Session S5 - Poster Session III.
POSTER session, Friday afternoon, May 18
, London Convention Centre

[S5.001] Quantum Optics/Ultrafast Phenomena: Wavepacket Dynamics and Quantum Control

[S5.002] Semiclassical Approximation to Direct Part of Channel Specific Photodissociation Cross Sections

The quantum mechanical photodissociation cross section can be expressed in a time independent semiclassical form using the Wigner transformation. Expanding the Wigner transform of the delta function to lowest order in \hbar gives one a simple, tractable method to determine the direct part of the cross section. For off diagonal matrix elements, the channel specific cross sections may have an imaginary part. The method is used to determine the direct part of the channel specific cross sections for the collinear two channel systems CO_2 and CH_2BrI. For small excitations in the initial state, this semiclassical calculation accurately determines the real and imaginary parts, capturing all the features of a quantum calculation.

[S5.003] Control of Raman transitions driven by shaped microwave pulses

Transitions driven by multiphoton processes depend on the relative phases of the spectral components in an electromagnetic pulse as well as on the spectrum of the pulse. We have explored Raman transitions between the nd_3/2, nf_5/2, and nd_5/2 states in Rydberg states of sodium using shaped pulses of microwave radiation. The microwave pulses have peak fields of up to 5 V/cm, corresponding to Rabi rates of up to 1000 MHz. The microwave pulses are incident on nd_3/2 Rydberg atoms of Na in zero static electric field within a microwave transmission line. We present measurements of population transfer to the nd_5/2 state using pulses with simple spectral phase modulation, \phi(f) = \textrmm sin \left(2 \pi \tau_o \left(f-f_o\right)\right) for a variety of modulations depths, central frequencies, and modulation periods. The data is compared with numerical integration of Schrödinger's equation and a model of the two-photon spectrum of the pulse. A simple explanation in terms of time-domain sidebands is given.

[S5.004] Quantum Optics/Ultrafast Phenomena: Atom Interferometry

[S5.005] How far are electrons deflected by the Kapitza-Dirac effect?

Data from our experiment demonstrates that the motion of free electrons is influenced by laser light. A standing wave, formed with a pulsed Nd-YAG laser, acts as the optical analogue to a material grating. Our first experiments, done with the 1^st harmonic at 1064 nm, showed that the electrons were scattered by the laser but diffraction peaks were not resolved. In this case, we predict that the greatest angle that an electron can be scattered into can be calculated using a classical channeling model. Surprisingly, this maximum angle is the same as given by the Heisenberg uncertainty limited focus of the laser. We will present a discussion of this issue. To reduce the electron beam divergence we improved our magnetic shielding. Additionally, by using the 2^nd harmonic at 532 nm, the expected diffraction angle was doubled and individual peaks were resolved thereby demonstrating diffraction of electrons by a standing wave of laser light as proposed by Kapitza and Dirac in 1933^1. ^1 P.L. Kapitza and P.A.M. Dirac, Proc. Cambridge Philos. Soc. 29, 297 (1933).

Support: Research Corporation, Nebraska Research Initiative

[S5.006] Progress Report: Atomic Diffraction Experiments*

We propose to diffract multiple species of atoms, using one far off-resonance standing laser light wave as a diffraction grating. The motivation behind the experiment is to eliminate the need for a resonant laser for each respective atom to be diffracted. The use of far off-resonance light for the lightshift potential requires intense laser power. We constructed a simple build-up cavity to obtain the needed intensity. We then used Rayleigh scattering to determine the power of a laser beam, without placing a detector directly in the beam. This technique will be utilized to measure laser intensity inside the build-up cavity. A liquid nitrogen cooled metastable atom source will produce the atomic beams to be diffracted. Our source closely follows the design of J. Kawanaka et al. (Appl. Phys. B56, p.21-24, 1993); Ar* and He* beam characterizations will be presented.

*Support: Research Corporation and Nebraska Research Initiative.

[S5.007] Quantum Optics/Ultrafast Phenomena: Nonlinear Optics

[S5.008] Green's Function for Electromagnetic Waves in Periodic Structures

A general method for constructing the Green's function for electromagnetic waves in finite one-dimensional inhomogeneous layers is developed. Using the results of this method the exact analytical Green's function for layered dielectric structures is found. As an example of its application, the influence of fluctuations in the widths of the basic layers on the reflection and transmission of electromagnetic waves propagating through a two-layered periodic dielectric structure is found in the first Born approximation. Then, the convergence of the total Born (Neumann) series is investigated for a simpler case of one layer with fluctuations in the refractive index. The correspondence between the Born and the multiple scattering series for this problem is discussed. Applications to the design of optical switches will be presented.

[S5.009] Quantum Optics/Ultrafast Phenomena: Quantum Information

[S5.010] Storing the quantum states of photons in matter: Theory

We show that it is possible to ``store'' the quantum state of light fields by mapping it onto collective meta-stable states of an optically dense medium. An adiabatic technique is suggested which allows for ideal transfer of the quantum state. In contrast to previous approaches involving single atoms, the present technique does not require strong coupling.

We identify form-stable coupled excitations of light and matter (``dark-state polaritons'') associated with the propagation of quantum fields in electromagnetically induced transparency. Their properties such as the group velocity are determined by the mixing angle between light and matter components and can be controlled by an external coherent field as the pulse propagates. In particular, light pulses can be decelerated and ``trapped'' in which case their quantum state is mapped onto metastable collective states of matter, and vice versa.

Possible applications include transfer of quantum information between light and matter and entanglement of collective qubits.

[S5.011] Dynamical Accessibility in the Control of Mixed, Multipartite Quantum Systems

Quantum information technology relies on the manipulation and control of quantum states. A natural question arises as to which target states may be reached from which initial states through unitary quantum evolution. While any pure state is dynamically accessible from any other pure state via a general time-dependent Hamiltonian, accessibility for mixed states is more restrictive - two n-level mixed density matrices are dynamically connected to each other via unitary evolution if and only if the values of their Hioe-Eberly kinematic invariants c_j = tr \rho^j;\ j = 1,\ldots,n are identical. It is often of interest to consider special classes of allowable Hamiltonians possessing some dynamical symmetry, though the issue of dynamical accessibility for such cases has not been previously addressed. One such class is the set of local quantum operations on bipartite or multipartite quantum systems. We show that for such cases there are additional dynamical invariants which must be preserved and demonstrate how these further restrict dynamical accessibility using local quantum operations. We present a general framework for discussing dynamical accessibility in pure, mixed and multipartite quantum systems, and, for the latter, discuss the relation of the associated invariants to entanglement measures (which have recently been connected to the issue of dynamical accessibility.)

[S5.012] Experimental system for the storage of light in atomic vapor

In a recently reported experiment (D.~F.~Phillips, A.~Fleischhauer, A.~Mair, R.~L.~Walsworth, and M.~D.~Lukin, Phys. Rev. Lett. 86), 4783 (2001)., we reversibly stored a light pulse in a Zeeman (spin) coherence of Rb vapor for times \sim 0.5 ms. In this experiment, the Rb is warmed slightly above room temperature (\sim 80^\circC) and constrained by a buffer gas of a few torr of He. Experimental details of this light storage system will be presented.

[S5.013] Quantum Optics/Ultrafast Phenomena: Cavity QED

[S5.014] Intensity dependence of the conditional electromagnetic field emitted from a cavity QED system.

We have developed a correlation technique that permits us to follow the time evolution of the conditional electromagnetic field emitted from a cavity QED system. By conditioning the homodyne photocurrent on a photon detection we are able to record the time evolution of both the amplitude and phase of the emitted field. Our system operates in the regime of strong coupling between the atoms and the cavity mode of the electromagnetic field. This permits us to observe the dynamics of the exchange of excitation at rates many orders of magnitude slower than optical frequencies. We have undertaken a systematic study of the conditional field emitted from the system as we alter the driving intensity. We see the magnitude of the emitted field grow linearly with the driving field, up to a saturation point. At this point the contribution of atomic spontaneous emission is no longer negligible, and this incoherent process affects the dynamics of the system. Theoretical models show the transition from symmetric to asymmetric conditional fields as the driving intensity increases. Work supported by the NSF.

