption and working on precise control of the temperature and flux of the beam. We are also evaluating a precision method to align the thermal beam relative to gravity using Fraunhofer diffraction.   

Controlled entanglement of two atoms in movable traps

We propose a scheme for controlled entanglement of two separately trapped atoms. In our setup, the two atoms become entangled after the two initially separated traps are translated towards each other, overlap, and moved apart adiabatically. Cumulative adiabatic phase shifts arising from atomic interactions during the protocol give rise to a final two-atom state that can be conveniently expressed in terms of separable states involving single atoms in well defined traps. We provide a thorough investigation of the efficiencies and effectiveness of our scheme. We further calibrate the dependence of the fidelities of the entangled states on the various control parameters such as the speed of the trap translation. Finally, we show that our setup possesses several advantages and can be easily employed to accomplish a nontrivial quantum gate.   

Constructing atom optical elements from periodic potentials of finite length

The manipulation of the dispersion properties of a Bose-Einstein condensate (BEC) with moving optical lattices has enabled considerable control of atomic matter waves and, more recently, the generation of bright matter wave solitons [1]. Here, we computationally propagate BEC's through periodic optical potentials of finite spatial/temporal lengths. It is seen that to vary the effective mass requires potentials that are relatively strong compared to the transverse waveguide confinement. The role of both the linear and non-linear wave mechanics in practical issues such as loading the atoms into the potentials are explored. We also report on work in progress examining matter waves propagation through a chip-based magnetic lattice [2]. \\ $[1]$ Eiermann, B \textit{et.al} Phys.~Rev.~Lett. \textbf{92} 230401 (2004) \\ $[2]$ G{\"u}nther, A \textit{et.al} Phys.~Rev.~Lett. \textbf{95} 170405 (2005)   

Beamsplitting of a Bose-Einstein Condensate in a Microtrap by a Standing Light Wave

We have developed an in-guide atom beamsplitter and demonstrated the coherent nature of the process by observing interference between the split wavepackets. Pre-cooled atoms are captured by the on-chip waveguide and trapped by confining fields in a ``microtrap'' region of the guide. Atoms are then evaporatively cooled to form a Bose-Einstein condensate. Finally, we are able to split the condensate, propagate two wavepackets in opposite directions along the waveguide and read their relative phase by exposing the trapped BEC to a sequence of standing light pulses. We carefully aligned the standing light field with the waveguide by directly mounting mirrors on the chip substrate. Pre-cooled atoms reach the trapping region by following the guide through a 180-um-height tunnel under one of the mirrors. We control the phase shift between the two wavepackets by applying an external magnetic gradient parallel to the guide. After recombining the clouds, we observed coherence signals for up to 10 ms of propagation time. The in-guide production of a condensate, the numerous wires and features available on the chip and the proven coherence of the beamsplitter, make this device a useful tool for understanding and improving the propagation of coherent atomic samples in waveguides.   

Guiding atoms in a hollow-core photonic bandgap fiber

We discuss the current progress of our experiment to guide rubidium atoms in hollow-core photonic bandgap fiber. The atoms are contained within the hollow region of the fiber by the dipole potential created with a strong red-detuned laser. This technique has several significant advantages over other atom guiding experiments using hollow core fiber. First, the design of the air/silica structure allows low attenuation propagation ($<$ 0.1 dB/m) at certain wavelengths down the hollow core. As a result, the optical potential is uniform over the length of the fiber. Also, the light field is almost exclusively inside the hollow core, and it is relatively easy to couple light into the fiber. Since the field inside the fiber can be relatively high, it is possible to detune the laser far from resonance while maintaining a strong dipole potential, and thereby greatly reduce the scattering rate.   

Applications of cold, magnetically-guided atomic beams

In parallel with work aimed at developing a continuous-wave atom laser in a high-gradient magnetic guide, we are exploring tools suited to manipulate cold atomic beams in atom guides. We present an experimental demonstration of using RF-filtering to decrease the number of modes occupied by an atomic flow propagating in a high-gradient atom guide. Through sufficient filtering of this type, a near-single-mode guided atomic beam should be achievable, allowing basic atom-interferometric experiments. We present a new inline beam-splitting scheme using RF-dressed-state potentials. It is shown how this scheme could be employed to build fairly simple large-area Sagnac atom interferometers. Finally, we will present Monte Carlo collision simulations of novel evaporative cooling techniques in a guided atomic beam.   

Donut modes and photonic hollow fibers: a possible scheme for atom transport

Bragg fibers are a specific class of photonic bandgap fibers that have the capacity to be optimized for low-loss transmission of ``donut'' modes. This ability makes these fibers attractive as possible tool for atom optics. One example would be to transport neutral atoms through harsh environments. This would be possible by co-propagating a blue-detuned donut mode with the atoms through the fiber. We have studied the transmission efficiency of ``donut'' Bessel and Laguerre-Gaussian modes through a fiber designed to transmit 780 nm light both experimentally and theoretically. In this poster we will describe the results and discuss the prospects for atom loading and other applications.   

Observation of quantum accelerator modes in Rb atoms

We report the observation of Quantum Accelerator Modes (QAM) for cold Rb-87 atoms. Quantum accelerator modes are produced by the diffraction of atomic De Broglie waves. When a standing light wave which acts as a thin phase grating is produced, a group of atoms that have certain initial velocity gets accelerated. The momentum gained by these atoms scales linearly with the number of kicks. Gravity plays an important role in QAM through the phase evolution of the De Broglie wave between any two kicks. QAM can be used in the study of quantum chaos and atom optics.   

Loading and Manipulating Atoms on a Chip.

We describe a method of efficiently loading and manipulating neutral atoms in atom chip traps. Cooled 87Rb from a MOT is transported via coil-based magnetic traps into chip-based wire traps and precisely directed in wire-guides. Our loading method begins with the collection of a MOT located 4 cm away from the chip's trapping region. At this distance, a conventional MOT of six beams can be made without obstruction from the chip and its mounting structure. The MOT's anti-Helmholtz coils are aligned along an axis normal to the chip surface, and this pair of coils also serves as a magnetic quadrupole trap. A second pair of anti-Helmholtz coils is centered on the chip's trapping region. Trading currents between the two coils smoothly translates a magnetic trap over to the chip region. Finally, the atoms transfer to a U-shaped wire on the chip surface. We have achieved near unity transfer efficiency. Once in the U-trap, the atoms can transfer into a Z-trap and single wire guides. We report on investigations of manipulating atoms with external gradients, and splitting into reflected and transmitted components as they traverse a potential barrier. We also discuss results of studies to precisely control the output coupling of the atoms into the guide.   

Time-dependent analysis of pulsed EIT processes in atomic clocks

Narrow resonances established via Electromagnetically Induced Transparency under continuous excitations have been proposed as new optical frequency standards using either single trapped ions $[1]$ or neutral atoms trapped in an optical lattice $[2,3]$. In a similar approach to ultra high resolution spectroscopy, time separated Dark Resonance pulses in a three level $\Lambda$ system have been proposed $[4]$ as an alternative clock interrogation tool for probing a narrow transition between two long-lived states $[5,6]$. Pulse sequences are designed that mix steady states or transient regimes with a free evolution time of the metstable ground state coherence, with the goal to optimally recover the clock information prepared by EIT. Raman-Ramsey nutations are then demonstrated using a set of effective damped two-level Optical Bloch equations. To evaluate potential accuracy of an EIT based clock, AC Stark shifts are carefully considered. These light shifts can be expressed as phase shifts in the cosine function describing the Raman-Ramsey oscillations resulting in a frequency shift of the central fringe minima. $[1]$I. Siemers et al, EuroPhys. Lett.\textbf{18}, 139 (1992).$[2]$R. Santra et al, Phys. Rev. Lett.\textbf{94}, 173002 (2005).$[3]$T. Hong et al, Phys. Rev. Lett.\textbf{94}, 050801 (2005).$[4]$T. Zanon et al, Phys. Rev. Lett.\textbf{94}, 193002 (2005).$[5]$J.E. Thomas et al, Phys. Rev. Lett.\textbf{48}, 867 (1982).$[6]$P. Knight, Nature.\textbf{297}, 16 (1982).   

Generation, Storage, and Retrieval of Single-Photon Pulses using Electromagnetically Induced Transparency

We demonstrate the use of electromagnetically induced transparency (EIT) for the controllable generation, transmission, and storage of single photons with tunable frequency, timing and bandwidth. We study the interaction of single photons produced in a `source' ensemble of rubidium-87 atoms at room temperature with another `target' ensemble. This allows us to simultaneously probe the spectral and quantum statistical properties of narrow-bandwidth single-photon pulses, revealing that their quantum nature is preserved under EIT propagation and storage. We measure the time delay associated with the reduced group velocity of the single-photon pulses and report observations of their storage and retrieval. Finally, we discuss experimental progress towards application of these results to long-distance quantum communication.   

Optimal Control of Storage and Retrieval of Photon States in Atomic Ensembles

We describe an optimal control strategy for storage and retrieval of a photon wavepacket of a given shape in a radiatively broadened $\Lambda$-type atomic medium with a given optical depth (OD). The control is provided by an appropriately shaped classical laser field. We present a universal theoretical framework for analyzing various approaches to pulse storage ranging from adiabatic reduction of photon pulse group velocity and pulse propagation control via off-resonant Raman fields to photon-echo based approaches. We show that when properly optimized these three approaches yield identical efficiency. We extend our model to include Doppler broadening and, in particular, show that at high enough OD Doppler broadening is irrelevant.   

Investigation of lasing from dye doped plastics using flash lamp and Nd:YAG excitation.

We present an investigation of organic dye doped plastics as a lasing medium. The host materials examined are poly(methyl methacrylate) [acrylic], epoxy, polyester and polyurethane. Various solvents are used to improve dye dispersion within the material. Two forms of excitation (flash lamp and frequency doubled Nd:YAG) are used. For the Nd:YAG pumped dye lasers, a disk of dye doped plastic is mounted in a housing to provide random orbital motion. The disk is within a Littmann configuration cavity. Each dye disk is tested for threshold, durability, power output, bandwidth, and tuning range. An end pumped cylinder is also explored. For the flash lamp pumped dye lasers two configurations are used: a traditional dye cylinder within an elliptical reflector and a hollow cylinder with the flash lamp within the hollow. A monolithic cavity for the flash lamp pumped system is investigated.   

Observation of Electromagnetically Induced Transparency and Dark Fluorescence in a Lithium Molecule

We observed the electromagnetically induced transparency and dark fluorescence in a Lithium molecule. We used density matrix methods to simulate the response of an open molecular three-level system to the action of a strong coupling field and a week probe. The analytical solutions obtained under the steady state condition are in excellent agreement with the experimental spectra. We show that the coherence is remarkably preserved even when the coupling field was detuned far from the resonance transition.   

Toward Nonlinear Optics with Confined Photons and Atoms

Cold atoms trapped inside a hollow core photonic bandgap fiber create medium with unique optical properties, such as large optical depth and long coherence times. Furthermore, the fiber itself guides the interacting light in tight spatial confinement over distances not limited by diffraction and dramatically increases electric field intensity. Optical nonlinearities achievable under these conditions can be potentially used for coherent nonlinear interactions between single photon light pulses. In this work we present an atom cooling and trapping setup that loads cold Rb atoms into a dipole trap localized within the hollow core of the fiber and we study properties of the cold Rb atoms confined in the fiber.   

Optical coupling and parametric sideband generation in a semiconductor bound exciton

Group theoretical techniques are used to deduce the selection rules and energy splitting of the electric dipole absorption lines $\Gamma_6\rightarrow\Gamma_8$, $\Gamma_7 \rightarrow\Gamma_8$ of a donor exciton in a tetrahedral semiconductor, e.g., GaAs. We obtain selection rules for the above transitions for the spin states $\Delta m_j$. The application in a bound exciton system in a magnetic field for the purposes of obtaining electromagnetically induced transparency is discussed. In particular, Stokes and Anti Stokes couplings have been experimentally observed in such a system. We theoretically calculate the expected gains of the Stokes and anti Stokes couplings for $\sigma$- and $\pi$- polarization of the pump field. We show that the system can be interpreted as one exhibiting double $\Lambda$-type transitions, and therefore could be used for coherent non-linear optics and, ultimately, quantum-optics based quantum information processing.   

Dark-state polariton collapses and revivals

We investigate the dynamics of dark-state polaritons in an atomic ensemble with ground-state degeneracy. A signal light pulse may be stored and retrieved from the atomic sample by adiabatic variation of the amplitude of a control field. During the storage process, a magnetic field causes a rotation of the atomic hyperfine coherences, leading to collapses and revivals of the dark-state polariton number. These collapses and revivals are observed in measurements of the retrieved signal field, as a function of storage time and magnetic field orientation. We explain the observed reduction of revival amplitudes by accounting for magnetic field gradients within the atomic sample.   

Diffusion-Induced Ramsey Narrowing

Diffusion-induced Ramsey narrowing is a general phenomenon in which diffusion of coherence in and out of an interaction region such as a laser beam induces spectral narrowing of the associated resonance line shape. We will present an intuitive analytical model, detailed numerical calculations, and experiments illustrative of this spectral narrowing effect. Diffusion-induced Ramsey narrowing occurs commonly in optically interrogated atomic systems and may also be relevant to quantum dots and other solid-state spin systems.   

EIT spectra in coated cells

We use rubidium vapor cells with paraffin-coated walls, which greatly reduce the ground state decoherence rate due to wall collisions, to measure electromagnetically-induced transparency (EIT) spectra.  Characteristic line shapes have a dual structure, with a wide feature corresponding to the transit time-scale and an ultra-narrow feature corresponding to the coherence lifetime allowed by the coating.  Such narrow features can exhibit large contrast, and so are of interest to slow light studies.  Using a model based on Ramsey pulse sequences, we can explain qualitative behavior for both Zeeman and hyperfine EIT, with good line width agreement in the Zeeman case in the small beam limit.    

Slow light propagation in coated cells

Rubidium vapor cells with walls coated with paraffins such as tetracontane can have very long coherence times due to the suppression of decoherence during wall collisions by the coating. Here we report on the use of such cells (with an intrinsic coherence time of ground-state hyperfine and Zeeman transitions longer than 10 ms) for slow- and stored- light.  Guided by our static Ramsey-narrowing EIT model and recent dynamical simulations, we improve upon past results in terms of fractional pulse delay and storage efficiency.   

EIT noise spectroscopy with a broadband laser

Laser PM-AM noise conversion is of great interest in atomic clocks based on coherent population trapping (CPT) and the related process of electromagnetically induced transparency (EIT). We report a study of the role of EIT ground state coherence on the intensity-noise spectrum using a broadband laser such as a VCSEL. We also discuss possibilities of extending the result to photon statistics.   

