Session Z1: Hot Topics

Experimental evidence for Efimov quantum states

Three interacting particles form a system which is well known for its complex physical behavior. A landmark theoretical result in few-body quantum physics is Efimov's prediction of a universal set of weakly bound trimer states appearing for three identical bosons with a resonant two-body interaction [1]. Surprisingly, these states even exist in the absence of a corresponding two-body bound state and their precise nature is largely independent of the concrete type of the two-body interaction potential. Efimov's scenario has attracted great interest in many areas of physics; an experimental test however has not been achieved. We report the observation of an Efimov resonance in an ultracold thermal gas of cesium atoms [2]. The resonance occurs in the range of large negative two-body scattering lengths and arises from the coupling of three free atoms to an Efimov trimer. We observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied near a Feshbach resonance. We also report on a minimum in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point with which to explore the universal properties of resonantly interacting few-body systems. [1] V. Efimov, Phys. Lett. 33B, 563 (1970). [2] T. Kraemer, M. Mark, P. Waldburger, J. G. Danzl, C. Chin, B. Engeser, A. D. Lange, K. Pilch, A. Jaakkola, H.-C. N\"{a}gerl, R. Grimm, accepted for publication in Nature, cond-mat/0512394.   

Ultracold three-body collisions and their influence on ultracold quantum gases

In this talk we will discuss general properties of three-body collisions and their influence on ultracold quantum gases in the regime where the interatomic interactions are strongly affected by a Feshbach resonance. We have developed a simple and unifying picture [1] capable of predicting the energy, mass, and scattering length dependence of the three-body collision rates for all systems relevant for current experiments on ultracold quantum gases. As it turns out, this picture reveals that the scattering length dependence of the three-body rates is strongly influenced by so-called Efimov physics [2]. Efimov's original work in nuclear physics was published roughly 35 years ago, but the first experimental evidence was only recently found using ultracold quantum gases [3]. We will discuss conditions favorable for extending such experiments to enable even more definitive observations of Efimov physics. We will also discuss other processes that might be of interest experimentally such as the formation of long-lived weakly bound boson-fermion molecules. We hope that our results will help experimentalists find ways to take advantage of three-body collisions in their experiments and to encourage them to look for manifestations of few-body physics in this interesting regime. [1] J. P. D'Incao and B. D. Esry, Phys. Rev. Lett. {\bf 94}, 213201 (2005); physics/0508119. [2] V. Efimov, Phys. Lett. {\bf 33}, 563 (1970). [3] T. Kraemer, {\em et al.}, cond-mat/0512394.   

Phase Engineering of Entangled Number States (aka Schr\"{o}dinger cats) in Gaseous Bose-Einstein Condensates in ``Two," and ``Many" Wells

It has been demonstrated that a phase offset may be imprinted on ``part'' of a single ground state Bose-Einstein condensate (BEC), and that such a phase imprint can then, via the natural subsequent dynamics of the condensate, generate both solitons and vortices. A similar phase imprint on one or more wells of a coherently connected (Josephson regime) set of BECs yields, again simply from the natural time evolution of the condensate ground state following the phase imprinting, highly entangled number states, the extreme version of which would be the macroscopic N-body superposition state: $\vert $N,0,0,0{\ldots}$>+\vert $0,N,0,0{\ldots}$>+\vert $0,0,N,0{\ldots}$>+\vert $0,0,0N,{\ldots}.$>$ +{\ldots} with appropriate normalization. The notation is intended to indicate that all N particles are in all wells simultaneously. A simple physical model is introduced for the two well case allowing control of both the extremity and sharpness of the number entangled states. Less extreme states are rather more robust than the extreme superposition illustrated above. Similar results are found in systems with 3,4, and 8 wells indicating the generality of the proposed methods, although visualization of the results becomes progressively more difficult, and the computations become intractable surprisingly quickly. Extension of the Bose-Hubbard model where fully coupled GP wavefuctions are combined with exact solution of the correlation problem for the two mode system shows the importance of strong mean-field effects in the understanding and modeling of such systems. Time allowing, a discussion of ``detection'' of such states may be included. The author delightedly acknowledges collaboration with Heidi Perry, Khan Mahmud, Mary Ann Leung and David Masiello.   