[S5.015] Cooling and Trapping: Laser Cooling and Trapping

[S5.016] Transverse Atomic Beam Velocimetry

Stimulated Raman transitions between two motional states of a ground state atom can cause a controlled momentum exchange with the light field (the internal structure of the atom plays no role). Such stimulated Optical Compton Scattering (SOCS) has been used for velocimetry in a cold gas(D. Boiron et. al., Phys. Rev. A50), R1992 (1994), and extraction of atoms from a BEC(M. Kozuma et al., Phys. Rev. Lett. 82), 871 (1999). Atoms can transfer a photon between two light beams only when the difference of their k-vectors \vecq and their velocity \vecv satisfy \vecq \cdot \vecv = \delta + 4 ømega_r \sin^2(\theta/2), where \theta is the angle between \veck_1 and \veck_1, \delta is their frequency difference, and ømega_r \equiv \hbar k^2/2M. We report transverse atomic beam velocimetry using SOCS in a much sparser beam sample. Transverse velocimetry is usually done by measuring the spatial distribution in a long beam line, and good resolution requires narrow beam-defining slits. Since SOCS comprises direct velocimetry, the beam apparatus can be short, there is no broadening from the longitudinal velocity spread, and no need for any slits. In our experiment the two SOCS beams are generated from one diode laser and are at \pi/2 to the atomic beam. Their \delta is swept by passing one of them through a glass plate rotating at \sim10 Hz about an axis parallel to its surfaces. The absorption of the other one is recorded and used with the equation for \vecq \cdot \vecv to extract the velocity distribution.

[S5.017] Velocity Selective Coherences in a Magnetic Field

We have studied VSCPT(M. Doery et al., Phys. Rev: A52), 2295 (1995) and references therein. in metastable He in a \vecB field and have begun to unravel the connection to magnetically induced velocity selective resonances (VSR)(S.Q. Shang et al., Phys. Rev. Lett 65), 826 (1990).. One very obvious difference between these is the two-peaked velocity distribution split by 2v_r \equiv 2 \hbar k/M of VSCPT, and the single peak of rms width < v_r of VSR. But the evidence for a strong connection is that both phenomena produce velocity distributions with rms widths below v_r when a velocity-selective Raman resonance is achieved by matching the Doppler and Zeeman shifts of two ground states |1\rangle and |2\rangle. The coherence produced by such a resonance suggests a basis |\pm \rangle = \|1\rangle \pm |2\rangle \/\sqrt2, where |-\rangle is a dark state^2. Thus there are two time scales, one for the excitation of |+ \rangle that quickly pumps its atoms away from velocities near the Raman resonance, and \Gamma^\prime, a much slower rate for atoms in |- \rangle to evolve to |+ \rangle and be pumped, often into the velocity trapped dark state^2. When \vecB_z \neq 0 the VSCPT signals are centered at 2 \veck \cdot \vecv = g \Delta M \mu_B |\vecB|/\hbar instead of v=0, just as in VSR, as long as the interaction time satisfies \Gamma^\prime \tau_int > few. But if a \vecB field compromises the optical selection rules so atoms can be pumped out of |- \rangle, or if the laser parameters make \Gamma^\prime < few/\tau_int, then only a single peak appears^2. We will present an appealing semi-classical model of these phenomena.

[S5.018] Bichromatic Sisyphus Cooling

Sisyphus cooling arises when the conservative dipole force of a monochromatic optical standing wave (SW) is modified by optical pumping among multiple ground state sublevels at low intensity(J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. B6), 2023 (1989)., or among dressed state manifolds at high intensity(A. Aspect et al., Phys. Rev. Lett. 57), 1688 (1986). As part of our ongoing exploration of optical forces in non-monochromatic light, we have discovered a new type of Sisyphus cooling in a two-level atom where the optical pumping is driven by a second SW produced as a sideband from weak frequency modulation. Each beam of the carrier's SW has a Rabi frequency Ømega_c \sim 20 \gamma and is tuned below atomic resonance by \delta_c \sim -38 \gamma. Thus the light shift at the antinodes is ømega_c^ls \sim 8.6 \gamma. For the sideband, Ømega_s \sim 1.4 \gamma and \delta_s \sim +1 \gamma so ømega_s^ls \sim 1 \gamma. The resulting forces satisfy F_c > 8 F_s. By contrast, the excitation rate \gamma_s^p > 2 \gamma_c^p. We choose the relative spatial phase of the SW's to be \pi, so moving atoms are most likely to be excited at the red-tuned carrier nodes, and thus they climb more hills than they descend. We observe transverse cooling of a beam of He metastables when \delta_c < 0 and heating otherwise, in contrast to Ref. 3 because here the excitation is at the nodes of the high intensity carrier SW. We also observe channeling of the slow atoms in the carrier's SW.

[S5.019] Coherent Exchange of Momentum between Atoms and Light

Non-monochromatic light can produce velocity-dependent forces, that are \gg \hbar k \gamma /2 \equiv F_rad, the limit of the radiative forces used for laser cooling for the past 20 years. For example, the measured velocity-dependent bichromatic force \gg F_rad.(M. R. Williams, Phys. Rev. A61), 023408 (200) and references therein. It results from a coherent momentum exchange between atoms and a light field mediated by amplitude beats derived from mixing the two frequencies. Here we report demonstration of a similarly strong and dissipative force, where the coherent momentum exchange is mediated by adiabatic rapid passage (ARP), as the optical frequency is swept through a range 2\delta_0 at a rate ømega_m centered about atomic resonance. The modulation parameter \beta \equiv \delta_0 / ømega_m and \dot\delta=2 \delta_0 ømega_m/\pi . ARP requires the Rabi frequency Ømega to satisfy \delta_0 \gg Ømega \gg ømega_m \gg \gamma where \tau \equiv 1/\gamma is the excited state lifetime. We use \delta_0 = 100 \gamma,~ Ømega = 50 \gamma,~ and~ ømega_m = 10 \gamma, where \gamma = 1.6 MHz for our 2^3S \rightarrow 2^3P transition in He. A simple model of \Delta p = 4 \hbar k for each cycle of duration 2 \pi/ ømega_m suggests F = 2 \hbar k ømega_m/\pi \sim 12 F_rad in the absence of spontaneous emission (SE). Our model to include SE in the ARP force suggests a reduction by 50% \Rightarrow ~F \sim 6 F_rad, about twice what we observe. We attribute the discrepancies to various experimental imperfections that we plan to address.

[S5.020] Velocity Selective Raman Resonances at High Recoil

We are continuing our exploration of the unusual domain of laser cooling where the ratio of the recoil frequency ømega_r to the natural width \gamma no longer satisfies ømega_r/\gamma \equiv \varepsilon \ll 1. Among the unusual properties is that VSCPT can be performed in a two-level atom(J. Hack et. al., Phys. Rev., A62), 013405 (2000).. We use the 2\,^3S\rightarrow3\,^3P transition of metastable He at \lambda = 389 nm, where \varepsilon \approx 1/5 and the recoil velocity is >25 cm/s, comparable to the Doppler limit. Thus sub-recoil resolution is readily achieved in a modest atomic beam apparatus. We have observed the magnetic field and laser detuning dependence of the usual three-level VSCPT(A. Aspect et al., Phys. Rev. Lett., 61) 826 (1988). on the J = 1 \rightarrow 1 transition, and velocity selective resonances on the J = 1 \rightarrow 2 transition in magnetic fields. We have developed a simple quantum mechanical model of these phenomena as well as an appealing semi-classical model.

[S5.021] Bose-Fermi Mixture in a Magneto-Optical Trap

We report on a two-species magneto-optical trap (MOT) used for the simultaneous cooling and trapping of the fermionic atom ^40K and the bosonic atom ^87Rb. This trap represents the first phase in cooling a Bose-Fermi mixture to quantum degeneracy. Trapping light for the MOT is provided by external cavity diode lasers (ECDLs) that are frequency-locked to the cycling transition of each species via saturated absorption spectroscopy. Two diode lasers are injection-locked to the ECDLs, and current modulated in order to obtain light for the hyperfine repump transitions. We characterize the behavior of the two-species MOT, including its dependence on laser power and detuning. This work is funded by: DOE

[S5.022] A laser-cooled positron plasma

We present results on trapping and cooling of positrons in a Penning trap. A few thousand positrons are trapped and lose energy through Coulomb collisions (sympathetic cooling) with laser-cooled ^9Be^+ ions. By imaging the ^9Be^+ laser-induced fluorescence, we observed centrifugal separation of the ^9Be^+ ions and positrons, with the positrons coalescing into a ``dark'' column along the trap axis. This indicated that the positrons had densities up to \sim4 \times 10^9 cm^-3 which is \sim50 times greater than the highest positron density previously achieved(R. G. Greaves and C. M. Surko, Phys. Rev. Lett. 85), 1883 (2000). By comparing the observed centrifugal separation with a modified theoretical model(T. M. O'Neil, Phys. Fluids 24), 1447 (1981). we place an upper limit on the positron temperature for motion parallel to the magnetic field of \sim5 K. The positron lifetime was greater than 8 days in our room temperature vacuum of 10^-8 Pa. Cold positron plasmas are useful as a source for cold beams of high brightness, for positron-normal matter interaction studies and for anti-hydrogen production.