Experimental study of light storage in Rb vapor

We study the propagation and storage of weak optical pulses in warm Rb vapor under conditions of electromagnetically induced transparency (EIT). We investigate the effects of various experimental parameters (such as buffer gas pressure, atomic density, etc.) on storage time and fidelity.   

Fluorescence spectrum of spontaneous emission in cavity.

We study the probe spectrum of light generated by spontaneous emission into the mode of a cavity QED system. We identify the spontaneous emission process by the polarization of the transmitted light when the excitation of the atoms is with linear polarization in a $\Delta m=0$ transition in the $D_2$ line of $^{85}$Rb. The probe spectrum has a maximum on-resonance when the number of inverted atoms for an input drive is maximal. For a larger number of atoms N, the maximum splits and develops into a doublet, but its frequencies are different from those of the so-called vacuum Rabi splitting.   

Atom-Field Entanglement in a Cavity QED System

We consider the entanglement in a cavity QED system as a function of driving field strength via the entanglement of formation and the logarithmic negativity. There is an optimal field strength for generating entanglement, around the saturation intensity. When the atoms become saturated, the system tends towards a product state where the field is in a coherent state. We also consider conditioned homodyne and conditioned photo as entanglement witnesses. Further we consider the time development of entanglement, and the amount of information about entanglement contained in time dependent cross correlation functions.   

Casimir force in a cylinder-plane configuration

We have developed and tested an apparatus [1] to measure the Casimir force in a cylinder-plane configuration, which is a compromise between the parallel plane and sphere-plane configurations, with intermediate advantages. Preliminary calibrations with electrostatic forces show that the Casimir forces should be detectable in a range large enough to observe the expected thermal corrections. \newline \newline [1] M. Brown-Hayes, D.A.R. Dalvit, F.D. Mazzitelli, W.J. Kim, and R. Onofrio, Phys. Rev. A 72, 052102 (2005).   

Quantum optics with surface plasmons: engineering strong coupling and efficient single-photon generation

We propose a method that enables strong, coherent coupling between individual optical emitters and electromagnetic excitations in conducting nano-structures. The excitations are guided optical plasmons that can be localized to sub-wavelength dimensions. The sub-wavelength confinement and small mode volumes associated with these plasmons lead to strong coupling with nearby emitters. We show that under realistic conditions, this coupling causes optical emission to be almost entirely directed into the plasmon modes via a mechanism analogous to the Purcell effect in cavity quantum electrodynamics. We first illustrate this result for the case of a nanowire, before considering the optimized geometry of a nanotip. We describe an application of this technique involving efficient single-photon generation on demand, in which the plasmons are efficiently out-coupled to a dielectric waveguide. Finally, we discuss a preliminary experiment to probe and observe the strong coupling regime between a silver nanowire and quantum dot.   

Barium Ion Trap Cavity QED

We report our progress toward the development of a scalable trapped ion and optical cavity system. Due to their long confinement times and the relative ease in trapping them individually, atomic ions remain an excellent candidate for tomorrow's qubit memories. The optical cavity system will provide the coherent coupling between single cavity photons and single trapped ions required to efficiently exchange quantum information between distant ion qubits. Combining atom-based quantum memories with photon-based quantum communication channels offers a compelling architecture for a quantum information network.   

Spectroscopy and coherent control of single nitrogen-vacancy (NV) centers

The nitrogen vacancy (NV) center in diamond has received considerable attention in recent years because it offers the opportunity to coherently manipulate the spin and electronic transitions of a single quantum system in the solid state. We describe optical spectroscopic measurements of single NV centers at low temperatures, via resonant excitation within the zero-phonon line, and observations of extremely sharp ($\sim $ 50 -- 100 MHz), stable spectral lines. We have also carried out experiments to measure the fine structure, determine the optical transition strengths, and perform coherent control on single NV centers. In particular, optically detected single spin Rabi nutations and Hahn echoes show long coherence times and coherent coupling to nuclear spins even at room temperature. NV centers represent a promising candidate for implementation of a recently proposed scheme for long distance communication. Experimental progress toward implementation of these ideas will be presented.   

Sudden switching in two-state systems

Analytic solutions are developed for two-state systems strongly perturbed by a series of rapidly changing pulses, called 'kicks'. The evolution matrix may be expressed as a time orrdered product of evolution matricies for single kicks. Single, double and triple kicks are explicitly considered, and the onset of time ordering is examined. The effects of different order of kicks on the dynamics of the system is studied and commpared with effects of time ordering in general. To determine the range of validity of this apporach, the effect of using pulses of finite widths for 2s - 2p transitions in atomic hydrogen is examined numerically.   

Noise Induced Decoherence of Rydberg Atoms in a DC Field

Application of a sudden field step to a Rydberg atom leads to creation of a Stark wavepacket whose evolution can be monitored using a half-cycle probe pulse applied after a variable time delay. We analyze the effects of noise on such wavepackets that is generated by quasi-randomly modulating the amplitude of the dc field. This noise induces decoherence which is manifested as a damping of the Stark quantum beats. We discuss the effects of different types of noise and present calculations and measurements for K(350p) atoms and ``colored'' noise, i.e., noise with a non-uniform power spectrum that possesses a characteristic frequency. We show that damping is most rapid when this frequency matches the orbital frequency of the Rydberg electron.   

Navigating in Phase Space

A Rydberg atom subject to a periodic train of unidirectional electric field pulses, termed half-cycle pulses (HCPs), of duration much less than the classical electron orbital period, is a ``kicked'' quantum system whose classical counterpart displays ``soft'' chaos, i.e., a mixture of regular and chaotic dynamics. Poincar\'{e} surfaces of section for the kicked atom contain a number of stable islands enclosed by KAM tori that are embedded in a chaotic sea. We show how different dynamical behaviors are observed if an initial state that is transiently localized in phase space is placed in different regions of large islands immediately before the train. If the initial state is localized at the center of the island little evolution of the excited-state distribution is observed during the HCP train. In contrast, placing the initial state in an outer region leads to periodic changes in this distribution that are associated with motion on the KAM tori. This work points to the feasibility of manipulating atomic states by navigating in phase space. Research supported by NSF, DoE, the R. A. Welch Foundation, and the FWF (Austria).   

Probing the momenta of Stark eigenstates

Approximate momentum distributions of Rydberg electrons in static electric fields have been obtained using an improved Impulse Momentum Retrieval (IMR)technique. An imaging detector enables the measurement of half-cycle pulse (HCP) ionization probability across the spatial profile of a focused HCP beam. By modulating the HCP amplitude [Zeibel and Jones, Phys. Rev. A \textbf{68}, 023410 (2003)], we directly measure the derivative of the ionization vs. HCP impulse curve, enabling the recovery of momentum distributions with finer resolution than previously attainable. For example, for Stark states with nearly zero dipole moments, we observe a notch in the projection of the momentum distribution along the Stark field axis. We have developed a semi-classical method for simulating the effect that the finite HCP duration has on our measurements. Reasonable agreeement between simulated and measured momentum distributions is obtained. This work has been supported by the AFOSR and the NSF.   

Measurements of rotation wave packets for molecular phase modulation

In recent years molecular phase modulation of light has been vigorously investigated as a method for optical pulse manipulation. We characterize rotational wave packets formed by intense laser pulses using the transient index of refraction. In particular, we are looking to find optimal conditions for spectral modulation of a probe pulse. Maximizing spectral modulation requires exciting wave packets with coherences between high angular momenta.   

Chaotic Escape of Specularly Reflecting Rays From a Vase-shaped Cavity

We study the escape of rays from a two dimensional, specularly reflecting open cavity having the shape of a vase. At the narrowest point of the neck of the vase there is an unstable periodic orbit which defines a dividing surface between rays that escape and rays that are turned back into the cavity. We imagine a point source on the cavity wall emitting rays in all directions and we record the time to reach a detector forming the mouth of the vase. We find that the rays arrive at the detector in pulses. The escape time, as a function of the initial conditions, displays a weak self-similarity which is understood upon transformation to a suitable phase space. Here, we find that the self-similarity arises from the intersection of the initial conditions with a homoclinic tangle, which is formed by the intersections of stable and unstable manifolds emanating from the unstable periodic orbit. We present a topological theory that partially predicts the self-similarity. We conclude with an example comparing the predictions to numerical calculations.   

Laboratory Observability of a Cosmologically Changing Light Speed

Einstein's axiom of special relativity was not an invariant light speed, but less restrictive: The velocity of light is independent of the motion of the light source. This is compatible with an expanding hyperbolic position space tangent to Minkowski four-space [1]. In this geometry $c$ decreases as $t^{-1/2}$ and a new Hubble-Lorentz expansion constant appears, $\sigma =c_0 ^2H_0 ^{-1}=3.89\times 10^{34}$ m$^2$s^{-1}$. The practical choice of $c$ as a defined constant is then not relativistically invariant, and should be modified. The logarithmic rate of change of $c$ is directly connected with the Hubble parameter, $d\ln c/dt=-H\left( t \right)/2$, with the present value $-3.65\times 10^{-11}\mbox{ y}^{-1}$. In 1972 $c$ was measured to 3.5 parts in $10^9$. If this precision can now be improved by 10 or 100, the predicted rate of change of $c$ can be tested. The issues involved in converting between cosmological and laboratory time and distance scales will be reported. Ultimately, a laboratory measurement of $H_0 $ may be in prospect. \newline \newline [1] F. T. Smith, Ann. Fond. L. de Broglie, \textbf{30}, 179 (2005); http://www.ensmp.fr/aflb/AFLB-302/table302.htm   

The Fundamental Constants if $c$ is Changing: A New Mass Constant and its Connection with the Electron

When special relativity is extended to expanding hyperbolic position space [1], $c$ decreases as $t^{-1/2}$ and there is a new expansion constant, $\sigma =c_0 ^2H_0 ^{-1}=3.89\times 10^{34}$ m$^2$s^{-1}$. Many fundamental constants become time-dependent and must be corrected by a small power of $c$. The corrected electrical permittivity of space is $\bar {\varepsilon }_{o} =\varepsilon_o c$, and $\alpha $ remains constant. The corrected gravitation constant is $\bar {G}=G/c$. A new fundamental mass constant of gravitation and cosmology occurs, $m_\ast =\left( {\hbar ^2/\bar {G}\sigma } \right)^{1/3}=\left( {\hbar ^2H_0 /G_0 c_0 } \right)^{1/3}$, with the value $1.087\left( {\pm 0.010} \right)\times 10^{-28}\mbox{ kg}$. Its product $\alpha m_\ast $ with $\alpha $ accounts for 87{\%} of the observed inertial mass $m_e $ of the electron. This establishes a new phenomenological relationship between the constants of electromagnetism and the electron on the one hand and those of gravitation and cosmology on the other. \newline [1] F. T. Smith, Ann. Fond. L. de Broglie, \textbf{30}, 179 (2005); ); http://www.ensmp.fr/aflb/AFLB-302/table302.htm   

Atomic structure measurements and tests of fundamental symmetries in a thallium atomic beam

Using a thallium atomic beam apparatus, we are undertaking a series of laser spectroscopy measurements with the goal of providing precise, independent cross-checks on the accuracy of new calculations of parity nonconservation in thallium, as well as probing possible new symmetry-violating forces. In our apparatus, a diode laser beam interacts transversely with a dense, thallium beam and reveals roughly tenfold Doppler narrowing of the absorption profile. Having completed a new 0.4\% measurement of the Stark shift in the 378 nm E1 transition in thallium, we are now studying the M1/E2 1283\,nm $6P_{1/2}-6P_{3/2}$ transition in the atomic beam. To enhance the detectability of this weak transition, we are utilizing both a two-tone frequency modulation method, as well as an entirely new scheme to measure differential optical cavity phase shifts induced by the atoms. In the course of this work, we have developed a new laser stabilization method suitable for locking near this E1-forbidden transition. We use low-field Faraday rotation polarimetry and achieve sub-MHz frequency stability. Future work includes two-step atomic beam excitation and Stark shift experiments in thallium, as well as a search for long-range T-odd, P-even symmetry-violating forces in thallium. Current results will be presented.   

Is the photon recoil equal to the photon momentum?

It is well known that an isolated atom recoils with the momentum of the photon when it absorbs a photon from an infinite plane wave. When the transverse electromagnetic field has a finite extent, the photon wave vector in the longitudinal direction is smaller. When an isolated atom absorbs a photon from a finite laser beam, is the atomic recoil smaller than that for an infinite plane wave? We show that it is smaller and it has a peculiar dependence on the transverse variation of the field. For atom interferometers that measure the photon-recoil, the difference in the size of the photon recoil is safely below the current measurement accuracy for the laser beams that are used. A related problem is the photon-recoil frequency-shift for microwave atomic clocks. For a cesium clock, the usual photon-recoil frequency shift of h$^{2}$k$^{2}$/2m gives a fractional frequency shift of 1.5$\times $10$^{-16}$, which is not far below the accuracy of current clocks. We show that the frequency shift does not have the usual form and has a similar behavior as for the transverse field variations above. It depends in unusual ways on the interrogation time, and the size of the atomic wavefunction at the first interaction.   

Progress toward improved Lorentz symmetry tests with H and noble gas masers

Measurements using atomic clocks can be sensitive to violations of Lorentz and CPT symmetry through differential frequency changes as the direction or velocity of the clocks change with respect to an inertial frame. We will present the status of experiments underway utilizing atomic hydrogen masers and the two-species noble gas masers which will improve constraints on potential Lorentz and CPT violations in the proton and neutron respectively.   

Demonstration of an Electron Electric Dipole Moment Experiment Using Electric-Field Quantization in a Cesium Cold Atom Fountain

A Cs fountain electron electric dipole moment (EDM) experiment using electric-field quantization is demonstrated. With magnetic fields reduced to $\le$ 200 pT, the electric field lifts the degeneracy between hyperfine $|m_F|$ levels and, along with the fountain geometry, suppresses systematics from motional magnetic fields. Transitions are induced and the atoms polarized and analyzed in field-free regions. Our results suggest that a fountain experiment can detect (or rule out) an electron EDM far smaller than the present experimental limits.   