Generation and Applications of Femtosecond Optical Vortices

An optical vortex is a singularity point in a (scalar) electric field where the amplitude vanishes and the phase is undetermined. Laguerre-Gaussian modes are examples of modes containing an optical vortex. Our interest in vortex modes stems from the fact that their photons possess optical orbital angular momentum (OAM).$^{2}$ Our goal is to make strong ultrashort pulses with a vortex, so we can study the influence of optical OAM on intense-field ionization. Our motivation is the role of the photon's \textit{spin} angular momentum: in its manifestation as polarization, this affects intense-field ionization. Notable are electron recollision processes, central to many schemes to generate attosecond pulses. What role optical \textit{orbital} angular momentum plays in intense-field processes is to the best of our knowledge experimentally unexplored territory. In 2005, we were the first to report the generation of a pure femtosecond vortex.$^{3}$ Our setup uses holographic diffraction and properly deals with bandwidth (tens of nm). We now use a programmable hologram.$^{4}$ We are currently increasing the intensity of our fs vortices to reach ionization levels so we can image focused vortices with our spatially-resolved ion detector. 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; $^{4}$Strohaber J \textit{et al.} 2006 \textit{J. Phys B}. subm.   

Session Z2: Gaseous Electronics Conference Session

Site Selective Bond Cleavage Upon Dissociative Electron Attachment - A Tool to Control Chemical Reactions.

Free electron attachment to gas phase nucleobases (NB) and these molecules embedded in superfluid He droplets and Ne clusters is studied experimentally. For most of the biomolecules studied so far, the dominant reaction channel is e$^{-}$ + NB $\to $ (NB$^{-})^{\# } \quad \to $ (NB-H)$^{-}$ + H. (1) For the DNA bases adenine (A) and thymine (T) the attachment cross section in the electron energy range between 1 and 3 eV reveals several narrow resonances. By using partially deuterated and methylated NB molecules it is possible to assign these resonances to the loss of hydrogen from a specific nitrogen site [1]. The complementary reaction channel of (1) is the formation of H$^{-}$. For the formation of H$^{-}$ from A and T the attachment cross section shows several resonances in the energy range between 5 and 12 eV. Experiments with partly deuterated T and methylated NB show that the different peaks in the H$^{-}$ ion yield can be associated to the loss from the different molecular sites [2,3]. The energy dependence for H$^{-}$ abstraction from the carbon sites shows a remarkable resemblance to the energy dependence of strand breaks observed in plasmid DNA [4] suggesting that this reaction may be an important initial step towards strand breaks. Free electron attachment to NB embedded in superfluid He droplets exhibits a novel two-step process for electron energies higher than 5~eV. From an initially formed H$^{-}$ an electron is transferred to the opposite neutral radical and forms the (NB-H)$^{-}$. References [1] S. Ptasi\~nska et al., \textit{Angew. Chem. Int. Ed.} \textbf{44} (2005) 6941 [2] S. Ptasi\~nska et al., \textit{Angew. Chem. Int. Ed.} \textbf{44} (2005) 1647 [3] S. Ptasi\~nska et al., \textit{Phys. Rev. Lett.} \textbf{95} (2005) 093201 [4] B. Boudaiffa et al., \textit{Science} \textbf{278} (2000) 1658   

Electron-impact ionization and dissociative ionization of biomolecules

Oxidative damages by ionizing radiation are the source of radiation-induced damages to human health. It is recognized that secondary electrons play a role in the damage process, particularly important is the damage of DNA by electrons, potentially leading to mutagenesis. The damage can be direct, by creating a DNA lesion, or indirect, by producing radicals that attack the DNA. Molecular-level study of electron interaction with DNA provides information on the damage pathways and dominant mechanisms. This investigation focuses on ionization and dissociative ionization (DI) of DNA fragments by electron-impact. For ionization we use the improved binary-encounter dipole (iBED) model [W.M. Huo, Phys. Rev. A64, 042719-1 (2001)]. For DI it is assumed that electron motion is much faster than nuclear motion, allowing DI to be treated as a two-step process and the DI cross section given by the product of the ionization cross section and dissociation probability. The ionization study covers DNA bases, sugar phosphate backbone, and nucleotides. An additivity principle is observed. For example, the sum of the ionization cross sections of the separate deoxyribose and phosphate fragments is in close agreement with the C$_{3}$'- and C$_{5}$'-deoxyribose-phospate cross sections, differing by less than 5{\%}. The result implies that certain properties of the DNA, like the total ionization cross section, are localized properties and an additivity principle may apply. This allows us to obtain properties of a larger molecular system built up from the results of smaller subsystem fragments. The DI of guanine and cytosine has been studied. For guanine, a proton is produced from the channel where the ionized electron originates from a molecular orbital with significant charge density along the N(1)-H bond. The interaction of the proton with cytosine was also studied.   