[S5.023] Stick-Slip Dynamics in Stressed Laser-Cooled Ions

We trap up to 10^5 Be^+ ions in a Penning trap and utilize laser cooling to reduce the ion temperature to less than 5 mK. We then exert a torque on a planar (2D extended) ion cloud crystallized into a bcc structure(T. B. Mitchell et al.), Science 282, 1290 (1998). with a resonant laser beam, and measure the statistics of the resultant intermittent angular shifts of the ion crystal within a stabilizing `rotating wall' perturbation. We observe power-law energy distributions and log-normal distributions of the waiting times of successive events. These properties are also seen with earthquakes, and with soft \gamma-ray events believed to be caused by `starquakes' of the magnetized ion crystals which comprise the outer crusts of neutron stars. Simulations of the system are being run, and slips and dislocations similar to those seen in the experiment have been observed. They appear to originate from thermal fluctuations, and consist of rearrangements of small number of ions which produce large changes in the elastic forces within the crystal. Details of the observations and simulations will be presented, and their relation to self-organized criticality theories will be discussed.

[S5.024] Laser Induced Wakes in a Rotating Ion Crystal

We trap approximately 30,000 Be^+ ions in a Penning trap and utilize laser cooling to reduce the ion temperature to less than 10 mK. In this regime, the ions form spheroidal Coulomb crystals, which we vary in shape from lenticular (pancake-shaped) with a radius of R \approx 2 \,mm to near spherical with R \approx 0.3 \, mm. These crystals rotate about a central z-axis due to the trapping fields in a Penning trap at a rate of f_Rot \sim 100 \, kHz. With a relatively narrow waist beam (w \approx 50 \, \mum) directed parallel to but 0.2 \,mm to 0.4 \, mm from the rotation axis, we use laser radiation pressure to push on the rotating crystals. The ``push" beam excites a multitude of axial modes which interfere to produce a wake pattern that is stationary in the lab frame. Doppler shifts due to ion oscillations cause spatial variations in the intensity of the cooling beam fluorescence; this enables us to obtain velocity images of the wakes. Both the observed wake patterns and a dispersion relation for the excited modes are accurately described by new analytical calculations of drumhead modes in a rotating crystal slab.

[S5.025] Optical trapping of photoassociated cold cesium molecules

The number of Cs_2 molecules trapped at the focus of a CO_2 laser (\lambda = 10.6 \mu m) [1] has been enhanced by using an additional laser tuned to a "giant" photoassociation line. These features were first observed at Orsay [2]. The one utilized here is located 2.136 cm^-1 below the atomic 6S_1/2(F=4) to 6P_3/2(F=5) transition. It corresponds to long-range excitation of ground state atoms to the outer well of the 0_g^-(6S_1/2 + 6P_3/2) potential followed by quantum tunneling to the inner well. The subsequent spontaneous emission is very efficient due to strong Franck-Condon overlap with the ^3\Sigma _g^+ (6S_1/2 + 6S_1/2) ground states. [1] T. Takekoshi, B.M. Patterson, and R.J. Knize, PRL 81, 5105 (1998). [2] M. Vatasescu, O. Dulieu, C. Amiot, D. Comparat, C. Drag, B. Kokoouline, F. Masnou-Seeuws, and P. Pillet, PRA 61, 044701 (2000).

[S5.026] On the efficiency of Counting 81Kr Atoms with ATTA

Atom Trap Trace Analysis (ATTA) has been used to count the rare 81Kr atoms in atmospheric krypton samples with a counting efficiency of about 2 x 10-7. Practical applications of this new technique, such as dating ancient groundwater or polar ice, demand that the efficiency should reach 10-4 or higher. We have made some improvements in order to increase the total efficiency of the system. A new metastable krypton source using a RF-driven discharge has been developed. A gas recirculation system has also been implemented, which can recycle the gas from the intermediate chamber and trap chamber back to the source chamber [2]. In addition, cryogenic cooling will be applied in the source region to cool down the atoms before they enter the Zeeman slower. Details of these improvements and changes will be discussed at this poster. This work is supported by the U.S. Department of Energy (Contract W-31-109-ENG-38). [1] C. Y. Chen et al., Science 286, 1139 (1999); [2] C. Y. Chen et al., Rev. Sci. Instr. 72, 271 (2001) [3] URL: http://www-mep.phy.anl.gov/atta/

[S5.027] Evolution of Zeeman coherences in the presence of magnetic fields

We have studied the decay of a spatially periodic coherence (grating) established between adjacent magnetic sublevels of the 5S_1/2 F=3 ground state in Doppler broadened ^85Rb vapor. The coherence is established by two simultaneous, orthogonally polarized Laser pulses incident on the sample at a small angle (a few mrad). The pulses are tuned to the F=3\rightarrowF=4^\prime resonance. The decay of the coherence (due to thermal motion) can be rephased using a second excitation pulse that has the same field configuration as the pulse that initially established the coherence. The rephasing can be observed on a time scale determined primarily by the transit time of atoms across the Laser beam. We have studied the decay and rephasing of the coherence in the presence of uniform magnetic fields. We discuss how this experiment can be used to make a precision measurement of the Zeeman shift in a sample of Laser cooled atoms.

[S5.028] Recent Results on Atom Trap Trace Analysis of 41Ca

41Ca has a half-life of 1.03X10^5 years and a natural isotopic abundance at the level of 10^-15. Trace analysis of 41Ca has promising applications in dating ancient bones and in the research of osteoporosis [1].We are developing an Atom Trap Trace Analysis (ATTA) system in order to count 41Ca atoms in natural samples [2] . Our system consists of a well-collimated oven, a 40 cm - long Zeeman slower and a MOT chamber. Trapping of all stable calcium isotopes has been demonstrated. For the most abundant isotope 40Ca, a loading rate of 1.2X10^10 atoms/s has been reached at the overall capture efficiency of 1X10^-4. The latest results will be reported at this poster. This work is supported by the U.S. Department of Energy (Contract W-31-109-ENG-38). 1. See our web page: http://www-mep.phy.anl.gov/atta/ 2. C.Y. Chen et al. Science 286, 1139 (1999).

[S5.029] Destabilization of Dark States, Optical Spectroscopy and Laser Cooling in Zeeman Degenerate Atomic Systems

When the sub-levels of an atomic ground state are degenerate, many optically driven atoms can optically pump into a dark state. Because such dark states are not coupled to the excited state, the atoms cannot be optically detected or cooled by laser radiation. Often a magnetic field can be applied to the atom to remove the degeneracy of its ground states. When the magnetic field must be negligible, other methods include separately detuning different polarization components of the laser field, and modulating the amplitudes of the laser field polarization components. These methods can restore atomic fluorescence but may result in an optical resonance that is much broader than what would be expected from the decay rate of the excited state, decreasing the efficiency of Doppler cooling. We discuss the adverse effects of dark states on laser driven optical resonances in real atomic systems, and outline general methods of destabilizing dark states to reduce these effects. We give detailed examples of the effectiveness of each of these methods in some commonly used atomic systems, and illustrate the results on the shapes on the optical resonance curves.

[S5.030] Progress Toward a Higher Density Spin-Polarized MOT

We have previously demonstrated a modified tetrahedral Magneto-Optical Trap (MOT) in which the atomic sample has a high degree of spin-polarization.(P. Feng and T. Walker, Bull. Am. Phys. Soc. 41), 1111 (1996) In this trap, the atoms absorb a plurality of photons with a particular angular momentum, leading to optical pumping of the ensemble. We are directing our present efforts to increasing the density of this spin-polarized tetrahedral MOT.

[S5.031] Trapped Atomic Fermi Gas

A many-body system of fermion atoms with a model interaction characterized by the scattering length a is considered. We treat both a and the density \rho as parameters assuming that the system can be created artificially in a trap. If a is negative the system becomes strongly correlated at densities \rho \sim |a|^-3, provided the scattering length is the dominant parameter of the problem. It means that we consider |a| to be much bigger then the radius of the interaction or any other relevant parameter of the system. The point \rho _c1 at which the compressibility vanishes is defined by \rho _c1\sim |a|^-3, while the radius of the effective inter-atom interaction, being formed by many-body correlations, tends to infinity. Thus, a system composed of fermion atoms with the scattering length a\rightarrow -\infty is completely unstable at low densities, inevitably collapsing until the repulsive core stops the density growth. As a result, any Fermi system possesses an equilibrium density and energy if the bare particle-particle interaction is sufficiently strong to make a negative and to be the dominant parameter. This behavior can be visualized in a trap. The results can be important also for studies of neutron matter.