Estimation of One- and Two-Photon Rydberg Transition Rates in Helium Driven Directly by an Optical Frequency Comb

Direct frequency comb spectroscopy (DFCS) involves the resonant excitation of atoms or molecules directly with one or multiple components of an optical frequency comb, allowing high resolution spectroscopy and absolute frequency measurements across a wide spectral bandwidth. While DFCS has been proven with alkali atoms, extension of the technique to atomic helium will lead to precision measurements of this important atom. For helium atoms formed in a metastable helium MOT at milli-Kelvin temperatures we have estimated transition rates for excitation by a frequency comb, using a quantum defect model with scaled oscillator strengths. In the triplet system, Rydberg $n^3D \leftarrow $2$^3S$ and $n^3S \leftarrow $2$^3S$ transitions can be excited by resonant or near-resonant two-photon excitation via the intermediate 3$^3P$ state. The rates are highly favorable, $>10^6$ s$^{-1}$ per atom even for $n \approx 40$. The 1$^1S$ ground state could also be studied by ``dumping" metastable atoms from the MOT using an additional laser. Although the two-photon 2$^1S \leftarrow $1$^1S$ transition presently looks unfeasible, rates for one-photon $n^1P \leftarrow $1$^1S$ transitions driven by a far-UV comb are reasonable.   

An Overview of the Search for the Electron Electric Dipole Moment Using Trapped Molecular Ions

The current limit on the electron electric dipole moment ($d_{e} < 1.6 * 10^{-27}$ e*cm) was set using an atomic beam of Tl \footnotemark. We have proposed the use of supersonically cooled molecular ions in an RF trap to improve this limit. This experiment should benefit from the large effective electric fields experienced by an electron in polarized molecules and the long spin coherence time of trapped ions. We will outline the motivation behind the two current candidate ions, HfH$^{+}$ and PtH$^{+}$. Recent experimental progress will also be discussed. \footnotetext[1]{B.C. Regan et. al., Phys. Rev. Lett. 88, 718051 (2002).}   

Precision mass measurement using two ions in a Penning trap

We have implemented a technique for precision mass comparison of two ions simultaneously trapped in a Penning trap in which each ion is alternately positioned at the center of the trap -- where its cyclotron frequency is measured -- or else parked in a large cyclotron orbit. Using the method to compare $^{28}$SiH$_{3}^{+}$/$^{31}$P$^{+}$ we have obtained a new atomic mass for $^{31}$P of 30.973 761 999 7(61) u. We have also used the method to observe shifts in the cyclotron frequency of the molecular ions CO$^{+}$ and PH$^{+}$ due to the interaction between the ion's polarizability and the motional electric field. Progress towards a) implementing \textit{simultaneous} cyclotron frequency comparisons using two ions in a coupled magnetron orbit, b) a precision measurement of the mass difference between $^{3}$T and $^{3}$He, c) the use of polarizability shifts for single ion molecular spectroscopy, and d) a precision mass measurement of $^{40}$Ca will also be reported.   

Progress on single trapped indium and barium ion optical frequency standards using all solid-state light sources

Single trapped ions cooled to the Lamb-Dicke regime are spectroscopic systems free of many external perturbations and are therefore attractive as optical frequency standards. We report continued development of single indium ion and barium ion rf Paul-Straubel traps and laser cooling systems. The forbidden ${^1}S_0 \leftrightarrow {^3}P_0$ transition in In$^+$ at 237 nm has a quality factor of $10^{15}$ and is immune to $\sim 1$ Hz quadratic Stark shifts that can limit other systems. In addition, the extraordinarily long $5D_{3/2}$ lifetime ($\tau \sim 80$~s) in a single trapped barium ion yields an electric dipole forbidden 2051 nm $6S_{1/2} \leftrightarrow 5D_{3/2}$ transition with a quality factor of $10^{16}$. Further, the odd isotope $^{137}$Ba$^+$ (I = 3/2) has an excited state with total angular momentum $F' = 0$ so an optical frequency standard based on this transition also avoids significant quadratic Stark shifts. We present our latest experimental probes of these transitions using new low linewidth diode pumped solid state laser systems (a frequency quadrupled non-planar ring oscillator Nd:YAG at 946 nm and a diode pumped Tm,Ho:YLF at 2 $\mu$m), new stable reference cavities, and propose a laboratory constraint on fundamental constant drift.   

Development of a compact atomic co-magnetometer

We have developed a high-sensitivity atomic co-magnetometer for tests of Lorentz and CPT symmetries. It also may be used as a gyroscope. Optical pumping of a high-density alkali metal vapor creates a spin-exchange relaxation free (SERF) magnetometer. The noble gas atoms in the cell are polarized by the alkali atoms. With an appropriate applied field, the polarized noble gas atoms cancel transverse magnetic fields, leaving the system sensitive only to non-magnetic spin interactions and rotation. We have performed a test of CPT and Lorentz symmetries by looking for a sidereal signal in the lab frame. To avoid long term drift, we are designing a small version of the magnetometer on a rotary platform. The smaller system will be more sensitive to the Johnson noise generated by thermal currents in the magnetic shields. In order to reduce this noise, we will use ferrite, rather than mu-metal, for the innermost layer of magnetic shielding. It is expected that sensitivity will also be increased by enclosing the optics in a vacuum chamber and using $^{21}$Ne instead of $^3$He as the noble gas.   

Progress towards an improved search for a permanent EDM of Hg atoms

The measurement of a finite permanent electric dipole moment (EDM) on any atom or particle would reveal a new source of CP violation outside of the Standard Model. At present, the tightest bound on any EDM comes from our measurement with $^{199}$Hg atoms, which set an upper limit of $|d| < 2.1 \times 10^{-28} \,e\,{\rm cm}$ [1]. In that work, a comparison was made of the spin precession frequencies in two $^{199}$Hg vapor cells placed in a common magnetic field and oppositely directed electric fields. The signature of an EDM would be a frequency shift correlated with the electric field direction. The present version of the experiment uses a stack of four vapor cells. The two additional cells are at zero electric field and are used as magnetometers to help reduce magnetic field gradient noise and to help diagnose magnetic systematic effects. Initial data taken with the four cell apparatus would often show electric field correlated magnetic field shifts. These effects were possibly due to HV discharges orienting trace ferromagnetic impurities, and the replacement of some materials near the vapor cells and an improved cleaning procedure have greatly reduced their occurrence. We expect to report data with at least a factor of two improvement in statistical sensitivity over our previous result. [1] M.V. Romalis, W.C. Griffith, J.P. Jacobs, and E.N. Fortson, Phys. Rev. Lett. {\bf 86}, 2505 (2001).   

Three-Photon EITA for Observing the $^{1}$S$_{0} \rightarrow\,^{3}$P$_{0}$ Clock Transition in Atomic Yb

Recent experiments have observed the $^{1}$S$_{0} \rightarrow\,^{3}$P$_{0}$ clock transition in odd isotopes of atomic Yb, where the transition is weakly allowed through internal hyperfine coupling. We report on progress towards an observation of this transition in the even isotopes, which offer the advantage of a narrower clock transition in which the energy interval is not affected by external magnetic fields or light polarization. While the single-photon transition is strictly forbidden in this case, three-photon electromagnetically induced transparency and absorption (EITA) can be used to produce a sharp resonance line. With this method, the width and rate of the clock transition can, in principle, be continuously adjusted from the MHz level to sub-mHz without loss of signal amplitude by varying the intensities of the three light fields. Doppler and recoil effects can be eliminated by proper alignment of the three optical beams. Theoretical calculations have shown that sharp Doppler-free EITA features can be expected on the three-photon clock transition and also on a simpler three-photon scheme using the $^{1}$S$_{0} \rightarrow\,^{1}$P$_{1}$ (399~nm) and $^{1}$S$_ {0} \rightarrow\,^{3}$P$_{1}$ (556~nm) transitions. Experimental work is underway to test this arrangement, with eventual application to the clock transition via the 556~nm, 680~nm, and 649~nm transitions involving the $^{1}$S$_{0}$, $^{3}$P$_{1}$, $^{3}$S$_{1}$, and $^{3}$P$_{0}$ states.   

Some Investigations with Fiber Coupled Laser Diode Modules for Use in Precision Spectroscopy

Mass produced commercial fiber-coupled pump laser diodes are particularly attractive laser sources because of their relatively high power (200-500 mW) and low cost compared to other laser systems. We incorporate narrow bandwidth fiber Bragg gratings (FBG) to form an external cavity using these single-mode fiber-coupled pump lasers at 960-980 nm and 1420- 1500 nm. The lasers normally operate in many longitudinal modes. Under appropriate conditions single frequency operation results with small tuning about the FBG center wavelength. We also discuss our use of a common diode laser model that characterizes the laser operation, along with some simple measurements to help fix the model parameters. In our particular application (1S to 2S transition in the atomic hydrogen isotopes), we need an ultra violet 243 nm laser source. Frequency doubling of a stabilized laser at 972 nm can be achieved using nonlinear crystals. Results of employing PPLN and PPKTP waveguides and PPKTP in a self contained resonant build-up cavity to generate blue laser at 486 nm are presented.   

Novel Scheme to Measure the Electric Dipole Moment of the Electron Using PbO

The unveiling of an electron electric dipole moment (EDM d$_{e})$ within the next few orders of magnitude beyond the current limit of $\vert $d$_{e}\vert <$1.6x10$^{-27}$ e-cm would be of great interest in the fundamental physics as an evidence for physics beyond the standard model. An experiment to look for EDM of the electron using the metastable a(1) ($^{3}\Sigma )$ state of PbO molecule is being implemented. High level of sensitivity would be achievable because of the extreme polarizability of diatomic molecules with a vapor cell. Here we would explore a novel scheme of signal detection using microwave absorption. Based on the nowadays available technology and experiment setup, we estimated microwave absorption cross-section, signal size and noise feature of the system. We also report the state preparation result using microwave technique as demonstration.   

Precision calculation of intense-laser-field multiphoton ionization (MPI) rates of {H}$_2^+$ at critical internuclear distances

We extend the time-independent non-Hermitian Floquet formalism [1] for high precision calculation of the MPI rates of {H}$_2^+$ at internuclear distances ($R$) from 2.0 to 20.0 a.u.\ in intense laser fields with intensity $1 \times 10^{14}$ W/cm$^2$ and wavelength 791 nm. The procedure involves the use of the complex-scaling generalized pseudospectral (CSGPS) method for \textit{non-uniform} spatial discretization of the Hamiltonian expressed in prolate spheroidal coordinates. We found that the MPI rates strongly depend upon $R$ and are significantly enhanced at several critical distances ($R \sim $~8, 11, and 15 a.u.) in good agreement with the recent experimental results [2]. [1] S.~I.~Chu and D.~A.~Telnov, Phys.\ Rep.\ \textbf{390}, 1 (2004). [2] D.~Pavi{\v c}i{\'c}, A.~Kiess, T.~W.~H{\"a}nsch, and H.~Figger, Phys.\ Rev.\ Lett.\ \textbf{94}, 163002 (2005).   

Application of Coulomb Wave Function DVR to Atomic Systems in Strong Laser Fields

We present an efficient and accurate grid method for solving the time-dependent Schr\"odinger equation (TDSE) for atomic systems interacting with short laser pulses. The radial part of the wave function is expanded in a DVR (Discrete Variable Representation) basis constructed from the positive energy Coulomb wave function. The time propagation of the wave function is implemented using the well-known Arnoldi method. Compared with the usual finite difference (FD) discretization scheme for the radial coordinate, this method requires fewer grid points and handles naturally the Coulomb singularity at the origin. As examples, the method is shown to give accurate ionization rates for both H and H$^-$ over a wide range of laser parameters.   

Parametrization of the Transition Amplitude and the Triply-Differential Cross Section for Two-Photon Double Ionization

We present model-independent representations for the transition amplitude and the triply-differential cross section for two-photon double ionization (TPDI) of He, in which the kinematical and dynamical parameters of the process are separated. For the case of DPI by two photons having different polarizations, the transition amplitude is parametrized by {\it five} polarization-independent amplitudes, which can be expressed in terms of exact two-electron radial matrix elements. For the case of TPDI by two identical photons, only {\it four} amplitudes are necessary. For this latter case we analyze photon polarization effects and predict the existence of both circular dichroism (CD) and elliptic dichroism (ED) effects in TPDI electron angular distributions. This contrasts with single-photon double ionization, in which only the CD effect exists. We also analyze the dynamics of the TPDI process within the lowest-order perturbation theory in the interelectron interaction and estimate the magnitudes of these effects.   

Low-frequency Bremsstrahlung for the Critical Geometry

The discrepancy between the experimental [1] and theoretical [2,3] results for the critical geometry, i.e., when $({\bf e} \cdot\Delta{\bf p})=0$ (where ${\bf e}$ and $\Delta{\bf p}$ are the polarization vector and the transferred electron momentum), is analyzed for examples of one-photon and two-photon low- frequency Bremsstrahlung (BrS) in a Coulomb field. For this geometry, the well-known Kroll-Watson approximation yields a zero BrS cross section while no significant decrease of the BrS radiation intensity is observed in experiments [1]. We present an analytical expression for the low-frequency cross sections for one- and two-photon stimulated BrS for the $({\bf e} \cdot\Delta{\bf p})\approx 0$ - region and find them to be small (of the order of $x^2\ln^2{x}$, where $ x=m\hbar\omega/p^2$ for the one-photon case) as compared to the cross section outside the critical geometry region. Thus our results are in accordance with those in Refs. [2,3] and disagree with Ref. [1]. [1] B. Walbank and J.K. Holmes, Phys. Rev. A {\bf 48}, R2515 (1993); [2] K.M. Dunseath and M. Terao-Dunseath, J. Phys. B {\bf 37}, 1305 (2004); [3] S. Hokland and L.B. Madsen, Eur. Phys. J. D {\bf 29}, 209 (2004).   

Two-photon above-threshold ionization of atoms

Two-photon ionization of alkali atoms by laser photons with above-threshold energies $(\hbar\omega > |E_0|)$ is investigated. We use the Fues model potential (FMP) for an optical electron and Sturmian expansion for the FMP Green function. The convergence of Sturmian series for radial matrix elements of two-photon bound-free transitions is achieved by using the $\epsilon$-algorithm (a numerical version of Pade- approximation). Such an approach allows one to calculate above- threshold ionization cross-sections over a wide range of photon energies above the threshold. The accuracy of numerical calculations is controlled by an independent calculation for the amplitude of stepwise transitions to the continuum (which are determined by the imaginary part of the FMP Green function) and by an analytical study of the ``low-frequency'' (near-threshold) limit. Similar calculations are performed also for rare gas atoms.   