Resonant Dissociative Recombination

In the collision of electrons with molecules and molecular ions, excitation and dissociation are dominated by resonant processes, where the electron becomes temporarily trapped, changing the forces felt by the nuclei. We will outline our method for treating these collision processes, where one or more resonant states exist. We separate the problem into two steps. First, the resonance parameters are obtained from accurate electron scattering calculations using the Complex Kohn variational method. Then these parameters are used as input to the dynamics calculations. We will illustrate the method with the study of dissociative recombination for the He$_{2}^{+}$, Ne$_{2}^{+}$, and Ar$_{2}^{+}$ molecular ions following collision with low energy electrons. Dissociative recombination of the rare gases are important processes in the ionosphere as well as laboratory plasmas and gaseous discharges. Comparison will be made to the available cross sections and rate coefficients. In collaboration with V. Ngassam and J. Royal. Work supported by the NSF PHY-02-44911, The Center for Biophotonics, an NSF Science and Technology Center PHY 0120999. and the NATO Science Program PST.GLG.9794033   

Low-Energy Electron Interactions with Complex Targets.

We have examined low-energy electron collisions with complex targets such as pristine nanoscale ice films and water/DNA interfaces by monitoring the reactive scattering processes leading to the formation of H (H$^{+})$, H$_{2}$ (H$_{2}^{+})$, O $^{3}$P$_{J}$, O $^{1}$D, OH$^{+}$, H$^{+}$(H$_{2}$O)$_{n}$ and DNA fragments. This work has shown that temperature-induced changes in the yields are due to subtle geometric and electronic structure changes brought about by changes in the interfacial hydrogen bonding structure. We have then exploited the fact that the two-hole localized states governing cation production and excitations involving a$_{1}$ levels are good probes of subtle structural changes in the water network. Since low-energy electrons can cause lethal damage to DNA, understanding the role of water and the DNA constituents in the damage event has recently received wide-spread attention. We have modified our multiple scattering ``path approach'' used to describe diffraction effects in stimulated desorption to calculate the diffraction and incident electron intensity at particular sections within a DNA double-strand. This approach assumes hypothetical electron scattering paths inside the target and calculates the interference of all elastically scattered components with the initial incoming wave. Constructive interference at zones localized within the DNA may locally enhance the dissociation probability.   

Session Z3: Fermionic Superfluidity in Ultracold Gases

Fermionic Superfluidity with Imbalanced Spin Populations and the Quantum Phase Transition to the Normal State

Whether it occurs in superconductors, helium-3 or inside a neutron star, fermionic superfluidity requires pairing of fermions, particles with half-integer spin. For an equal mixture of two states of fermions (``spin up'' and ``spin down''), pairing can be complete and the entire system will become superfluid. When the two populations of fermions are unequal, not every particle can find a partner. Will the system nevertheless stay superfluid? In this talk we present our study of this intriguing question in an unequal mixture of strongly interacting ultracold fermionic atoms. The superfluid region vs population imbalance is mapped out by employing two complementary indicators: The presence or absence of vortices in a rotating mixture, as well as the fraction of condensed fermion pairs in the gas. Due to the strong interactions near a Feshbach resonance, the superfluid state is remarkably stable in response to population imbalance. The final breakdown of superfluidity marks a new quantum phase transition, the Pauli limit of superfluidity.   