[S5.032] Trapped Atoms as a Cold Target for Recoil Ions Momentum Spectroscopy

X. FLECHARD, H. NGUYEN, J. GU, E. WELLS, C.L. COCKE, and B.D. DePAOLA. J.R. Macdonald Laboratory, Department of Physics, Kansas State University, Manhattan, KS 66506-2604. - We have developed a Magneto-Optical-Trap apparatus to prepare a cold Rubidium target for atomic collisions. The cold and localized target is an ideal extension to the well-established COLTRIMS technique because the low temperature of the trapped atoms should yield increased resolution compared to the traditional supersonic gas jet. In addition, while alkalis cannot easily be used as cold gas jet targets, they are ideal for trapping in MOTs. Our initial system under study is low energy (1-5 keV) charge transfer collisions between singly charged alkali ions and trapped rubidium atoms. By employing a longitudinal extraction, we anticipate especially high-resolution measurements of the longitudinal (along the projectile beam) recoil momentum, which directly yield Q values for the collisions. * Supported by the Division of Chemical Sciences, Geosciences and Biosciences Divisions, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy.

[S5.033] Spatial Heterodyne Imaging of a Holographic Atom Trap (HAT)

We demonstrate the trapping of cold Rubidium atoms in a Holographic atom trap (HAT). Four diffracted beams are created as a 15-Watt 1.06 \mum laser beam passes through a holographic phase plate. The phase plate is imaged at the center of a dark-spot MOT, and the interference of these four off-resonant beams creates an optical lattice. The lattice contains approximately 500 potential wells each of volume of 10 \mum x 10 \mum x 100 \mum . Images of the HAT were taken using the method of Spatial Heterodyne Imaging(S. Kadlecek, J. Sebby, R. Newell, T. G. Walker, "Non-destructive spatial heterodyne imaging of cold atoms", Opt. Lett. 26, 137, 2001.). This technique is well suited to experiments which are sensitive to heating and optical pumping from absorbed photons, such as Bose-Einstein condensation, magnetic trapping, and far-off resonant trapping. The images are generated by interfering a weak, near resonant probe beam passed through the HAT with a strong reference beam. The resulting fringe pattern is detected by a CCD camera and, after demodulation in software using standard Fourier techniques, gives directly the phase shift caused by the atom cloud. This technique permits direct measurements of the temperature and number of atoms held in the HAT. This work is funded by the National Science Foundation.

[S5.034] Simultaneously Forbidden Resonances and Ion Cooling

Recently, an ion cooling scheme was proposed (Morigi, J. Eschnerand C. Keitel, Phys. Rev. Lett. 85), 4458 (2000) and experimentally demonstrated (C.F. Roos, et al., Phys. Rev. Lett. 85), 5547 (2000). This technique is based on the concept of simultaneously forbidden resonances (V.N. Smelyanskiy, R.S. Conti, and G.W. Ford, Phys. Rev. A 55), 2186 (1997) combined with electromagnetically induced transparency. Possible improvements and extensions will be discussed.

[S5.035] An Ultra-Low Density Magneto-Optical Trap for Cr

Recent reports of successful magneto-optical trapping of Cr have suggested that Cr may be suitable for some proposed applications such as quantum information processing. Because the magnetic moment of Cr is six times that of the alkalis, tight, purely magnetic confinement of Cr atoms is possible using relatively small fields even in the absence of sub-Doppler cooling. Here we describe an apparatus designed to detect single atom fluorescence of an ultra-low density Cr MOT. Ultimately, this could serve as a deterministic source of atoms to load an array of magnetic traps defined by lithographically deposited charge and/or current carrying microstructures on a surface. Such a system would be a crucial component of proposed architectures for quantum information processing.

[S5.036] Cooling and Trapping: Bose-Einstein Condensation

[S5.037] Trends in Resonance Energy Shifts and Decay Rates for Bose Condensates in a Harmonic Trap

Perturbation theory is used to derive an implicit equation for the width, \gamma, of excitations of BEC in a harmonic trap. Landau and Beliaev decay processes(K.Das and T.Bergeman, submitted to PRA)^,(L. P. Pitaevskii and S. Stringari, Phys. Lett. A 235),398 are contrasted with radiative decay as modeled by Weisskopf-Wigner theory. We compute \gamma numerically for a spherically symmetric trap to obtain trends as a function of temperature(T), energy(E), particle number(N) and scattering length(a). In particular, we find that the Landau width rises rapidly for low E and then declines, while the Beliaev width rises slowly with E. As T\rightarrow 0, the Beliaev width reaches a constant >0, but the Landau width \rightarrow 0. The total width is approximately linear in a. The widths are often sufficiently smaller than the energy intervals to justify a discrete quasi-particle representation.

[S5.038] Bose Condensates in Large Aspect Ratio Harmonic Traps

In view of ongoing work in several laboratories on quasi--one-dimensional traps, we have extended previous work on Bose condensates in spherically symmetric(T. Bergeman, D. Feder, N. Balazs and B. Schneider, Phys. Rev. A 61), 063605 (2000).(K. Das and T. Bergeman, submitted to Phys. Rev. A.) to oblate traps with high aspect ratios. For \gamma=ømega_\rho/ømega_z = 1000, for example, we find that the Thomas-Fermi approximation worsens as atom number, N, decreases from infinity relative to spherical traps because kinetic energy effects for motion in the z are less negligible. Also for zero temperature and \gamma=1000, we find that for a_s, the s-wave scattering length <0, the maximum value N_c|a_s|/a_0, where N_c is the number of condensate atoms, a_0^2 = \hbar/M ømega and ømega^3 = =ømega_|rho^2 ømega_z, is less than half the critical value for a spherically symmetric trap. Excitation frequencies and damping rates will be presented indicating the possibility of experimentally resolving longitudinal excitations.

[S5.039] Hybrid Variational Solutions of the Gross--Pitaevskii Equation

When a Bose--Einstein condensate is exposed to pulsed laser light the potential experienced by the condensate atoms exhibits a rapid spatial variation. In such cases this rapid variation occurs along a single direction. Solving the Gross--Pitaevskii (GP) equation for such cases presents a challenging numerical task because of the fine mesh required to represent the solution along the fast direction. We describe a novel hybrid Lagrangian Variational Method for obtaining approximate dynamical solutions of the GP equation when its solutions exhibit fast spatial oscillations along a single direction and which vary much more slowly transverse to this direction. The trial wavefunction used in this variational approach assumes no specific form for the solution along the fast direction and assumes gaussian behavior for the other two directions. The gaussian part of the trial wavefunction has time--dependent widths and phases. The result is a system of ordinary differential equations in time for the width and phase parameters that describe the transverse behavior coupled to a pseudo--1D GP--like equation for the fast direction. We have compared the results of this method with the results for a three--dimensional GP solver by studying the effects of various laser pulses on the BEC wavefunction.

[S5.040] Three particles in a trap: What can we learn from tiny Bose-Einstein condensates?

For three particles in a spherical trap, the center-of-mass motion can be separated out, and the original 9-dimensional Schrödinger equation reduces to six dimensions. Restriction to total angular momentum states J=0 then leads to a three-dimensional problem. Here, we report on full quantum calculations of three bosons with J=0 in a spherical trap using a wide range of interaction parameters and trapping frequencies. Hyperspherical coordinates are well suited to describe this complicated system, which shows two different length scales, a ``molecular length scale'' (~ 10a.u.) and a ``BEC length scale'' (>1000a.u.). We present results for the Bose-condensed ground state energies and frequencies for condensates with positive and negative scattering length, and compare these with the mean-field Gross-Pitaevskii energy and mean-field RPA frequencies. Specifically, we focuss on the behavior of condensates with negative scattering length. Whether such condensates are stable or not depends on the magnitude of the scattering length and the frequency of the trapping potential. Finally, we compare the behavior of three particles in a trap, which interact via a sum of two-body model potentials with identical s-wave scattering length, but different number of two-body s-wave bound states.

This work was supported in part by NSF. DB acknowledges support through a DFG Postdoktorandenstipendium.