Negative molecular ion in a strong DC field

We study the simplest model of a negative molecular ion, i.e., two attractive 3D zero-range potentials (ZRP) separated by a distance $R$, in a static electric (DC) field ${\bf F}$. For this model, both the Green function and the equation for its poles (resonances) are expressed in terms of Airy functions. For a weak field $F$, we obtain simple analytical expressions for the decay rate and polarizability for an arbitrary orientation of ${\bf F}$ with respect to the molecular axis. We also present large scale calculations of the Stark-shift and decay rate as functions of $R$ and $F$. Our analyses show that decay rates are largest if the molecular axis is orthogonal to ${\bf F}$. The poles of the Green function as functions of $F$ are found numerically to include not only those for the quasistationary states but also an infinite number of broad resonances which merge to a continuum when $F$ tends to zero (as found previously for 1D [1] and 2D [2] two ZRP models). We also analyze the complex quasienergies of molecular ions in a low-frequency AC field using an adiabatic approximation [3]. [1] H.J. Korsch and S. Mossmann, J. Phys. A {\bf 36}, 2139 (2003); [2] G. Alvarez and B. Sundaram, Phys. Rev A 68, 013407 (2003); [3] B.Borca et al., J. Phys. B {\bf 34}, L579 (2001).   

Multi-photon resonant effects in strong-field ionization: origin of the dip in experimental longitudinal momentum distributions

We studied ionization of neon and argon by intense linearly polarized femtosecond laser pulses of different wavelengths (400 nm, 800 nm and 1800 nm) and peak intensities, by measuring momentum distributions of singly charged positive ions in the direction parallel to laser polarization. For Ne the momentum distributions exhibited a characteristic dip at zero momentum at 800 nm, a complex multi-peak structure at 400 nm and no structure at 1800 nm. Similarly, for Ar the momentum distributions evolved from complex multi-peak structure (400 nm) to a smooth distribution characteristic of pure tunneling ionization (800 nm high intensities and 1800 nm). In the intermediate regime (800 nm, medium to low intensities), for both molecules we observed recoil ion momentum distributions modulated by quasi-periodic structures usually seen in the photoelectron energy spectra in multi-photon regime (ATI spectra). Ne did show a characteristic ``dip'' at low momentum, while longitudinal momentum distribution for Ar exhibited a spike at zero momentum instead. Based on our results, we conclude that the structures, observed in Ne and Ar momentum distributions, reflect the specifics of atomic structure of the two targets and should not be attributed to effects of electron re-collision, as was suggested earlier. Instead, as our results indicate, they are due to effects of multi-photon resonant enhancement of strong-field ionization.   

Ionization and Dissociation of O$_{2}^{+}$ and N$_{2}^{+}$ in Intense Short Pulse Laser Fields

The momentum distributions for ionization and dissociation of O$_{2}^{+}$ and N$_{2}^{+}$ exposed to intense short laser pulses have been studied experimentally using a 3D coincidence momentum imaging method. Both 790nm laser pulses of 8 to 120fs at intensities up to 10$^{15}$ W/cm$^{2}$ and 395nm pulses of 45fs at intensities up to 10$^{13}$ W/cm$^{2}$ have been used. The momentum distributions yield a rich structure in kinetic energy release and angular distribution that is used to deduce the dissociation pathways. The angular distributions for these two molecules, which are theoretically predicted to be significantly different [1], will be presented. [1] X. M. Tong, Z. X. Zhao, A. S. Alnaser, S. Voss, C. L. Cocke and C. D. Lin, J. Phys. B \textbf{38}, 333 (2005)   

Effect of electron correlation on high harmonic generation of helium atoms in intense laser fields

We present a time-dependent generalized pseudospectral (TDGPS) approach in {\em hyperspherical coordinates} for fully {\em ab initio} nonperturbative and high-precision treatment of multiphoton electron-correlated dynamics of atomic systems in intense laser fields [1]. The procedure is applied to the investigation of high-order-harmonic generation (HHG) of helium atoms in ultrashort laser pulses at a KrF wavelength of 248.6 nm. The 6D coupled hyperspherical-adiabatic-channel equations are discretized and solved efficiently and accurately by means of the TDGPS method. The effects of electron correlation and doubly excited states on HHG are explored in detail. A HHG peak with Fano line profile is identified which can be attributed to a broad resonance of doubly excited states. Comparison of the HHG spectra of the {\em ab initio} two-electron and the single- active-electron model calculations is also presented. \vspace{1mm} \noindent [1] X. Guan, X.-M. Tong, and S. I. Chu, Phys. Rev. A (in press).   

Wavelength-dependence of momentum-space images of low-energy electrons generated by short, intense laser pulses at high intensities

We have measured highly resolved momentum-space images of low energy electrons generated by the interaction of short intense laser pulses with argon atoms at high intensities (tunneling regime). We have done this over a wavelength range from 400 to 800 nm. The spectra show considerable structure in both the energy and angular distributions of the electrons. Some, but not all, energy features can be identified as multi-photon resonances. The angular structure shows a regularity which transcends the resonant structure and may be due instead to diffraction. We have also measured electron momentum-space images for aligned N$_{2}$ and O$_{2}$ molecules at 800nm. Rotational wave packets were used to align the targets. We will preliminary results on the effects of alignment on the energy and angular structure.   

Creation and control of single attosecond XUV pulse by few-cycle intense laser pulse

We present a theoretical investigation of the mechanisms responsible for the production of single atto-second pulse by using few-cycle intense laser pulses. The atto-second XUV spectral is calculated by accurately integrating the time- dependent Schr\"odinger equation. The detailed mechanism for the production of the XUV pulse are also corroborated by analyzing the classical trajectories of the electron. Our study shows that the first return of the rescattering electron is responsible for the high energy atto-second pulse. Furthermore, we can optimize the production of atto-second XUV pulses by modifying the trajectory of the rescattering electron by tuning the laser field envelope.   

AMO Science with fsec x-ray pulses at the LCLS

The Linac Coherent Light Source (LCLS), a linac-drive x-ray free electron laser (XFEL), is currently under construction at the Stanford Linear Accelerator Center (SLAC) with funding from the Office of Basic Energy Sciences, U.S. Department of Energy. When completed in 2008, the LCLS will provide $10^{12} - 10^{13}$ x-ray photons at energies from 800$-$8000~eV in 230~fsec pulses at 120~Hz with unprecedented flux and brightness. This regime of power and energy is completely unexplored in atomic, molecular and optical sciences (AMOS) and is expected to provide many new discoveries in light-matter explorations. An AMOS facility at the LCLS is being designed to capitalize on the unique high flux, high field and high temporal resolution of the x-ray pulses generated by the light source. A brief overview of the LCLS facility will be presented along with a description of the AMO research capabilities envisioned. An AMOS working group comprised of many researchers at several institutions has contributed to the design parameters for the instrumentation under design.   

Ab Initio Electronic Dynamics of H$_{2}$ in Strong Attosecond Laser Field

Using Multi-Configuration Time-Dependent Hartree Fock with adaptive multiresolution methods and self-adaptive time propagation techniques with controlled accuracy we analyze ionization yields, electron spectra and high-harmonic radiation of a hydrogen molecule in an attosecond strong laser pulse. We follow single- and two-electron dynamics of the process of ionization during a single field cycle, including rescattering imaging of a molecular orbital and the scattering production of harmonics.   

An analytical description of carrier-envelope phase effects

We consider a quantum system interacting with a short intense linearly polarized laser pulse. Using the two-dimensional time representation and the Floquet representation, we establish a straightforward connection between the laser carrier-envelope phase (CEP) and the wave function. This connection is simply a unitary transformation in the space of Floquet components. This approach allows us to interpret any CEP effect as an interference between the Floquet components and to put limits on using the CEP in coherent control. In particular, we discuss the dependence of the CEP effect on the pulse duration. We illustrate the theory for a two-level system as well as for atomic and molecular systems.   

Dissociation and ionization of HD$^{+}$ in intense few-cycle laser pulses

All the dissociation and ionization channels of an HD$^{+}$ molecular ion beam exposed to intense laser fields, namely H$^{+}$+D, D$^{+}$+H and H$^{+}$+D$^{+}$, have been studied simultaneously using a 3D coincidence momentum imaging method. These breakup channels are experimentally separated from each other. The laser pulse durations are from about 8 fs up to those comparable to the dissociation time scale of the molecule, with a wavelength of 790 nm and an intensity range of 10$^{13}$-10$^{15}$ W/cm$^{2}$. The focus of this study is on the phenomena in few-cycle laser pulses. The 3D momentum of each fragment is retrieved from its position and time signals, which provides angular and kinetic energy release spectra for each breakup channel. The dissociation of HD$^{+}$ is found to be governed by bond-softening and above threshold dissociation, depending on the laser intensity. The ionization of HD$^{+}$ is strongly aligned along the laser polarization and has a broad kinetic energy distribution which shifts to higher values at higher intensity.   

Signatures of multiphoton and tunneling ionization in the electron-momentum distributions of atoms by intense few-cycle laser pulses

We present angle-resolved electron momentum distributions for above-threshold ionization (ATI) of argon in an intense, linearly polarized laser pulse. Our results were obtained by solving the time-dependent Schrodinger equation and by using a model based on the strong field approximation (SFA). Many features of the spectra such as ATI peaks, their substructure in the energy domain and their dominant angular momentum can be understood within the familiar SFA model.   

Interaction of cold atoms with short laser pulses.

We present a powerful diagnostic system to observe the interaction of ultrafast laser pulses with trapped $^{87}$Rb atoms. The ionization of cold atoms and the formation of cold molecules in an intense laser field in the $\mu $K temperature range open new branches of research in chemistry, metrology, and quantum physics. However, the interaction of cold atoms with short laser pulses and the subsequent ionization or molecule formation are processes which are not well understood and can be easily misinterpreted. In our proposed experimental setup, an existing ultrafast laser system at the University of Wisconsin-Stevens Point will be used in conjunction with Magneto Optical Trap Recoil Ion Momentum Spectroscopy (MOTRIMS) to directly measure the products formed by the interaction of ultrafast laser pulses with the cold trapped $^{87}$Rb atoms.   

Normal mode selectivity in ultrafast Raman excitations in $\rm \bf C_{60}$

Ultrafast Raman spectra are a powerful tool to probe vibrational excitations, but inherently they are not normal-mode specific. For a system as complicated as $\rm C_{60}$, there is no general rule to target a specific mode. A detailed study presented here aims to investigate normal mode selectivity in $\rm C_{60}$ by an ultrafast laser. To accurately measure mode excitation, we formally introduce the kinetic energy-based normal mode analysis which overcomes the difficulty with the strong lattice anharmonicity and relaxation. We first investigate the resonant excitation and find that mode selectivity is normally difficult to achieve. However, for off-resonant excitations, it is possible to selectively excite a few modes in $\rm C_{60}$ by properly choosing an optimal laser pulse duration, which agrees with previous experimental and theoretical findings. Going beyond the phenomenological explanation, our study shines new light on the origin of the optimal duration: The phase matching between laser field and mode vibration determines which mode is strongly excited or suppressed. This finding is very robust and may be a useful guide for future experimental and theoretical studies in more complicated systems.   

Pump-probe time-dependent interferometry performed using an infrared pump and soft $x$-ray probe in a COLTRIMS geometry

We have developed an apparatus for performing laser-pump/$x$-ray-probe experiments in a COLTRIMS (Cold Target Recoil Ion Momentum Spectroscopy) geometry. A soft $x$-ray beam is produced by focusing an intense (2$^{.}$10$^{14}$ W/cm$^{2 }$-- 2$^{.}$10$^{15}$ W/cm$^{2})$ and fast (6 fs -- 50 fs) laser beam into a thick (5 Torr -- 80 Torr) gaseous medium using three different techniques: an effusive jet, a gas cell and a hollow fiber. This beam is crossed with a room-temperature effusive (10$^{-3}$ Torr) gaseous target of Ar or Ne. The $x$-ray beam is analyzed in terms of its flux, harmonic energies and angular divergence by measuring full three dimensional photoelectron momentum images in coincidence with the recoil-ions. This apparatus will be used to perform time-dependent interferometry of dissociating H$_{2}^{+}$ (D$_{2}^{+})$ ions. Neutral H$_{2}$ (D$_{2})$ will be ionized and excited using an infrared pump pulse and probed after a time delay up to 240 fs with the soft x-ray pulses. The $x$-rays will be focused onto the target, and delayed relative to the pump pulse, using a two-component coaxial coated mirror to select a photon energy band in the 36-48 eV range. Preliminary results will be presented. *This work was supported by Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U. S. Department of Energy.   

Probing Fast Dynamics in N$_{2}$ and H$_{2}$ molecules in strong laser field with ultra-short pulses

We used pump-probe technique with few-cycle pulses and COLTRIMS detection to study dynamics of ionization and dissociation of molecules following ionization/excitation by a strong field of ultra-short laser pulse. We detected in coincidence pairs of H$^{+}$ ions and single and multiple charged ions of nitrogen N$^{q+}$ produced by pump and probe pulses in ionization and dissociation processes. Setting the delay between the two pulses we measured the kinetic energy release dependence on the delay time, which vibrational and dissociative dynamics. We were able to follow the contribution of each separate channel to the total ions yield at each delay.   

The role of plasma oscillations of C60 collectivized electrons in photoionization of 5s subshell of Xe atom in Xe@C60

It is demonstrated that the plasma oscillations of collectivized electrons of the fullerene C60, affects dramatically the photoionization cross section of the 5s-subshell of the endohedral Xe. The calculations were performed within the framework of a simple ``orange skin'' model that makes it possible, in spite of its simplicity, to describe the modification of photoionization cross section of encapsulated atom due to the photoelectron's waves reflection by the C60 shell. It is shown that the virtual excitations of collectivized electrons in fullerenes shell become decisively important when the photon frequency is close to the frequencies of plasma oscillations of the C60. These calculations illustrate the role of the intershell interactions in the fullerene-like molecules, qualitatively similar but even stronger than in the isolated atoms.   

Two-electron photoionization of endohedral atoms

Using $He@C_{60}$ as an example, we demonstrate that static potential of the fullerene core essentially alters the differential in one-electron energy cross section of the two-electron ionization $d\sigma ^{++}(\omega,\varepsilon )/d\varepsilon $. We found that at high photon energy prominent oscillations appear in it due to reflection of the second, slow electron wave on the $ C_{60}$ shell, which dies out at relatively high $\varepsilon $ values, of about 2$\div $3 two-electron ionization potentials. The results were presented for ratios $R_{C_{60}}(\omega ,\varepsilon )\equiv d\sigma ^{++}(\omega ,\varepsilon )/d\sigma ^{a++}(\omega,\varepsilon)$, where $d\sigma^{a++}(\omega,\varepsilon) /d\varepsilon$ is the two-electron differential photoionization cross-section. We have calculated also the ratio $R_{i,ful}=\sigma_i^{++}(\omega)/\sigma_i^{a++}(\omega)$, that accounts reflection of both photoelectrons by the $C_{60}$ shell. We have calculated also the value of two-electron photoionization cross section $\sigma ^{++}(\omega )$ and found that this value is close to that of an isolated $He$ atom.   

Laser Threshold Photodetchment Spectroscopy of the P- Ion

The electron affinity of the P atom and the fine structure splittings of the P$^-$($^3$P$_J$) state have been measured in high resolution by use of the Laser Threshold Photodetachment method. In the collinear beams experiment, tunable infrared radiation from an OPO/OPA system was used to detach an electron from the P- ion. The relative cross section for the process was monitored by detecting the residual ground state P atom. Three thresholds were observed, corresponding to the opening of the channels: $\gamma$ + P$^-$(3s$^2$3p$^4$ $^3$P$_J$) $\rightarrow$ P(3s$^2$3p$^3$ $^4$S$_{3/2}$) + e$^-$ with J=2,1,0. The Wigner law was fitted to the threshold data and used to determine the threshold energies. The Doppler shift associated with the moving ions was eliminated by determining their velocity using the measured the red- and blue-shifted threshold energies associated with co-and counter-propagating laser and ion beams [1]. A calibrated wave-meter was used to establish the wavelength scale of the OPO/OPA system. The newly measured values of the electron affinity of the P atom and the fine structure intervals of the P- ion represent a significant improvement in precision over the current recommended values [2]. [1]. P.Juncar, et al., Phys. Rev. Lett., 54, 11(1985). [2] T.Andersen, H.K.Haugen and H.Hotop, J. Phys. and Chem. Ref. Data, 28, 1511 (1999).   

Near-threshold Inner-shell Photodetachment of Atomic Negative Ions: Post-collision Interactions and the Validity of the Wigner Law

The first studies of inner-shell photodetachment threshold laws will be presented. Experiments were conducted on the Ion-Photon Beamline on Beamline 10.0.1 at the Advanced Light Source. Inner-shell detachment of negative ions results in a core-excited neutral atom that quickly emits one or more further electrons (Auger decay) to produce positive ion products that are detected as a function of photon energy. Photodetachment of a 1s electron in He$^{-}$ [1] is found to be consistent with the Wigner p-wave threshold law despite strong post-collision interaction effects [2]. Photodetachment cross sections near the 2s and 2p thresholds in S$^{-}$ are found to closely follow the Wigner p- and s-wave laws respectively over a surprisingly large range, even when a total of 3 or 4 electrons are emitted [1]. Detailed analysis of these threshold law behaviors and high charge-state formation [3] will be presented. [1] R.C. Bilodeau \textit{et al.}, Phys. Rev. Lett. \textbf{95, }083001 (2005). [2] R.C. Bilodeau \textit{et al.}, Phys. Rev. A (in press). [3] R.C. Bilodeau \textit{et al.}, Phys. Rev. A \textbf{72}, 050701(R), (2005).   

Photodetachment Spectroscopy of Ce$^{-}$

Tunable infrared and visible laser photodetachment spectroscopy has been performed on Ce$^{-}$ using a crossed laser-ion beam apparatus. The relative photodetachment cross section for neutral production was measured over the photon energy range 0.5 eV -- 2.6 eV. The spectrum shows several continuum threshold features and reveals five narrow peaks associated with negative ion resonances. The present measurements will be compared to recent theoretical [1] and experimental [2] results which are in significant disagreement on fundamental physical quantities such as the electron affinity of Ce and the ground state configuration of Ce$^{-}$. [1] S.M. O'Malley and D.R. Beck, Phys. Rev. A \textbf{61}, 034501 (2000); X. Cao and M. Dolg, Phys. Rev. A \textbf{69}, 042508 (2004). [2] V.T. Davis and J.S. Thompson, Phys. Rev. Lett. \textbf{88}, 073003 (2002).   

Stabilization of Autoionizing States in Crossed Magnetic and Electric Fields

We demonstrate by numerical analysis of a zero-range potential model describing a negative ion in crossed magnetic and electric fields the existence of autoionizing states. We observe that with the increasing electric-field strength the lifetime of those states increases, reaches its maximum value, and then starts decreasing rapidly. Such a stabilization has been observed before for the so-called electric-field-induced resonances [1] but, to our knowledge, has never been recognized for autoionizing states. [1] K. Krajewska and J. Z. Kami\'{n}ski, {\it Phys. Lett.} A {\bf 301}, 369 (2002).   

DIQUIS observation of n=2$\to$7 He $2pnp~^1D$ autoionizing resonances.

We have applied the technique of DIpole-QUadrupole Interference Spectroscopy (DIQUIS) to make the first observation of an optically forbidden Rydberg series using photoelectron spectroscopy. The He $2pnp~^1D$ autoionizing levels appear as a series of resonances in the non-dipole $\gamma$ parameter.\footnote{B. Kr\"assig, E.P. Kanter, S.H. Southworth, R. Guillemin, O. Hemmers, D.W. Lindle, R. Wehlitz, and N.L.S. Martin, Phys. Rev. Lett. {\bf 88}, 203002 (2002).} The experiments were carried out at the Synchrotron Radiation Center, University of Wisconsin-Madison using an electron spectrometer system, designed and built at Argonne National Laboratory, to efficiently measure nondipole asymmetries in photoelectron angular distributions. We will present measurements of $\gamma$ for photon energies that cover the $n=2\to7$ resonance region. Fits to the data yield values of level positions, widths, and Fano $q$ parameters.   

First Observation of a Quadrupole Cooper Minimum in the Photoionization of Xe 5$p$

The nondipole photoelectron angular distribution parameter $\xi $ (= 3$\delta +\gamma )$ for xenon 5$p_{1/2}$ and 5$p_{3/2 }$has been studied experimentally in the 80 - 200 eV range. In addition, calculations have been performed using the relativistic-random-phase approximation (RRPA) methodology with all relativistic single excitation/ionization channels down to 4$s$ coupled in both the dipole and quadrupole manifolds. The results show significant disagreement between theory and experiment above about 130 eV photon energy, in contradistinction to the Xe 5$s$ case where rather good agreement is found. Since it is known that the dipole amplitudes are well-represented by RRPA, the difficulty must be in the quadrupole channels. It was expected that the quadrupole channels should be accurate as well since the f-wave is resonant in Xe and the main quadrupole transitions, the 5\textit{p$\to $}k$f$, are included in the calculation. However, we have found that these transitions each have a quadrupole Cooper minimum in the energy region of interest, so that quadrupole satellites, which are not included in the RRPA calculation, become important. This might be the first experimental indication of a quadrupole Cooper minimum.   

Deviation of $\beta$ from 2.0 for the Kr and Xe $4s$ and $5s$ Photoelectrons at the $nd \rightarrow mp$ (n=3 for Kr, n=4 for Xe) Excitations

In the absence of relativistic effects, the angular distributions, $\beta$, of s-subshell electrons in closed-shell atoms will be 2.0 independent of the energy of the ionizing photons. When relativistic effects are important, then deviations from this behavior can be expected and are generally more likely in the vicinity of Cooper minima, at high photon energies, or in the region of resonances [1]. We examine the latter case of the Kr $4s$ $\beta$ values in the region of the $3d \rightarrow mp \ (m \ge 5)$ excitations and the Xe $5s$ $\beta$ values in the region of the $4d \rightarrow mp \ (m \ge 6)$ excitations. We observe small but unmistakable variations of $\beta$ from 2.0 at these resonances. To understand these results in more detail we have carried out relativistic random phase calculations (RRPA). Preliminary results clearly indicate deviations of $\beta$ from 2.0 for these photolines, although the degree of variation is predicted to be larger than what is observed. We will present improved RRPA calculations as well relativistic multichannel quantum defect (RMQDT) calculations. [1] S. T. Manson and A. F. Starace, Rev. Mod. Phys. {\bf 54}, 389 (1982).   

Photoionization of the 4$f$ and 6$s$ Subshells of Atomic Thulium in the Region of the 5$p$ Excitations

The relative partial cross sections, $\sigma$, and the angular distribution parameters, $\beta$, of the photoelectrons originating from the $4f$ and $6s$ subshells of atomic thulium have been measured in the region of the $5p$ excitations (23~eV -- 38~eV). In qualitative agreement with the early absorption work of Tracy [1], our $\sigma$ curves show two regions of strong resonance enhancement, one around a photon energy of 27~eV corresponding to $5p_{3/2}$ excitations and the other near 32~eV corresponding to $5p_{1/2}$ excitations. The $\beta$ curves show considerable variation between the allowed extremes of -1.0 and 2.0 for many of the $4f$ photolines. In addition, the $6s$ photoline shows very marked deviations from $\beta = 2.0$ which is indicative of an open-shell atom. We also compare our calculated $4f$ partial cross sections, using a modified version of the Cowan code [2], with experiment. While there is good qualitative agreement between theory and experiment, quantitative details are not reproduced: i) the $5p_{3/2}$ excitations are too narrow and ii) have an intensity larger than what is observed experimentally. [1] D. H. Tracy, Proc. R. Soc. Lond. A {\bf 357}, 485 (1977), [2] M. Martins, J. Phys. B, {\bf 34}, 1321 (2001).   

Resonance Structures in Photoionization of $S^+$

Resonance structures in the photoionization of $S^+$ for the removal of a 3p or 3s electron from the ground 3s$^2$3p$^3$~$^4$S$^o$ and excited metastable $^2D^o$ and $^2P^o$ states have been studied in the B-spline R-matrix approach. The non-orthogonal orbitals are used for an accurate description of the $S^+$ initial bound states, the final $S^{2+}$ ion plus photoelectron states and $S^{2+}$ ionic thresholds. Calculations have been carried out in 17- and 27-state close-coupling approximations. The relativistic effects have been considered in the Breit- Pauli Hamiltonian. Photoionization cross sections are dominated by $3s^23p^2(^1D)ns~^2D$, $3s^23p^2(^1D)nd~^2F$, $^2D$, $^2P$ and $3s3p^3(^5$S$^o$,~$^3$S$^o$,~$^3$D$^o$,~$^3$P$^o$)np~$^4$P Rydberg series of resonances. Our results will be compared with merged ion-photon beam experiment.   

Photoionization of \textit{Cl-} like \textit{K}$^{2+}$ and \textit{Ca}$^{3+}$

Absolute photoionization cross-section measurements have been performed for $K^{2+}$ and\textit{ Ca}$^{3+}$ in the energy range from the ionization thresholds of their metastable state ($^{2}P^{o}_{1/2})$ and ground state ($^{2}P^{o}_{3/2})$ to the series limit of the dominant Rydberg series of resonances. The measurements were performed using the Ion-Photon Beam endstation on Beam line 10.0.1 of the Advanced Light Source (ALS) by merging an ion beam with a beam of synchrotron radiation from an undulator magnet. The data are compared to previous measurements for \textit{Cl-}like \textit{Ar}$^{+}$ [1]. Most of the resonances have been characterized by multiple Rydberg series of autoionizing states and assigned spectroscopically using quantum defect form of Rydberg formula. The measurements are compared with R-matrix calculations and with relativistic Hartree-Fock calculations of the energies and the oscillator strengths of the autoionizing transitions. [1]: A. M. Covington et al, Proc. XX11 ICPEAC, 48 (2001).   

Inner-shell Photodetachment of Na$^{- }$

Calculations of the photodetachment of a 2p core electron in the Na$^{-}$ ion over the photon energy range 30-41 eV have been performed using R-matrix theory with a perturbative method in the asymptotic region. Our results show a very strong Feshbach resonance in the Na 1s$^{2}$2s$^{2}$2p$^{5}$2s$^{2 }(^{2}$P) channel at about 34 eV, just below the 1s$^{2}$2s$^{2}$2p$^{5}$3s3p$^{ }(^{2}$D) threshold, the 1s$^{2}$2s$^{2}$2p$^{5}$3s3p$^{2 }(^{1}$P) resonance. Since 3s and 3p orbitals are about the same ``size'', they have a significant attractive exchange interaction; this attraction pulls the resonance below the 1s$^{2}$2s$^{2}$2p$^{5}$3s3p$^{ }(^{2}$D) threshold, making it a Feshbach resonance. The Auger decay 1s$^{2}$2s$^{2}$2p$^{5}$3s$^{2 }\to $1s$^{2}$2s$^{2}$2p$^{6 }$ (Na$^{+ })+e$ leads to the production of Na$^{+}$. Therefore, we expect experiment to find this resonance around 34 eV. But recent experiment explored in this region and found nothing [1]. We are puzzled by this discrepancy. Another resonance in our calculation is located at 36.318 eV, just below the 1s$^{2}$2s$^{2}$2p$^{5}$3s4s ($^{ 2}$P$^{o})$ threshold. This resonance is confirmed by experiment [1] which is found at 36.213 eV and assigned as a 1s$^{2}$2s$^{2}$2p$^{5}$ 3s 4s \textit{nl} resonance. The situation remains under theoretical scrutiny Work was supported by DOE, NASA and NSF. [1] A. M. Covinton \textit{et al}., J. Phys. B \textbf{34}, L735 (2001) and D. J. Pegg, private communication (2005).   

Photoionization and Electron-impact Ionization of Kr$^{3+}$

Using synchrotron radiation, photoionization cross sections for Kr$^{3+}$ were measured in the energy range 39 - 143 eV for single-ionization and 120 -- 137 eV for double-ionization. For comparison, electron-impact single ionization was measured in the energy range 43 - 179 eV. The Flexible Atomic Code (FAC) and Cowan atomic structure code were used to calculate energy levels, excitation and ionization energies and oscillator strengths for autoionizing transitions from the ground and metastable states. Ionization thresholds of metastable states ($^{2}$P$^{o}_{3/2}$, $^{2}$D$^{o}_{5/2})$ and ground state ($^{4}$S$^{o}_{3/2})$ were measured to be 46.62, 48.59 and 50.70 eV, 1-2 eV lower than NIST-tabulated values. Shifting the theoretical 3d-4p spectra by +1.56 eV for the FAC code and +0.81 eV for the Cowan code brings them into good agreement with experiment. Measured oscillator strengths agree with the calculations within experimental uncertainty. Resonant excitation-double-autoionization features are evident in the electron-impact ionization spectrum.   

Random-phase approximation with exchange for inner-shell electron transitions II: Effects of inter-shell correlations

A random-phase approximation with exchange (RPAE) method, which allows the inclusion of both the intra-shell correlations and the inter-shell correlations in photoionization calculations, has been developed for open-shell atoms (ions), such as I, Xe$^+$, and I$^+$. The equations for all types of matrix elements have been derived and implimented in a computer code. The program has been used to study the effects of inter-shell correlations on the Xe$^+$ 5$s$, 5$p$ and $4d$ photoionization processes, which are found to increase dramatically the cross sections for the Xe$^+$ $5s$ and $5p$ eletrons.   