[S5.041] Progress towards a temporal decoherence measurement using a two-component Bose-Einstein condensate

We report the creation of a Bose-Einstein condensate in 87Rb using a new system, which implements a novel mechanical technique for transferring atoms from the vapor cell to the UHV cell. We shall also describe progress towards a measurement of the temporal decoherence of the relative phase between two condensates. The temporal decoherence will be examined as a function of the temperature of the thermal cloud and the condensate number.

[S5.042] Simulations of a Simplified Ioffe Trap for Realizing Bose-Einstein Condensation

We present numerical simulations of the magnetic field due to a simplified Ioffe-Pritchard trap that has recently been used to obtain Bose-Einstein condensation using Laser cooling techniques. This trap converts a quadrupole field into an Ioffe configuration using a conical solenoid placed orthogonally to the axis of symmetry of a pair of quadrupole coils. In particular, we describe the details of 1-D and 2-D simulations used to calculate the magnetic field for this arrangement and point out the advantages of this configuration of magnetic field coils. We compare the results with the magnetic field obtained when the conical solenoid is replaced by a finite cylindrical solenoid. We also examine the re-scaling of the coil parameters to accommodate larger diameter trapping beams. Finally, we consider how an experiment based on these simulations can be realized.

[S5.043] Quasiparticle Excitations of a Two-Component Bose-Einstein Condensate

We consider a two-component, homogenous, Bose-Einstein condensate in the presence of an external radiation field which couples the two components. We examine the effect of the external field on the ground state and excitations of the condensate. When the energy splitting between the dressed states of the atom+field is much larger than the mean-field interaction energy in the condensate, the excitations have the same form as a condensate in the absence of a coupling field, but with an effective scattering length that depends on the dressed state angle associated with the atom+field system. We also consider the opposite limit when the interaction energy between the atom and field is comparable to the mean-field interaction energy and show that this leads to new minima in the ground state energy density. The excitation spectrum about these minima is discussed.

[S5.044] Progress Towards a Rb-87 Bose-Einstein Condensate with Tunable Interactions

We report on the design and construction of an apparatus with which we will create a Rb-87 Bose-Einstein condensate with Feshbach resonance-tuned interatomic interactions. The condensate will be confined by an optical trap in a spatially uniform and adjustable magnetic field. Operation over a wide range of atomic densities will enable us to explore inelastic collision rate dependences and the possible existence of exotic coherent loss mechanisms peculiar to the condensate in the vicinity of a resonance.

[S5.045] Quantum and semiclassical analysis of long-range Rydberg molecules

A recent study predicts the possibility of creating highly polar long-range Rydberg molecules under temperature and density conditions characteristic of a Bose-Einstein condensate. The electronic wavefunctions of such Rydberg molecules have an elliptically shaped nodal pattern and an oscillatory Born-Oppenheimer potential curve. We employ quantum and semiclassical methods to examine the origin of these structural features.

[S5.046] Aspects of Superfluidity in a Bose-Einstein Condensate

We have examined the superfluid properties of a Bose-Einstein condensate using optical dipole forces. By manipulating the condensate with far off-resonant light we can study its behavior under the influence of both static and dynamic potentials.

[S5.047] Slow light propagation in trapped quantum gases

We study semi-classical slow light propagation in trapped two and three level atomic quantum gases. The temperature dependent behavior of group velocities and transmissions for Bose, Fermi, and Boltzman gases are compared using the local density approximation for their density profiles. The role of non-uniform spatial density of an interacting condensate is shown to be critical in obtaining quantitative agreement with the experimental data(L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397), 594 (1999)..

[S5.048] Bose Einstein Condensation and wave-guide Interferometry

We are developing a new BEC apparatus to demonstrate a wave-guide interferometer. In our design, the atoms will be first collected into the MOT with a pyramidal mirror, and then loaded into a Quadrapole Trap(QT). After that they will be transferred into the higher vacuum region by moving the QT- coil. Then we will switch on the Ioffe-Pritchard Trap and do the evaporative cooling to get the BEC. After making the BEC we will to put the atoms into magnetic wave-guides to do intermerometry experiments. The magnetic fields will be generated by lithographically-patterned current-carrying wires which confines weak field seeking atoms strongly in two dimensions. The current status will be presented.

[S5.049] Ground-State Solutions for Charged Bosons and for Bosons Interacting with Yukawa Force Confined in a Harmonic Trap

A generalization of the Thomas-Fermi method has been developed for obtaining an analytical expression for the ground-state solution for N interacting bosons confined in a harmonic trap, in the limit of large N. The method is used to obtain ground-state solutions for charged bosons confined in a harmonic trap interacting via the Coulomb force, via both the Coulomb and contact forces, and also for bosons interacting via the Yukawa force.

[S5.050] Excitations of a Two-Component Degenerate Fermi Gas

We report the observation of interaction-dependent frequency shifts in excitations of a two-component Fermi atomic gas. Oscillations of the magnetically confined gas are excited by a time-dependent change in the trapping potential. For a single-component, non-interacting Fermi gas, these oscillations do not damp, and their frequencies depend only on the trapping potential. Trapping Fermionic ^40K atoms in two different spin states, however, allows s-wave collisions between the atoms, which influence the excitations. We have observed that a two-component Fermi gas has excitation modes which are shifted in frequency from the modes of each component alone. We also observe the damping of these oscillations due to collisions.

[S5.051] Bosons in cigar-shape traps: mean-field regime, Tonks regime, and between

We present a quantitative analysis of the experimental accessibility of the Tonks gas in the current day experiments with cigar-trapped alkali(D. S. Weiss, private communication). For this purpose we derive, using a Bethe anzats generated local equation of state, a set of hydrostatic equations describing a one-dimensional \delta-interacting Bose gas trapped in a harmonic potential. Resulting solutions cover the entire range of atomic densities and are exact in the thermodynamic limit.

[S5.052] Quantum limitations on atom-molecule oscillations in a Bose-Einstein condensate

We study the system of coupled atomic and molecular condensates within the two-mode 'second-harmonic generation' model and beyond mean-field theory (MFT). Strict limitations on the atom-molecule Rabi-Oscillations predicted by MFT, are imposed by rapidly growing quantum corrections in the vicinity of the dynamically unstable molecular mode. The frequency of the damped oscillation is shown to scale as Ømega\sqrtN\logN (Ømega being the coupling strength between the modes) rather than the expected Bose-enhanced frequency \sqrtNØmega.

[S5.053] Collective excitations of a dipolar atomic condensate

Several methods are employed to study the low lying shape oscillations of a trapped dipolar atomic condensate. We find that the inherent dipole interaction due to the valance electronic spin magnetic dipole moment causes shifts to shape oscillation frequencies. These shifts can become detectable even for a condensate containing several thousand atoms, provided the usual s-wave scattering length can be tuned to zero using the Feshbach resonance(J. L. Roberts, N. R. Claussen, S. L. Cornish, and C. E. Wieman, Phys. Rev. Lett. 85), 728 (2000)..

[S5.054] Two cold atoms in a trap and the D-dimensional pseudopotential

We introduce the exact (regularized) s-wave pseudopotential in D dimensions. We apply dimensional perturbation theory to two trapped atoms, and in order to estimate the efficacy of this method when extended to a Bose condensate of N atoms, we compare our analytical approximation with exact pseudopotential energies(T. Busch, B-G. Englert, K. Rzazewski and M. Wilkens, Found. of Phys. 28), 549 (1998). and with energies obtained using a detailed ^87Rb-^87Rb ^3\Sigma_u two-body potential(E. Tiesinga, C. J. Williams, F. H. Mies and P. S. Julienne, Phys. Rev. A 61), 63416 (2000).. We also compare this detailed microscopic potential with energies obtained using other shape dependent models, as well as with the Gross-Pitaevskii (GP) and the modified (GP) energies.

[S5.055] Bose-Einstein condensation in D-dimensions

We introduce dimensional perturbation techniques to Bose-Einstein condensation of inhomogeneous alkali gases. The perturbation parameter is 1/\kappa, where \kappa =3D D + 2 l, D is the effective dimensionality of the condensate and l is the angular momentum quantum number. We present a dimensional scaling of the Gross-Pitaevskii equation, and using the large-D limit, we derive a simple approximation that is more accurate and flexible than the N \rightarrow \infty Thomas-Fermi approximation for the ground state. The accuracy of the large-D approximation of the ground-state chemical potential is comparable to corrections to TF due to the boundary layer at the condensate surface. The approximation presented here is well-suited for calculating properties of states in low effective dimensionality, including vortices.