K-shell photoionization of Li-like carbon ions: experiment, theory and comparison with time-reversed photorecombination

Absolute cross-sections for the K-shell photoionization of Li-like C$^{3+}$(1s$^2$\,2s\,\,$^2$S) ions were measured by employing the ion-photon merged-beams technique at the Advanced Light Source. The energy ranges 299.8--300.15 eV, 303.29--303.58 eV and 335.61--337.57 eV of the [1s\,(2s\,2p)$^3$P]$^2$P, [1s\,(2s\,2p)$^1$P]$^2$P and [(1s\,2s)$^3$S\,\,3p]$^2$P resonances, respectively, were covered using resolving powers of up to 6000. The width of the [1s\,(2s\,2p)$^1$P]$^2$P resonance was measured to be $27 \pm 5$~meV and compares favourably with a theoretical result of 25.5 meV obtained from the R-Matrix method. The present photoionization results are compared with the outcome of the photorecombination measurements by employing the principle of detailed balance. The agreement between both experimental approaches is within the experimental uncertainties. Further details will be presented at the meeting.   

Asymmetry of the Compton profile

Compton scattering of a photon by bound electrons is one of the fundamental processes of interaction of radiation with matter. It is often used to investigate structure of atomic systems, molecules and solids. In studying structure, an approximate theoretical approach is used (impulse approximation, IA) which allows interpretation of the measurements in terms of the structure of the system under investigation. Accurate measurements of the Compton profile (which is an appropriately normalized Compton scattering doubly differential cross section, differential in outgoing photon energy and angle) have revealed discrepancies between measurements and simple IA results. These discrepancies are described as an asymmetry of the Compton profile. We investigate these asymmetries numerically by using S-matrix calculations of the Compton process, and we find that they can largely be understood as a shift of the Compton profile maxima. We compare our results with other theoretical investigations of this issue.   

Double Excitations of Helium in Weak Static Electric Fields

A dramatic electric field dependence has been observed in the photofluorescence yield spectrum of the doubly excited states in helium, where a rich phenomenology is encountered below the $N=2$ threshold. Fluorescence yields of certain states can be tuned to zero, while other dipole-forbidden states are significantly enhanced, for fields much weaker than 1 kV/cm. Using an R-matrix multichannel quantum defect theory, spherical-to-parabolic frame transformation method, we are able to reproduce the main features of the observed spectrum, and we explain the qualitative behavior in terms of weak electric field mixing.   

Doubly Excited Resonances in the Photoionization Spectrum of Li$^{+}$: experiment and theory

Absolute cross-section measurements for resonant double photoexcitation of Li${^+}$ ions followed by subsequent autoionization have been performed in the photon energy range from 148 eV, just below the (2s2p, $_2$(0,1)$_2^+$) resonance to 198 eV (the region of the double ionization threshold) at high resolution. The measurements have been made using the photon-ion merged-beam endstation at the Advanced Light Source, Lawrence Berkeley National Laboratory. The absolute cross section measurements when compared with theoretical results from the R-matrix plus pseudo-state (RMPS) method show excellent agreement. Comparisons made between theory and experiment for the Auger resonance energies, autoionization linewidth ($\Gamma$) and the Fano line profile index $q$ for several members of the principal (2snp, $_2$(0,1)$_n^+$) and (3snp, $_3$(1,1)$_n^+$) Rydberg series found in the photoionization spectra for the $\rm ^1P^o$ symmetry show suitable accord. Further details will be presented at the meeting.   

Resonant Double Photoionization of Li Studied with High Energy Resolution

Employing monochromatized synchrotron radiation of the new VLS-PGM beamline at the Synchrotron Radiation Center (SRC), we have measured with high energy resolution the relative photoionization cross-sections for the formation of Li$^{+}$ and Li$^{2+}$ ions between 148 and 161 eV photon energy. This energy region is characterized by double and triple excitations that lead to strong enhancements in the cross sections, particularly in the Li$^{2+}$ cross section. In an earlier study performed by Huang {\it et al.} \footnote{M.-T.\ Huang, R.\ Wehlitz, Y.\ Azuma, L.\ Pibida, I.A.\ Sellin, J.W.\ Cooper, M.\ Koide, H.\ Ishijima, and T.\ Nagata, Phys.\ Rev.\ A {\bf 59}, 3397 (1999)} only a moderate energy resolution was used. Our high-resolution data exhibit a dramatic resonance structure in the double-to-single ionization ratio not seen before.   

Design and Commissioning of a new Ion Momentum Imaging Spectrometer

We have built a velocity map ion imaging spectrometer designed for valence and core-shell photoionization studies of molecules, ions and clusters. The spectrometer is equipped with 4 electrostatic lenses, which focus the fragment ions on a position-sensitive Roentdek Hex-80 anode. It can be employed for electron-ion coincidence experiments in both multi- as well as two-bunch mode using static or pulsed ion extraction fields. First results for the photoionization of small molecules and clusters will be presented.   

Dipole and nondipole photoelectron angular distributions of molecular hydrogen

Molecular hydrogen has long been a prototype system for experimental and theoretical studies of photoionization. Measurements of angle-integrated cross sections and the anisotropy parameter $\beta $ provide experimental tests of molecular photoionization theory and calculational approaches within the dipole approximation. Nondipole interactions distort dipole angular-distribution patterns and can be probed by measurements of forward-backward asymmetries with respect to the photon propagation vector. Nondipole asymmetries can be calculated to first order in theoretical treatments that include cross terms between electric-dipole and electric-quadrupole or magnetic-dipole photoionization amplitudes. In this work we report measurements of the dipole anisotropy parameters $\beta $ and the nondipole asymmetries $\gamma $+3$\delta $ of H$_{2}$ over the 20--150 eV photon-energy range. Comparison is made with calculations based on first-order corrections to the dipole approximation with amplitudes calculated within the single-channel, static-exchange approximation.   

Double-photoionization of CO few eV above threshold

We measured double photoionization of CO molecules at 48 eV photon energy. The double ionization of CO produces mostly C$^{+}$ + O$^{+}$ fragments with non-measurable amounts of CO$^{2+}$. The formation of C$^{+}$ + O$^{+}$ can proceed through two possible channels: a) Direct ionization of two electron into the continuum -- similar to the H2 double ionization -- direct channel. b) Ionization of one electron into the continuum followed by autoionization of a second electron -- Indirect channel. The electron distribution measured with a COLTRIMS shows a very clear distinction of the direct and indirect channels. The kinetic energy release spectrum shows a series of peaks corresponding to the transient vibrational states of the various electronic states of (CO$^{2+})$*. These states are similar to previous measurements at higher energies (K-shell photoionization). (CO$^{2+})$* is found to predissociate through a $^{3}\Sigma ^{-}$ and $^{1}\Delta $ dissociative states leading to considerably faster dissociation times than natural lifetimes of the electronic bound states.   

$N_2^+ $ fluorescence in photoionization of $N_2 $ by 16.3-150 eV photons

We have studied the intensity of fluorescence from the $B^2\Sigma _u^+ -X^2\Sigma _g^+ $ (${\nu }'=1,{\nu }''=4)$ transition (514.9 nm) in $N_2^+ $ as a function of incident photon energy following the photoionization of $N_2 $ by linearly polarized light with energy between 16.3 and 150 eV. This experiment was conducted at beamline 10.0.1.2 of the ALS. To our knowledge, this measurement represents the first unambiguous observation of a specific molecular transition in such collisions. A broad maximum peaked at $\sim $23 eV is observed in the production cross section for this specific vibrational state. Non-state specific measurements were taken from 115 to 200 nm which includes multiple $N^+$ ionic fluorescence lines as previously measured from 19.7 to 37.6 eV by Erman \textit{et al.} [1]. Our current measurements extend this observation from 16.3 to 150.0 eV. [1] P. Erman \textit{et al.}, J. Phys. B \textbf{26} (1993) 4483.   

Acetylene/Vinylidene Isomerization after Carbon K-shell Photo-Ionization

Comprehensive study of the acetylene/vinylidene isomerization dynamics after the carbon k-shell photoionization followed by the Auger decay was performed by means of the COLTRIMS (COLd Target Recoil Ion Momentum Spectroscopy) technique. The Auger electrons, produced in this reaction, were detected in coincidence with the products of the Coulomb explosion of the dication C$_{2}$H$_{2}^{2+}$. Measurement of the 3d vector momenta for all detected particles inferred the Auger electron energies and directions in the body fixed molecular frame along with the KER (Kinetic Energy Release) for different break up channels. This highly differential reaction cross-section study provided very unique information about the fragmentation pathways of the doubly charged acetylene molecule.   

Modulations in the Relative Double-Photoionization Cross Section

A modulation in the C$_{60}^{2+}$/C$_{60}^{+}$ photoionization cross-section ratio has been observed by using monochromatized synchrotron radiation between 19 and 280 eV \footnote{P.N.\ Juranic {\it et al.}, Phys.\ Rev.\ Lett. {\bf 96}, 023001 (2006)}. The modulations in the ratio have local maxima at certain excess energies (=photon energy minus double-ionization threshold). Each energy corresponds to an electron's de Broglie wavelength that fits between certain locations of two carbon atoms in the C$_{60}$ molecule. While these modulations are small at near-threshold energies, they become much more pronounced at higher energies. It seems that in the double-photoionization process, one of the electron bounces between two carbon atoms if its de Broglie wavelength matches that distance. Eventually, it will transfer some of its energy to the second electron, which is then able to escape together with the first electron.   

Photodetachment of the Terbium Anion

Laser Photodetachment Electron Spectroscopy (LPES) has been used to study the terbium anion. Photoelectron kinetic energy spectra were measured at photon energies ranging from 457.9-514.5 nm using a crossed laser-ion beams apparatus. In addition, photoelectron angular distributions were measured as a function of the angle between the laser polarization vector and the linear momentum vector of the collected photoelectrons. Photoelectron kinetic energy spectra from the photodetachment of Na$^{-}$ and C$^{-}$ were used to calibrate the energy scale for the Tb$^{-}$ photoelectron energy spectra. Preliminary results from the analysis of these data will be presented.   

Improvements in the understanding of the spectrum and photodetachment of Ce$^-$

We have undertaken new relativistic configuration interaction calculations of the electron affinity of the $4f~5d^2~6s^2$ $^4$H$_{7/2}$ Ce$^-$ ground state in an effort to resolve the differences among our earlier work\footnote{S. M. O'Malley and D. R. Beck, Phys. Rev. A {\bf 61}, 034501 (2000)} (428 meV), newer calculations\footnote{X. Cao and M. Dolg, Phys. Rev. A {\bf 69}, 042508 (2004)} (530 meV), and the much larger experimental value\footnote{V. T. Davis and J. S. Thompson, Phys. Rev. Lett. {\bf 88}, 073003 (2002)} (955 meV). Inclusion of correlation involving the $4f$ electron brings us in good agreement with the other calculation$^3$ (511 meV), but addition of core-valence effects that would further bind the system is prohibitively difficult: several eV of core-valence correlation disrupts the relative positioning of the valence correlation configurations, resulting in unacceptable (up to $\sim$30\%) losses in their energy contributions. Thus, instead of opening the core, we have made a series of photodetachment cross section calculations. These results, along with a reinterpretation of the experimental data$^4$, lead us to a new value for the Ce$^-$ electron affinity of $\sim$660 meV.   

Efficient Rydberg Excitation of He with STIRAP

We have used Stimulated Rapid Adiabatic Passage (STIRAP)\footnote{U. Gaubatz et al., Chem. Phys. Lett., {\bf 149} 463 (1988)} for highly efficient excitation of Rydberg states, and developed an absolute measure of the efficiency. The metastable 2$^3$S$_1$ state (He*) comes from a dc discharge atomic beam source. A blue laser beam ($\lambda$ = 389 nm) excites He* to the 3$^3$P$_2$ state, and a red laser beam ($\lambda$=796 nm) then excites the 26$^3$S$_1$ state. If this intuitive order of excitations is reversed (STIRAP) the theoretical excitation efficiency $\rightarrow$ 100\%. In our experiment, He* atoms cross both blue and red beams whose positions can be shifted to affect the order that the atoms encounter them. We observed a large increase in the Rydberg population as we shift the red beam upstream of the blue one (the counterintuitive order appropriate for STIRAP). We also use 389 nm light to measure the excitation efficiency with blue detuned optical molasses directly downstream of the STIRAP area. It spreads the spatial distribution of remaining He* but Rydberg atoms are unaffected. We present the results of our first measurements.   

Autler-Townes Effect in Rydberg Excitation of Metastable He Atoms

We have studied the Autler-Townes (AT) effect in the two-step excitation of He atoms from the metastable 2$^3$S$_1$ state (He*) that serves as an initially populated ground state in an atomic beam (He* is produced in a dc discharge source). A relatively strong blue laser ($\lambda$ = 389 nm) couples this He* state to the 3$^3$P$_2$ state, which in turn can be excited to the 26$^3$S$_1$ Rydberg state by a relatively weak red laser ($\lambda$ = 796 nm) that serves as a probe. Keeping the laser frequencies fixed, we exploit the large Stark shift of the Rydberg state to measure the AT splitting of the 3$^3$P$_2$ state {\it vs.} the intensity of the 389 nm light. We do this by scanning a weak dc electric field (few V/cm) and observing the AT effect through the subsequently ionized Rydberg atoms using an ion detector located just downstream of the field plates (the scan amplitude exceeds the AT splitting). We compare our experimental results with a dressed atom picture of the AT effect.   

Collapse in Mixture of Two Component Fermi Gases

Trapped Fermi alkali gases are spin polarized and cannot interact in the s-wave channel. A two component system realized by mixtures of two Fermi alkali gases, say $^6$Li and $^{40}$K, interacts in an s-wave channel and can be viewed as a Fermi gas with effective scattering length $a_{LK}$. Our consideration based on the thermodynamic properties gives strong evidence that the compressibility becomes negative as soon as $a_{LK}$ is negative and sufficiently large. As a result, the system collapses when $p_F|a_{LK}|\sim1$, where $p_F$ is the Fermi momentum. In the regime of large particle numbers in mixtures such as in traps, the Fermi momentum can be estimated as $p_F\simeq (3\pi^2\rho)^{1/3}$ with $\rho$ the average number density of the mixture. Our prediction [M.Ya. Amusia, A.Z. Msezane, and V.R. Shaginyan, Phys. Lett. A{\bf 293}, 205 (2002)] that two component systems composed of Fermi and Bose gases, which retain the significant features of the considered two component Fermi system, collapse is in good agreement with recent facts [C. Ospelkaus {\it et al.,} Phys. Rev. Lett. {\bf 96}, 020401 (2006)]. Our results suggest that the equation of state of a low density neutron matter has peculiarities at $|a_{nn}|p_F\sim 1$ ($a_{nn}$ is the neutron-neutron scattering length), which can lead to the equilibrium state of neutron matter.   

New Parallel Divide-and-Conquer Algorithm for Computing Full Spectrum of Polyacetylene

The Su-Schrieffer-Heeger (SSH) model is a simple tight-binding model that includes nearest neighbors and is frequently used to study the fundamental properties of trans-polyacetylene (trans-PA), as well as many other materials. In these studies, the essential and most time consuming step is the computation of the eigen-decomposition of the Hamiltonian matrix. In this poster, we present a new scalable parallel algorithm that efficiently computes the full spectrum of Hamiltonian matrices to a prescribed accuracy. Given an accuracy tolerance $\tau$ and Hamiltonian matrix $A$, which is a real symmetric dense matrix, our parallel algorithm fully exploits the structure of the Hamiltonian matrix and computes eigen-solutions in two steps: (a) Construct a block-tridiagonal matrix that approximates the original dense matrix; (b) Use the highly efficient block-tridiagonal divide-and- conquer algorithm to compute approximate eigen-solutions. The computed approximate eigen-solutions satisfy the following conditions: 1) $ ||A-V\Lambda V^T|| \le O(\tau||A||) $; and 2) $ ||(VV^T - I)|| \le O(n\epsilon_{mach}) $, where $\epsilon_{mach}$ is the machine precision. Performance tests show that this algorithm is extremely efficient for the computation of electronic spectrum of trans-PA compared to traditional dense eigensolvers. In many tests, the savings is several orders of magnitude!   

Liouville-Space Descriptions for Intense-Field Coherent Electromagnetic Interactions

Liouville-space (reduced-density-operator) descriptions are developed for coherent electromagnetic interactions of quantized electronic systems, taking into account environmental decoherence and relaxation phenomena. Applications of interest include many-electron atomic systems and semiconductor nanostructures. Time- domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are developed in a unified manner. In a preliminary semiclassical perturbative treatment of the electromagnetic interaction, compact Liouville-space operator expressions are derived for the linear and the general (n’th order) non- linear electromagnetic-response tensors. Intense-field electromagnetic interactions are treated by an alternative reduced-density-operator approach based on the Liouville-space Floquet-Fourier representation.   

Recurrence Tracking Microscope: Atom optics for nanoscience

In order to probe nanostructures on a surface we present a microscope based on atom optics laws. A cloud of atoms bounces off an atomic mirror connected to a cantilever and exhibits quantum recurrences. The times at which the recurrences occur depends on the initial height of the bouncing atoms above the atomic mirror, and varies following the structures on the surface under investigation. The microscope has inherent advantages over existing techniques of scanning tunneling microscope and atomic force microscope. Presently available experimental technology makes it possible to develop the device in the laboratory.   

Measurement of Excited State Lifetime Using Two-Pulse Photon Echoes in Rubidium Vapor

We have observed two-pulse photon echoes in a Doppler broadened rubidium vapor. The system interacts with traveling wave optical pulses that are $\sim $20 ns in duration. The pulses are on resonance with the F=3 - F'=4 transition in $^{85}$Rb and F=2 - F'=3 transition in $^{87}$Rb. They are generated from a CW laser using acousto-optic modulators. The first pulse, occurring at t=0, induces a macroscopic dipole moment that dephases due to atomic motion. The second pulse, occurring at t=T, reverses the direction of the dephasing process so that the echo is formed at t=2T. The echo is detected using a heterodyne technique and its intensity decays exponentially as a function of 2T. We report a measurement of the excited state lifetime precise to $\sim $1{\%} that is in agreement with a previous measurement. Our results suggest that the excited state lifetime can be determined to a precision of $\sim $0.25 {\%} by additional data accumulation and by a more comprehensive study of systematic effects.   

Experimental Studies of Decoherence using a Single State Atom Interferometer

We have measured the decay time of a ground state grating echo produced by off resonant standing wave pulses tuned to the vicinity of the $F=3 \rightarrow F'=4 $ transition in trapped $^{85}Rb$ atoms. The time scale of the decay $(\sim 20 $ms$)$ is determined primarily by the transit time of the cold atoms through the region of interaction and is sufficiently long to investigate effects of decoherence due to light and velocity changing collisions. We find that the decay rate exhibits an exponential dependance on light intensity and scales inversely as the square of the detuning with respect to the excited state. We have also observed the effect of diffractive collisions on the decay time by varying the pressure of the background rubidium atoms. The data can be used to infer the total cross section for collisions between hot and cold rubidium atoms. These studies allow the time scale of the echo signal to be extended making it feasible to improve the precision of our measurement of $\hbar/M_{Rb}$.   

Effect of a magnetic field gradient and gravitational acceleration on a time domain grating echo interferometer

We have observed the effects of magnetic field gradients and gravitational acceleration on grating echoes in a time domain single state atom interferometer that uses laser cooled Rb atoms. These observations are compared to theoretical predictions based on a simplified model. The oscillatory dependence of the echo amplitude due to the magnetic field gradient is in agreement with the predicted quadratic scaling as a function of the time between excitation pulses. We also observe a linear dependence of this oscillation frequency as a function of the magnetic field gradient which is predicted by theory. In the presence of gravity, the calculations predict a quadratic dependence for the echo phase on the time between excitation pulses as well as a change in the shape of the echo envelope. We have observed both of these effects in the experiment, and we find that the change in shape is qualitatively consistent with our prediction. It is necessary to understand these effects in order to carry out high precision studies of the atomic fine structure constant and gravitational acceleration using this interferometric technique. We also present an improved measurement of gravitational acceleration using this technique that is precise to $\sim 15$ppm by exploiting the quadratic phase dependence.   

Measurement of atomic g factor ratios using laser cooled atoms

We have used pulsed laser excitation to create a spatially periodic coherence grating between adjacent magnetic sublevels of the ground state in a cloud of trapped Rb atoms. The light scattered from the grating exhibits Larmor oscillations in the presence of a magnetic field with the frequency defined by the energy level splitting between magnetic sublevels. We describe the progress in our measurements of the atomic g factor ratio using the F=3 to F’=4 transition in $^{85}$Rb and the F=2 to F’=3 in $^{87}$Rb. The current level of precision is $\sim$25 ppm achieved by acquiring data for about four hours. We describe studies of systematic effects due to fluctuating ambient magnetic fields and AC Stark shifts with the goal of achieving a precision of less than 1 ppm.   

Three-body resonances using slow variable discretization coupled with complex absorbing potential

We are investigating three-body resonances for a model three-particle problem using the slow variable discretization method of Tolstikhin \textit{et al.} [1] coupled with a complex absorbing potential. We compare the results with those of Fedorov \textit{et al.} [2]. We will also present preliminary calculations on Efimov resonances using our method. Efimov states are a universal set of bound trimer states which appear when there is a two-body weakly-bound or virtual state [3]. Bound states of Efimov trimers have been studied in a number of theoretical treatments. Efimov resonances can be viewed as three-body Feshbach resonances that decay into a two-body bound system and a free third body (diatomic molecule + free atom, for example). Recent experimental evidence for Efimov trimers in an ultracold gas of Cs atoms obtained by Kraemer \textit{et al.} [4] has made the study of their resonances especially relevant. [1] O. I. Tolstikhin \textit{et al.}, \textit{J. Phys. B: At. Mol. Opt. Phys.} \textbf{29}, L389 (1996). [2] D. V. Fedorov \textit{et al.}, \textit{Few Body Systems} \textbf{33}, 153 (2003). [3] B. D. Esry \textit{et al.}, \textit{Phys. Rev.} \textbf{A54}, 394 (1996) and references therein. [4] T. Kraemer \textit{et al.}, \underline {arxiv.org/abs/cond-mat/0512394}   

Detecting phonons and persistent currents in toroidal Bose-Einstein condensates

We theoretically investigate the dynamic properties of a Bose-Einstein condensate in a toroidal trap. We show that a time periodic modulation of the transverse confinement gives rise to a space periodic density pattern along the torus as a consequence of parametric amplification of pairs of Bogoliubov phonons propagating in opposite directions. This process is analogous to Faraday's instability of classical fluids in annular resonators. If the trap is switched off, the periodicity of both density and momentum distributions produces a peculiar flower-like density distribution of the freely expanding gas. By imaging the expanded condensate one obtains i) a precise determination of the Bogoliubov spectrum and ii) a sensitive detection of quantized circulation in the torus. The parametric amplification is also sensitive to thermal and quantum fluctuations.   

BEC in a time varying optical dipole trap

We have created BECs in a trap produced from a single high-powered (P$\sim$60~W) CO$_2$ laser beam. Atoms are loaded from a vapor cell MOT into a large volume dipole trap. Forced evaporation is performed by lowering the laser beam power while decresing the trap volume. This method enables us to maintian a sufficient elastic collision rate even at low temperatures. We will discuss the effects of trap volume and depth on the initial number of atoms loaded into our dipole trap as well as the limitations of our squeezing process and its effect on evaporation trajectory and condensate number.   

Deterministic Production of Photon Number States via Quantum Feedback Control

It is well-known that measurements reduce the state of a quantum system, at least approximately, to an eigenstate of the operator associated with the physical property being measured. Here, we employ a continuous measurement of cavity photon number to achieve a robust, nondestructively verifiable procedure for preparing number states of an optical cavity mode. Such Fock states are highly sought after for the enabling role they play in quantum computing, networking and precision metrology. Furthermore, we demonstrate that the particular Fock state produced in each application of the continuous photon number measurement can be controlled using techniques from real-time quantum feedback control. The result of the feedback- stabilized measurement is a deterministic source of (nearly ideal) cavity Fock states. An analysis of feedback stability and the experimental viability of a quantum optical implementation currently underway at the University of New Mexico will be presented.   

Imaging the Mott insulator shells using atomic clock shifts

We have used 2-photon microwave spectroscopy to probe the Superfluid- Mott Insulator transition in a 3D optical lattice. Using the mean field clock shift we were able to distinguish between sites with different filling factor due to their higher interaction energy. This also allowed us to directly image the shell structure of the Mott Insulator. In addition we could measure the on-site interaction and lifetime for individual shells. Filling factors of up to n=5 have been observed.   

A Fermi Mixture of $^{6}Li$ and $^{40}K$

We report on our progress in the construction of a new apparatus for the simultaneous cooling of the Fermionic alkali isotopes $^{6}Li$ and $^{40}K$. Our goal is to cool the mixture to degeneracy and search for novel pairing mechanisms involving Fermions of different masses. We have constructed, for the first time, a 2-D MOT source of cold Li atoms directly loaded from a thermal source, thereby circumventing the need for a Zeeman slower. The 2-D MOT is loaded from an effusive Li oven source and the trapping light is derived from a YAG-pumped dye laser. Atoms captured from the 400C thermal beam are clearly visible trapped in two dimensions by the four intersecting MOT beams. Furthermore we have constructed and realized a 2-D MOT for $^{40}K$ and a double recapture MOT mixing both species. We plan to soon start loading the mixture into an optically plugged magnetic trap for evaporative cooling.   

Time-Dependent Waveforms Associated with Optogalvanic Transitions Excited in CO Gas

We will present our experimental studies on the optogalvanic effect (OGE) in a hollow cathode lamp filled with CO gas. Our theoretical model, based on appropriate rate equations, predicts that the observed signals should be described in terms of a sum of exponential functions. We have also developed a least-squares fitting routine that is based on the Monte Carlo method and used it to fit the optogalvanic waveforms. We were able to fit the observed OG transitions in CO using either three or four exponential functions and the fits proved to be excellent with very small residuals.   

Nonperturbative quantum and classical calculations of multiphoton vibrational excitation and dissociation of Morse molecules$^1$

The multiphoton vibrational excitation and dissociation of Morse molecules have been computed nonperturbatively using Hamilton's and Schr$\phi $dinger's time-dependent equations, for a range of laser pulse parameters. The time-dependent Schr$\phi $dinger equation is solved by the state-specific expansion approach [e.g.,1]. For its solution, emphasis has been given on the inclusion of the continuous spectrum, whose contribution to the multiphoton probabilities for resonance excitation to a number of excited discrete states as well as to dissociation has been examined as a function of laser intensity, frequency and pulse duration. An analysis of possible quantal-classical correspondences for this system is being carried out. We note that distinct features exist from previous classical calculations [2]. For example, the dependence on the laser frequency gives rise to an asymmetry around the red-shifted frequency corresponding to the maximum probability. [1] Th. Mercouris, I. D. Petsalakis and C. A. Nicolaides, J. Phys. B\textbf{ 27}, L519 (1994). [2] V. Constantoudis and C. A. Nicolaides, Phys. Rev. E \textbf{64}, 562112 (2001). \newline $^1$This work was supported by the program 'Pythagoras' which is co - funded by the European Social Fund (75\%) and Natl. Resources (25\%). \newline $^2$Physics Department, National Technical University, Athens, Greece.\newline $^3$Theoretical and Physical Chemistry Institute, Hellenic Research Foundation, Athens, Greece.   

Optimal Strategies for Fast Control of Collective States of Atoms in Cavities

The ability to control quantum mechanical states is an essential requirement for the development of reliable quantum information processing systems. We propose strategies that use sub-picosecond laser pulses for optimal and fast control of the collective state of trapped neutral atoms in a cavity. We present computer simulation for experimentally feasible parameters and discuss potential applications to quantum computing technologies.   

Life Time of Charge Carriers in Double Walled Carbon Nanotubes.

We investigate the nature of low-energy excitations in double walled carbon nanotubes, DWNT, by pumping the states using fs IR pulses. The temporal evolution of the population is examined by ionizing the resulting population with delayed fs UV pulses. The electron time of flight of the ionized electrons is recorded for a range of energies above $E_{F }$to investigate the relaxation dynamics of the charge carriers. The initial, fast relaxation is attributed to the internal thermalization of the electronic system, and is primarily driven by electron-electron (e-e) scattering processes. After the system returns to a Fermi-Dirac distribution it continues to decay with a slower rate associated with electron gas cooling electron-phonon (e-ph) interactions. We specifically want to see if the (e-e) scattering in DWNT follow a Fermi-liquid behavior, as observed in our previous study of MWNT$^{1}$. 1. Zamkov, M.; Woody, N.; Shan, B.; Chang, Z.; Richard, P. \textit{Phys. Rev. Lett.} \textbf{2005}, 94, 056803.   