[S5.056] Cooling and Trapping: Ultra-cold Collisions

[S5.057] Calculations of Two-Body Scattering in the Presence of Tight Cylindrical Confinement

In recent experiments(D. S. Weiss, private communication), Cs atoms in the (F,m) = (3,3) state have been confined in a two-dimensional optical lattice. The characteristic transverse size a_\perp of each quasi-one-dimensional well is about 30 nm, as compared with the zero-field s-wave scattering length, a_sc, found to be negative and >140 nm in magnitude(P. Leo, C. Williams, P. Julienne, Phys. Rev. Lett. 85), 2721 (2000).. We test the validity of the zero-range potential approximation by comparing numerical results with analytic expressions in (M. Olshanii, Phys. Rev. Lett. 81), 938 (1998).. The atom-atom interaction is taken as a 6-12 potential with the Cs-Cs c6, and a variable c12 coefficient to produce varying a_sc. We find that even for a_\perp \ll a_sc, the zero-range model agrees well with the numerical results. In particular we reproduce the predicted confinement-induced resonance, which leads to the change of sign of the coupling parameter at a_\perp \approx 1.46 a_sc.

[S5.058] Classical and Quantal Collisional Stark Mixing

The Quantal-Classical correspondence, beyond the common Ehrenfest's Theorem, is investigated (D. Vrinceanu and M. R. Flannery, Phys. Rev. A 63) 032701 (2001) in connection with the underlying dynamical group symmetry. As a case study, the long standing problem of Collisional Stark Mixing is fully solved, both in classical and quantal formulations. Indeed, the rich algebraic structure of the hydrogen atom is demonstrated to be the foundation for the remarkable agreement. Exact analytical expressions for the classical dynamics of the Rydberg atom under the influence of the electric field of the incoming projectile at very large impact parameters, is provided. A novel approach for calculating the Classical Transition Probability, as a ratio of volumes in the phase space, is proposed. The Quantal Transition Probability is given by a compact formula in terms of simple functions. Using this exact expression, numerical results can be efficiently and accurately obtained, even for very large quantum numbers, n\approx 100. Both Classical and Quantal cross sections for the Stark Mixing process are in good agreement with the experimental data. \vskip0.1in Research Supported by NSF and AFOSR.

[S5.059] Cooling and Trapping Molecular Super Rotors

Collisional relaxation of highly rotating hydrogen molecules is investigated as a function of energy. Calculations demonstrate that inelastic collisions are dramatically suppressed for specific rotational levels of the molecule as the energy is lowered due to the closing of quasiresonant rotation-vibration channels. It is predicted that a ^3He buffer gas may be used to load these highly excited molecules into a trap without a significant loss of population. It is further predicted that evaporative cooling may be used to cool the ``super rotors" to even lower temperatures.

[S5.060] Inelastic Collisions of Ultracold Polar Molecules

The collisional stability of ultracold polar molecules in electrostatic traps is considered. Rate constants for collisions that drive molecules from weak-electric-field-seeking to strong-field-seeking states are estimated using a simple model that emphasizes long-range dipolar forces. The rate constants for collisional losses are found to vary substantially as a function of molecular parameters used in the model, such as dipole moment, mass, and the splitting of the molecular \Lambda-doublet. Varying these parameters over physically reasonable ranges yields rate constants as low as 10^-20 cm^3/sec and as high as 10^-10 cm^3/sec. Nevertheless, the loss rates rise dramatically in the presence of the externally applied trapping electric field. For this reason it is argued that electrostatic traps are likely to be less stable against collisional losses than their magnetic counterparts.

[S5.061] Cold atomic collisions in confined geometries

We study elastic collisions between ultracold atoms in geometries of reduced dimensionality. For s-wave scattering between identical bosons, our numerical calculation for a three-dimensional harmonic trap shows that a pseudopotential model is insufficient to compute the trap eigenenergies when the scattering length magnitude is larger than the smallest quantum-mechanical trap width. We examine generalizations of the delta-function pseudopotential approximation that can predict trap energies and scattering rates in systems of reduced dimensionality.

[S5.062] Calculations on threshold collisions of cold Cs atoms

We use our accurate model of cold Cs collisions [1] to calculate the collisional shift in clock frequency due to ground state collisions. The shift depends strongly on temperature below around 1 microkelvin and goes through a zero and changes sign with decreasing temperature. Our calculations are consistent with observed clock shifts above 2 microkelvin. We also calculate the shapes of narrow resonance features in threshold s-wave scattering due to Feshbach resonance states of g-wave symmetry. Comparison of our calculations with measurements by the Stanford group [2] allows us to make an independent verification that the van der Waals C_6 coefficient and scattering lengths previously determined by us [1] are correct within stated uncertainties. We also determine the C_8 coefficient to be 8.6(0.8) x 10^5 atomic units.

Supported in part by the Office of Naval Research.

[1] P. Leo, et al., Phys. Rev. Lett. 85, 2721 (2000).

[2] C. Chin, A. J. Kerman, V. Vuletic, and S. Chu, private communication, 2001.

[S5.063] Optical trapping of ultracold dimers produced via photoassociation

The number of molecules trapped in an optical dipole trap [1] (\lambda = 10.6 \mu m) has been enhanced by using a photoassociation laser detuned to a "giant" photoassociation line. Two such features were first observed in a MOT by the Orsay group [2]. They are a result of tunneling into the interior well of the 0_g^- (6S_1/2 + 6P_3/2) molecular potential, followed by efficient spontaneous decay to the triplet Cs_2 ground state. The one we used is located 2.136 cm^-1 below the atomic Cs F=4 to F=5 transition.

[1] T. Takekoshi, B.M. Patterson, and R.J. Knize, PRL 81, 5105 (1998).

[2] M. Vatasescu, O. Dulieu, C. Amiot, D. Comparat, C. Drag, V. Kokoouline, F. Masnou-Seews, and P. Pillet, PRA 61, 044701 (2000).

[S5.064] Angular characteristics of the most loosely bound diatomic molecular state

We show that the angular property of the most loosely bound molecular state is neither accidental nor arbitrary, but depends on the long range interaction between the two atoms. For a diatomic system with a -C_n/r^n asymptotic interaction with n being an integer and greater than 2, the angular momentum of the most loosely bound state can only be one of the l=0, 1,\dots,n-3. It means, for instance, that for a diatomic molecule with an asymptotic -C_3/r^3 interaction, the most loosely bound state has to be an s state. For a diatomic molecule with a -C_6/r^6 interaction, the most loosely bound state can only be one of the four types, s, p, d, or f. We further show that for a diatomic system with a -C_6/r^6 interaction and a negative scattering length, the most loosely bound state must be either an f state, if allowed by symmetry, or a d state otherwise.

[S5.065] Three-Body Recombination of Cold Atoms

In the present work, we shall study three-body recombination of cold helium atoms: \mathrm^4He+^4He+^4He\rightarrow^4He_2+^4He. This study extends previous work (B.D. Esry et al., Phys. Rev. Lett., 83;1751 (1999)) where \textitultra-cold alkali atoms were treated. An extra difficulty comes from the fact that not only zero total angular momentum J=0 states, but also J>0 states should be taken into account because of their higher binding energy. We will use a modified version of Smith-Whitten hyperspherical coordinates (B.K. Kendrick et al., J. Chem. Phys., 110;6673(1999)). Using these coordinates, one can easily introduce the symmetrization effects for three identical bosons, so that the configuration space can be reduced by a factor of 3. Coupled equations in an adiabatic hyperspherical representation are then solved using the variational R-matrix method. The interaction used is a sum of helium dimer potentials from A.R. Janzen and R.A. Aziz (A.R. Janzen and R.A. Aziz, J. Chem. Phys., 103;9626 (1995)). Our goal is to calculate the ''event rate constant'' K_3=\frac\hbar k\mu\sigma or the ''recombination length'' \rho_3=(\mu K_3/\hbar)^1/4, where \sigma is the cross section for three-body recombination, \mu is the three-body reduced mass.

[S5.066] Ultracold collisions of oxygen molecules

Collision cross sections and rate constants between two oxygen molecules are investigated and computed at translational energies below \sim 1K. We present calculations for elastic and spin- changing inelastic collision rates for different isotopic combinations of oxygen atoms as a prelude to understanding their collisional stability in ultracold magnetic traps. A numerical analysis has been made in the framework of a rigid- rotor model based on the (O_2(^3\Sigma_g^-) - O_2(^3\Sigma_g^- )) potential energy surfaces of (B. Bussery, P.E.S. Wormer, J.Chem.Phys, 99)(2), 1230 (1993).. We extract spin exchange rates by accounting fully for the singlet, triplet, and quintet surfaces in this system. The results offers insights into the effectiveness of evaporative cooling and the properties of molecular Bose- Einstein condensates, as well as estimates of collisional lifetimes in magnetic traps.