Ground state energy of dilute gas fermion/Bose-Eintein Condensate mixtures

The properties of distinguishable neutral atoms embedded in a Bose-Einstein condensate (BEC) are modified by their interactions with the surrounding superfluid - the atoms act as polarons. In addition, when the density of the atoms is high, the atoms have BEC-mediated interactions. If these atoms are indistinguishable fermions, the mediated interactions may be the only inter-particle interactions since the short-range atom-atom interactions are suppressed by the Pauli-exclusion principle. We have studied the many-body energy of the mixture using perturbation theory to uncover the effects of the polaron physics and those of mediated interactions. At low BEC density the mediated interactions are very weak, and at high density the interaction range becomes so short that the Pauli-exclusion principle reduces the effect. We try to find the optimal mixtures for studying correlation physics in cold atom fermion/BEC mixtures. We calculate the ground state energy as a function of the ratio of the BEC-sound velocity, $c$, and the Fermi velocity, $v_F$. When $c<v_F$, the energy shift is almost linear to $c/v_F$ with the proportionality $1.35/(m_F/m_B)$.   

Quantum-optical Space-time Wave Frames: When light coordinates itself coherently

Careful re-examination of details of quantum and classical optical wave interference leads to a more precise and elegant logic for two of the foundations of modern physics, special relativity and quantum theory. This provides a transparent unified development of both subjects together in a few simple logical steps with improved intuition and fewer ``mysteries.'' The first step is an Occam razor reduction of Einstein's axiom to a spectral form based on linear dispersion or, ``All colors go c.'' Then wave nodal planes of interfering CW beams or optical cavity modes provide their own space-time coordinate frames with a reciprocal per-space-time lattice.[1] These clearly display Lorentz-Poincare symmetry and hyperbolic dispersion characteristic of quantum matter with very simple Compton recoil analyses. Accelerated coordinate frames made by cavity chirping are used to relate Compton effects to the relativistic shifts and horizons that are present in an Einstein elevator and shows them to be an elegant result of wave interference. [1] W. G. Harter, J. Mol. Spect. 210, 166 (2001)   

Spin-symmetry conversion and internal rotation in high J molecular systems

Dynamics and spectra of molecules with internal rotation or rovibrational coupling is approximately modeled by rigid or semi-rigid rotors with attached gyroscopes. Using Rotational Energy (RE)$^{1}$ surfaces, high resolution molecular spectra for high angular momentum show two distinct but related phenomena; spin-symmetry conversion and internal rotation. For both cases the high total angular momentum allows for transitions that would otherwise be forbidden. Molecular body-frame J-localization effects associated with tight energy level-clusters dominate the rovibronic spectra of high symmetry molecules, particularly spherical tops at J$>$10. $^{2}$ The effects include large and widespread spin-symmetry mixing contrary to conventional wisdom$^{3}$ about weak nuclear moments. Such effects are discussed showing how RE surface plots may predict them even at low J. Classical dynamics of axially constrained rotors are approximated by intersecting rotational-energy-surfaces (RES) that have (J-S)$\cdot $B$\cdot $(J-S) forms in the limit of constraints that do no work. Semi-classical eigensolutions are compared to those found by direct diagonalization. $^{1}$ W.G Hater, in \textit{Handbook of Atomic, Molecular and Optical Physics}, edited by G.W.F Drake (Springer, Germany 2006) $^{2}$\textit{ W. G. Harter, Phys. Rev. A24,192-262(1981).} $^{3}$\textit{ G. Herzberg,}\underline {\textit{ Infrared and Raman Spectra}}\textit{ (VanNostrand 1945) pp. 458,463.}   

Resonant electric dipole-dipole interactions between cold Rydberg atoms in a magnetic field

Laser cooled Rb atoms were optically excited to 46d$_{5/2}$ Rydberg states. A microwave pulse transferred a fraction of the atoms to the 47p$_{3/2}$ Rydberg state. The resonant electric dipole-dipole interactions between atoms in these two states were probed using the linewidth of the two-photon microwave transitions 46d$_{5/2}$ -- 47d$_{5/2}$. The presence of a weak magnetic field (roughly 1 G) reduced the observed line broadening, indicating that the interaction is suppressed by the field. The field removes some of the energy degeneracies responsible foe the resonant interaction, and this is the basis for a quantitative model of the resulting suppression. A technique for the calibration of magnetic field strengths using the 34s$_{1/2}$ -- 34p$_{1/2}$ one-photon transition is also presented.   

Direct femtosecond laser excitation of the 2p state of H by a resonant 8-photon transition in $H_{2}^{+}$.

We observe Lyman-$\alpha$ radiation produced by the direct excitation of thermal $H_{2}$ molecules by 25-fs 800-nm laser pulses. The excitation proceeds in 4 steps. First the laser pulse ionizes the $H_{2}$ molecule. The $H_{2}^{+}$ molecular ion then begins to dissociate through bond softening. The expanding $H_{2}^{+}$ ion enters a region of strong multiphoton coupling with the laser field in which resonant excitation from the strongly coupled $1s\sigma_{g}$, $2p\sigma_{u}$ states to the $2s\sigma_{g}$, $3p\sigma_{u}$ states can occur. The population in the $2s\sigma_{g}$ and $3p\sigma_{u}$ states finally dissociate into H atoms in the 2s and 2p states. This scenario is supported by several independent experiments. 1) The Lyman-$\alpha$ fluorescence has a linear dependence on pressure, which is consistent with direct, but not plasma, excitation. 2) A weak probe pulse delayed by 500 fs can quench the radiation, as the H(2p) state is easily ionized. This shows that the excited state is populated within 500 fs of the first pulse, again ruling out plasma excitation. 3) The radiation is seen with circularly polarized light, ruling out excitation through rescattering. 4) Ion time-of-flight coincidence measurements show a new $H^{+} + H^{+}$ channel when a weak probe pulse is applied, as would be expected from the quenching experiment. All of these results are fully consistent with a new theory of high-order strong-field coupling in diatomic molecules.   

Recent Experiments in Ultracold Strontium

We present recent work toward achieving quantum degeneracy in Strontium. In the first stage of cooling, a MOT operating on the strong ($\Gamma $= (2$\pi )$* 32 MHz), $^{1}$S$_{0}\to ^{1}$P$_{1}$ transition cools 10$^{8}$ atoms to 2 mK. Approximately 50{\%} of these atoms are transferred to a second-stage MOT operating on the weaker ($\Gamma $= (2$\pi )$* 7.5 kHz) $^{1}$S$_{0}\to ^{3}$P$_{1}$ intercombination transition, further cooling the sample to 5 $\mu $K. Here we discuss transferring this sample to an optical dipole trap and using evaporative cooling techniques to reach quantum degeneracy.   

One-Dimensional Cooling of an Ultracold Neutral Strontium Plasma

The application of laser cooling to neutral plasmas opens a wide range of experimental possibilities. This would be a new method of plasma confinement. Trapped plasma can be stored for longer times enabling detailed investigations of strong coupling, recombination at ultracold temperatures, and ion-ion thermalization. Recently, the ultracold plasma group at Rice has developed a high power laser source capable of laser cooling an ultracold neutral strontium plasma. Preliminary results on one-dimensional laser cooling of the plasma will be presented.   

Lifetime and Branching Fraction Measurements for P II~

Lifetime and branching fraction measurements using foil excitation of a fast ion beam are reported for transitions within the 3s$^2$ 3p$^2$ -- 3s$^2$ 3p4s multiplet in P II. The studies were undertaken to test theoretical and semiempirical calculations which suggest that branching fractions within this multiplet can be accurately specified from intermediate coupling amplitudes deduced from measured energy level data. The results and their possible use a much-needed intensity calibration standard in the vacuum ultraviolet wavelength region will be discussed.   

Electron interferometry with nano-fabricated gratings

We have realized a three grating electron interferometer. We used free standing, metal-coated gratings with a 100 nm periodicity. Fringes are observed at 10, 8, 6, and 4 keV. Our best observed contrast is about 20 percent. This contrast exceeds our calculated maximum contrast for a Moire deflectometer by a factor of 4 and shows the quantum mechanical nature of this device. Our path integral calculation predicts a maximum contrast of about 40 percent for our experimental configuration. Our contrast does not exceed this value and is possibly limited by interferometer alignment. Our results also confirm our earlier prediction that neither image charge interaction, nor dephasing or decoherence effects prevent the construction of this electron interferometer.   

Progress Toward Buffer Gas Cooling of a 1 $\mu_B$ Species

Thermalization with a non-magnetic $^3$He buffer gas has been demonstrated to be an effective means of removing heat from a sample of hot magnetic atoms held in a magnetic trap[1]. To thermally isolate the atoms, it is necessary to remove the buffer gas without sweeping away the magnetically trapped atoms. The magnetic trap strength is proportional to the magnitude of the atom's moment. This is the primary reason that trapping a 1 $\mu_B$ species has never been realized in a buffer gas cooling experiment. Eventually, we plan to use this technique to trap and cool atomic hydrogen and deuterium. We have built a cryogenic valved cell suspended from a dilution refrigerator along the axis of a 4T quadrupole magnetic field. The cell is maintained at a base temperature of 100mK. The buffer gas is removed by opening the valve. Any remaining buffer gas may be energetic enough to scatter the atoms out of the trapping potential, thus limiting the lifetime. Therefore, we lower the temperature of the cell to decrease the vapor pressure of any $^3He$ remaining on the walls. We can mimic the conditions of a 1 $\mu_B$ species using atomic Mn (5 $\mu_B$) simply by lowering the trapping field strength by a factor of five. Further, we will report on efforts to trap and thermally isolate $^7$Li, a true 1 $\mu_B$ species. \\ \noindent [1]J. D. Weinstein et al., Phys.\ Rev.\ A {\bf57}, R3173 (1998). \\   

Experimental Analogy to Time-Independent Solutions to Schr\"{o}dinger's Equation: A Level Splitting Approach to Phononic Band Gaps

A delta barrier inside an infinite potential well is the usual starting point for discussing level splitting, avoided crossings, and band gaps. These same phenomena are found in physical systems such as electronic conductors/insulators and photonic crystals. Here, we explore another physical system---a continuous sound wave propagating through an array of partially reflecting acoustic mirrors. We show, experimentally and by calculation, that for the above system, the following general description holds. When two identical acoustic cavities are brought into each other's vicinity, a weak coupling between the two initially degenerate states (i.e. resonant frequencies) gives rise to level splitting. Adding a third identical cavity results in a triplet of states and so on. For an array of identical cavities, a one-dimensional crystal lattice forms where the multiplet merges into a band of states. These bands are separated by phononic band gaps.   

Toward Ultracold Atomic Hydrogen and Deuterium: An Application of Buffer Gas Cooling

Ultracold samples of atomic H and D offer unique possibilities for precision spectroscopy and studies of quantum fluids. Current techniques to cool H are limited by the small H-H elastic scattering cross section and require a superfluid He film in the initial thermalization. The film limits the optical access to the trapped atoms and precludes trapping of D due to high recombination rates on superfluid He films. We have built an apparatus that will use the technique of buffer gas cooling to thermalize 1 $\mu_B$ atoms. Ablation of a solid LiH(LiD) target will produce atomic Li and H(D). Initial thermalization will be achieved through elastic collisions with a $^3$He buffer gas at $\sim$350mK. The large Li-H elastic scattering cross section will enhance evaporative cooling of the H atoms. As a first step in this process, we are currently optimizing the system for trapping and cooling of atomic $^7$Li.   

Spinor dynamics-driven formation of a twin-beam atom laser

We demonstrate a novel twin-beam atom laser formed by outcoupling oppositely polarized components of an $F=1$ spinor Bose-Einstein condensate whose Zeeman sublevel populations have been coherently evolved through spin dynamics. The condensate is formed initially through all-optical means using a single-beam running-wave dipole trap. We initially form a condensate in the field-insensitive $m_F=0$ state, and drive coherent spin-mixing evolution through adiabatic compression of the initially weak trap. Such twin beams, nominally number-correlated through the angular momentum-conserving reaction $2m_0\leftrightarrow m_{+1}+m_{-1}$ have been proposed as tools to explore entanglement and squeezing in Bose-Einstein condensates. The twin beams are outcoupled from the opposite ends of a cigar-shaped trap; we compare observed images with the behavior of a single-species version outcoupled in the direction of gravity.   

Ionization of Xe using Femtosecond Optical Vortices

Photons in optical vortices possess optical \textit{orbital} angular momentum$^{2}$. What role this quantity plays in ultrafast intense-field processes is to the best of our knowledge experimentally unexplored territory. Using home-made laser-etched line holograms (with about 10 grooves per mm), we have recently created femtosecond optical vortices that are sufficiently intense to ionize Xe atoms. The simplest vortices we create are Laguerre-Gaussian modes with radial mode number $p$ = 0 and azimuthal mode number $l$ = 1 (a.k.a `donut mode'). In 2005, we were the first to report the generation of a (weaker) pure femtosecond vortex.$^{3}$ Using our time-of-flight ion mass spectrometer with confined detection volume we plan to spatially image ion clouds generated by focused vortices. Recent progress will be discussed. Refs: $^{2}$Allen L \textit{et al.} 2003 \textit{Optical Angular Momentum} (Bristol: IoP Publ.); $^{3}$Mariyenko I \textit{et al.} 2005 \textit{Opt. Expr.} \textbf{13} 7599.   

Stark Wave Packets in the Heavy Rydberg System H$^{+}${\ldots}F$^{-}$

Heavy Rydberg systems are unusual molecules that comprise a weakly-bound anion and cation orbiting their center of mass. Due to a combination of their size and simple internal structure these molecules represent novel systems with which to study molecular dynamics and light-molecule interactions. We report the formation and control of the weakly-bound H$^{+}$..F$^{-}$ system by exciting HF molecules using a 1 XUV + 1 UV excitation scheme in an electric field. By using a narrow-band laser pulse for the second step, Stark wave packets are formed that evolve in the DC field. A ramped, zero-crossing electric field pulse applied after a variable time delay results in fragment ions arriving at the detector at two distinct times, corresponding to products from two different dissociation channels. By increasing the delay time, these channels alternate in intensity with a period that agrees perfectly with the expected Stark oscillation frequency.\footnote{R. C. Shiell, E. Reinhold, F. Magnus and W. Ubachs, ``Control of diabatic vs adiabatic field dissociation in a heavy Rydberg system,''\textit{ Phys. Rev. Lett.} \textbf{95}, 213002 (2005)} This study verifies the mass-scaling of heavy Rydberg systems and the viability of these novel molecular systems for further wave packet studies.