This work is sponsored by the National Science Foundation.

[S5.067] Studies with Utracold Metastable Hydrogen

Recoil-free two-photon excitation of the 1S-2S transition is used to excite metastable (2S) hydrogen atoms from samples of magnetically trapped atomic hydrogen. The metastable atoms are also trapped, resulting in partial densities of more than 10^9 cm^-3. The metastable population has been observed to have lifetimes up to 90 ms in our trap, close to the 122 ms natural lifetime of the 2S state. We have measured the 2S decay behavior for temperatures ranging from more than 40 mK to less than 100 \muK and for ground state (1S) densities up to 10^14 cm^-3. We report rate estimates for collisional loss channels.

[S5.068] Cooling and Trapping: Applications to Fundamental Measurements

[S5.069] The sound of silence: sonic black holes in Bose-Einstein condensates

Sound waves in a moving fluid propagate in exact analogy to light waves in a curved spacetime. As suggested nearly twenty years ago by Unruh, a sonic analogue of an event horizon would allow a laboratory test of Hawking's famous theory that quantum effects cause black holes to radiate thermally. We show that with today's dilute Bose-Einstein condensates this proposal can finally be realized. And we discuss the resolution, within this analogue model, of the notorious information paradox of black hole thermodynamics.

[S5.070] Polarizing radioactive atoms from a MOT for \beta-decay studies

We have achieved \geq 90% nuclear polarization of ^41K by trapping ^41K atoms in a weak B field environment using a time-cycled MOT, and optically pumping with an additional circular polarized D_1 laser beam. The circular polarized D_1 beam (S_1/2 to P_1/2 transition), can in principle optically pump the atoms to the maximum angular momentum F =2, M_F = 2 state, where both nucleus and atomic angular momentum are fully polarized. The non-zero B field condition is realized by attenuating the retroreflected beams of the MOT in the horizontal plane, so the trapped atom cloud's equilibrium position is moved to finite B field. Then an additional uniform B field is applied along the axis to move the atoms back to the original MOT center. The polarizing process is to turn MOT beams and D_1 beam on and off alternatively; the D_1 fluorescence is monitored to measure the polarization while the MOT is off. We have also applied this technique to polarize radioactive ^37K, which has almost identical hyperfine structure, to study its nuclear \beta decays. *Supported by NSERC and CIPI.

[S5.071] Initial Developments Towards Polarizing Trapped ^37K for Charged Weak Interaction Studies

We have polarized radioactive \beta-decaying ^37K atoms using laser trapping and cooling techniques. The atoms are initially trapped in a MOT; to polarize them, we turn the MOT beams off and apply circularly polarized D1 light in an alternating 1 msec MOT\rightleftharpoonsD1 cycle. To the extent that the \sigma^\pm D1 light optically pumps the atoms to the |F,M_F\!=\!\pm F\rangle fully stretched state, complete atomic \emphand nuclear polarization can potentially be achieved. The nuclear polarization was probed in a test run by measuring the asymmetry of the emitted positron, the recoiling nucleus, and coincidences between them. These results will help guide the development of \beta-decay experiments which will test if parity violation in charged weak interactions is truly maximal, and if time-reversal is a good symmetry. *Supported by NSERC and CIPI.

[S5.072] Other DAMOP Topics: Experimental Techniques

[S5.073] Optical production of metastable rare gases.

Metastable rare gas atoms have numerous applications in fields such as medical imaging, tests of fundamental symmetries and rare isotope detection. We have demonstrated a new method for efficient production of metastable Kr atoms (5s J=2 level) which can be readily extended to other rare gases. In the scheme, an ultraviolet lamp is used to create a population of Kr atoms in 5s J=1 level in a gas cell. The excited atoms are then pumped to one of the 5p levels using 819-nm light from a Ti-Sapphire laser. This level decays to the metastable state with a branching ratio of 77%. We will report on current results and work aimed at increasing the rate of excitation of metastable Kr atoms by making improvements to the apparatus geometry and by switching from production of metastable atoms in a gas cell to production in an atomic beam. The scheme will then be applied to the ATTA project where we estimate that it could result in a gain of 10^2 to 10^3 in metastable excitation efficiency.

[S5.074] A high speed amplitude modulated retroreflector for Lasers

We have used an acousto-optic modulator (AOM) to impose an amplitude modulation on an incident Laser beam. The amplitude modulated beam can be sent back through the AOM so that it returns along the direction of the incident beam. However, the return beam is frequency shifted and orthogonally polarized with respect to the incident beam. This feature allows us to detect the amplitude modulated retroreflected signal with high signal to noise using heterodyne detection. Since the setup is very simple and compact, it may be ideally suited for certain forms of high-speed optical communication.

[S5.075] Optimization of high-energy short laser pulses using a genetic algorithm

We describe an experiment that is currently in progress for compression of high-energy (mJ ; 500 Hz) short laser pulses with a Spatial Light Modulator (SLM) controlled by a genetic algorithm (GA). We produce the laser pulses by coupling 50 fs pulses from a CPA into a hollow core fiber in order to obtain sufficient bandwidth for 5 fs pulses. GVD effects are significant at such broad bandwidths. From the traditional pulse compression techniques based on prisms or gratings, only second order dispersion can be removed. For higher orders, which are very important for the production of short laser pulses, these techniques are ineffective. To remedy this problem, we use the SLM to compensate for the higher orders of dispersion. Our SLM is a mask with 128 pixels whose birefringence can be controlled individually via their voltages. By putting this mask at the Fourier plane of a zero dispersion-grating stretcher, we can add or subtract phase from each spectral component. A GA executes this correction. By assuming that the energy in the laser pulses is constant, the algorithm optimizes the second harmonic generation by finding the optimum voltage settings. Because the intensity of the second harmonic signal varies inversely with the pulse duration, optimizing the second harmonic production in a thin crystal is equivalent to minimizing the pulse duration.

[S5.076] Other DAMOP Topics: Theoretical Methods

[S5.077] Self-Interaction-Free Density Functional Theoretical Study of the Electronic Structure of Quantum Dots

We present a study of the electronic structure of both spherical and vertical quantum dots by means of the DFT with optimized effective potential (OEP) and self-interaction-correction (SIC)[1]. The method eliminates the spurious self-interaction energy in the conventional DFT and the the highest occupied orbital energy of the N-electron quantum dots provides a direct measure of the electron affinity. We apply the theory to the study of the capacitive energy of N-electron quantum dots for N up to 70 [2]. The results show the instructive shell and subshell structure pattern and the electron filling pattern follows closely the Hund's rule. The calculated capacitive energy spectrum is in good agreement with recent experimental results, providing physical insights regarding the origin of electron shells and the role of electron-electron interaction in quantum dots [2]. [1] X.M. Tong and S.I. Chu, Phys. Rev. A55 (1997) 3406. [2] T.F. Jiang, X.M. Tong, and S.I. Chu, Phys. Rev. B63 (2001) 045317.

[S5.078] ATOMIC DATA NEEDS FOR X-RAY ASTRONOMY

The X-ray band from 0.1 to 10 KeV is rich in discrete and continuum spectral features, and comprises emission and absorption K-shell spectra of carbon through nickel, L-shell spectra from neon through nickel, and M-shell spectra from iron and nickel. The high spectral resolution of current satellite missions such as the Chandra X-ray Observatory and the X-ray Multi-Mirror Mission are opening the X-ray band to scientific research in an unprecedented fashion. However, the successful interpretation of the spectra requires large amounts of atomic data, as well as detailed account of all microphysical processes that dictate X-ray spectral formation. We report on the main conclusions of the workshop on "Atomic Data Needs for X-ray Astronomy" held in December 1999 at the NASA Goddard Space Flight Center. Next, we present an update on the currently available atomic data for energy levels, wavelengths, radiative transition probabilities, electron impact excitation rates, photoionization cross sections, recombination rate coefficients, electron impact ionization rates, charge exchange rate coefficients, and fluorescence and Auger yields. Finally we evaluate the state of data collection, Web-interfaced archives such as TIPTOPBASE, and the most urgently needed data in terms of quality and completeness for the present and upcoming observational satellites.

[S5.079] TIPTOPbase: THE IRON PROJECT AND THE OPACITY PROJECT ATOMIC DATABASE

The Opacity Project, the IRON Project, and the RmaX Network (The Opacity Project Team, Vol.1,2), IOPP, Bristol (1995,1996); Hummer et al., Astron. Astrophys. 279, 298 (1993) are international computational efforts concerned with the production of high quality atomic data for astrophysical applications. Research groups from Canada, France, Germany, UK, USA and Venezuela are involved. Extensive data sets containing accurate energy levels, f-values, A-values, photoionisation cross sections, collision strengths, recombination rates, and opacitites have been computed for cosmically abundant elements using state-of-the-art atomic physics codes. Their volume, completeness and overall accuracy are presently unmatched in the field of laboratory astrophysics. Some of the data sets have been available since 1993 from a public on-line database service referred to as TOPbase (Cunto et al Astron. Astrophys. 275), L5 (1993), (\tt http://cdsweb.u-strasbg.fr/OP.html at CDS France, and \tt http://heasarc.gsfc.nasa.gov/topbase, at NSAS USA). We are currently involved in a major effort to scale the existing database services to develop a robust platform for the high-profile dissemination of atomic data to the scientific community within the next 12 months. (Partial support from the NSF and NASA is acknowledged.)

[S5.080] Bound States of One-Dimensional Helium Atom by Discretization of Space and Time

The computational theory for calculation of the solution of the time-dependent Schrödinger equation for two electrons [C.A. Weatherford, Computational Chemistry: Reviews of Current Trends, Vol. 5, ed. J. Leszczynski, World Scientific 2000] is reviewed and adapted to the case of the one-dimensional helium atom. This results in a new computational time-dependent exchange/correlation theory. A solution algorithm which discretizes space using a spectral discrete variable basis of synthetic cartesian polynomials, and discretizes time using a spectral element discrete variable basis of Chebyshev polynomials, is presented.

Supported by NSF CREST grant HRD-9707076, and by NASA grant NAG5-10148.

[S5.081] The Hyperbolic Poincare Group And The N-Body Dirac Equation

A new symmetry group is developed that extends the 10-parameter Poincaré group from Minkowski space to an expanding hyperbolic relativistic geometry. It displays an important kinematic symmetry between the hyperbolic spaces of position and relativistic velocity. In the hyperbolic domain it sustains an n-body Dirac equation that is explicitly covariant and connects smoothly with the n-body Schrödinger equation. The covariance proof extrapolates to the Minkowski flat-space limit, explaining the success of Dirac wave-functions in n-body problems and making possible new tools for calculating relativistic effects in atoms, molecules and other systems. email: ftsmith@mplvax.sri.com

[S5.082] Post-deadline Posters

[S5.083] Ferromagnetic spinor Bose condensate in ^87Rb

We predict that the spinor Bose condensate for the spin-1 boson ^87Rb has a ferromagnetic nature, based on a revised analysis of the scattering lengths. The nature of such a spinor condensate hinges critically on the sign of the difference between two relevant scattering lengths(T.-L. Ho, PRL 81 742 1998). These scattering lengths were extracted previously, and found to be very similar and to have overlapping uncertainties, thus leaving the nature of the ^87Rb spinor condensate ambiguous. The present study develops a refined uncertainty analysis, which permits us to extract an unambiguous result for the sign of the difference between the scattering lengths. The resulting spinor condensate for ^87Rb is therefore predicted to be ferromagnetic in nature, in contrast to the antiferromagnetic spinor condensate in ^23Na.

[S5.084] Threshold krypton charge-state distributions coincident with K-shell fluorescence.

The distribution of Kr^q+ ionic charge states has been measured in coincidence with K-shell photon emission as a function of incident-photon energy across the krypton 1s threshold. With this scheme, we observe changes resulting from the contrast between resonant Raman and fluorescence effects. By selecting the radiative(U. Arp, T. LeBrun, S. H. Southworth, M. A. MacDonald, and M. Jung, Phys. Rev.) A 51 3598 (1995), as opposed to the non-radiative(G. B. Armen, J. C. Levin, and I. A. Sellin, Phys. Rev.) A 53 772 (1996) channel, excitation PCI effects are suppressed. In general, the higher charge states are seen to increase in importance as the edge is traversed. We present the experimental results in detail and an interpretation of the observed trends, based on a simple model of the excitation process\footnoteÅberg and Tulkki, in Atomic Inner-Shell Physics ed. B. Crasemann, Plenum 1985 and the ensuing cascade decay.

[S5.085] An efficient diagonalization basis for the hyperspherical angular equation

The Hyperspherical Adiabatic Approach is an ab-initio procedure which allows the precise analysis of the helium-like systems by means of potential curves and non-adiabatic couplings as functions of the hyperradius R, similar to the Born-Oppenheimer approach for diatomic molecules. The precision is controllable by the number of coupled radial channels, without any adjustable parameter. With the correct introduction of the asymptotic conditions the procedure gives binding energies with errors of only few parts per million, even for highly excited states(J.J. De Groote, M. Masili, and J.E. Hornos, J. Phys. B 31), 4755 (1998).. This work presents a diagonalization basis for the hyperspherical angular equation which allows fast convergency for all values of R. Potential curves and non-adiabatic couplings are accurately determined even for the potential curves anti-crossing regions(J.J. De Groote, M. Masili and J.E. Hornos, Phys. Rev. A 62), 32508 (2000).. The resulting algorithms are numerically fast and very efficient. The procedure is applied to different L and S symmetries of the isoelectronic series of the helium atom with Z=1 to 4. Supported by FAPESP grant n^\underlineo 97/06271-1.

[S5.086] THE ROLE OF THE JAHN-TELLER EFFECT IN THE DISSOCIATIVE RECOMBINATION OF H_3^+

We demonstrate that the Jahn-Teller effect plays a vital role in generating the high rate of dissociative recombination (DR) that has been observed when a rotationally-hot H_3^+ ion collides with an electron. Previous theoretical calculations^1 that omitted the Jahn-Teller effect are known to underestimate the experimental DR cross section^2 by several orders of magnitude at energies below 1 eV. The aim of this study is to propose a new theoretical framework that not only describes the Jahn-Teller physics quantitatively, but also provides qualitative intuition for polyatomic species akin to that familiar^3 for diatomic target ions. This formulation combines an adiabatic hyperspherical description of H_3^+ vibrational dynamics^4 with a frame transformation that generalizes Jungen's quantum defect theory^5. Several complex potential curves extracted from the quantum defect calculation then represent the various DR pathways. The new calculation achieves greatly improved agreement with measurements of the cross section, although a residual discrepancy remains to be understood in detail. This work is supported by a grant from the National Science Foundation.

1. I.F.~Schneider, A.E.~Orel, A.~Suzor-Weiner, Phys. Rev. Lett. 85, 3785 (2000); A.E.~Orel, I.F.~Schneider, A.~Suzor-Weiner, Phil. Trans. R. Soc. Lond. A 358, 2445 (2000); A.E.~Orel and K.C.~Kulander, Phys. Rev. Lett. 71, 4315 (1993).

2. M.~Larsson et al, Phys. Rev. Lett. 70, 430 (1993); G.~Sundström et al, Science 263, 785 (1994); S.~Datz et al, Phys. Rev. Lett. 74, 896 (1995); D.~Strasser et al, Phys. Rev. Lett. (in press 2001).

3. T.~O'Malley, J. Chem. Phys. 150, 14 (1966).

4. B.D.~Esry, C.D.~Lin, C.H.~Greene, Phys. Rev. A 54, 394 (1996).

5. Ch.~Jungen Molecular applications of quantum defect theory, Instutute of Physics (1996).

[S5.087]

This abstract not available.

[S5.088] Dynamic Polarizability of the Helium Atom using a Variationally Stable Calculation within the Coupled Adiabatic Hyperspherical Approach^*

Using a generalization(M. Masili and A. F. Starace, Phys. Rev. A 62), 033403 (2000). of the variationally stable method of Gao and Starace(B. Gao and A. F. Starace, Phys. Rev. Lett. 61), 404 (1988); Phys. Rev. A 39, 4550 (1989). for two-electron atoms and ions, which incorporates a coupled-channel adiabatic hyperspherical approach, we report results for the dynamic polarizability of the helium atom for frequencies below the single photon ionization threshold. Comparison of results of coupling one, two, three, and four adiabatic hyperspherical channels within each term level of the initial and intermediate states show good convergence. Comparisons are also given with results of prior work by others.

^*Supported by FAPESP (Brazilian agency) under Process No. 99/11363-8 and by the U.S. D.O.E, B.E.S., Div. Chem. Sci. under Grant No. DE-FG03-96ER14646.

Part S of program listing