Pairing and Phase Separation in a Polarized Fermi Gas

We have prepared an ultra-cold gas of atomic fermions ($^6$Li) with unequal numbers in two spin components. A Feshbach resonance is used to control the interaction strength between these components. In the unitarity regime within the Feshbach resonance, our data shows a critical polarization, beyond which the gas separates into a phase that is consistent with a superfluid paired core surrounded by a shell of normal unpaired fermions.\footnote{G. B. Partridge, W. Li, R. I. Kamar, Y. Liao, R. G. Hulet, \emph{Science}, \textbf{311}, 503 (2006); published online 22 December 2005 (10.1126/science.1122876) } For near zero polarization, we measure the parameter $\beta = -0.54 \pm 0.05$ describing the universal energy of a strongly interacting paired Fermi gas, and find good agreement with recent theory. We also find that the critical polarization diminishes with decreasing attractive interaction strength on the BCS side of the Feshbach resonance.   

Direct Observation of Resonance Condensation in Imbalanced Fermi Mixtures

We directly observe pair condensation in an unequal mixture of resonantly interacting fermionic $^6$Li atoms. Condensation is revealed by the sudden appearance of a bimodal density distribution in the minority spin component below a critical temperature. Already above the critical temperature for condensation, strong interactions between the two spin states are manifest in the deformed density distribution of the larger cloud. Temperatures can be directly determined from the non- interacting wings of the majority component. Beyond a critical population imbalance of $71(3)\%$ on resonance, no condensates are observed, in agreement with our earlier observation of the Pauli limit of superfluidity. We show that for higher than critical imbalance, the central densities of the two components are no longer matched.   

Pairing in a Strongly Interacting Polarized Fermi Gas

We have observed pairing in an atomic Fermi gas of $^6$Li atoms with unequal numbers of two components.\footnote{G. B. Partridge \textit{et al.}, \emph {Science}, \textbf{311}, 503 (2006).} Beyond a critical polarization, the gas separates into paired core surrounded by a shell of normal unpaired fermions. At polarization smaller than this critical value, however, the atoms of two spins are able to spatially coexist with mismatched Fermi surfaces. The nature of such a system has been a topic of debate for decades. In these experiments, we investigate possible pairing mechanisms in this regime. The results are relevant to predictions of exotic new phases of quark matter and of strongly magnetized superconductors.   

Trapped Fermions across a Feshbach resonance with population imbalance

We investigate the phase separation of resonantly interacting fermions in a trap with imbalanced spin populations, both at zero and at finite temperatures. We directly minimize the thermodynamical potential under the local density approximation instead of using the gap equation, as the latter may give unstable solutions. At zero temperature, on the BEC side of the resonance, one may cross three different phases from the trap center to the edge: the superfluid phase (SF), where all particles are paired and there is no population imbalance; the breached gap phase (BP), where superfluid and polarized fermions coexist; and the normal Fermi sea with different Fermi surfaces for different spin components. On the BCS side or at resonance, typically only the SF and the normal phase show up. At finite temperature, we show that there exist fermionic excitations even in the superfluid phase, which carry population imbalance of the spin components. As a result, it becomes easier to satisfy the population imbalance constraint, which helps to stabilize the superfluid phase. Because of the fermionic excitations at finite temperature, the boundary between the BP phase and the SF phase becomes obscure. The phase separation between the paired phase (SF/BP) and the normal phase however, is marked by a peak in the population difference. We compare our results with a recent experiment (M.W. Zwierlein, et. al., cond-mat/0511197), and the agreement is remarkable.   

Spontaneous Vortices in Imbalance Populated Fermion Gas, Finite Size System

Atomic Fermion gases with mismatched densities have attracted much interest recently both experimentally and theoretically. These gases are related to superconductors in a magnetic field, to color superconductivity in high density QCD and to other systems. The main focus of recent research is on the possibility of unusual pairing states, the Larkin-Ovchinnikov-Fulde-Ferrel(LOFF)[1] phase, the Deformed Fermi surface(DFS)[2] and other states have been suggested in the past few years. We work specifically on two-dimensional systems with circular hard walls which contain atoms with two different hyperfine states and different populations. In addition to phase separation, a phenomenon that has already been observed[3], we consider the possibility of the spontaneous formation of vortices and giant vortices in some regions of parameter space. [1] Qinghong Cui, C.-R. Hu, J.Y.T. Wei, and Kun Yang, cond-mat/0510717 [2] Armen Sedrakian, Jordi Mur-Petit, Artur Polls, Herbert M\"{u}ther , cond-mat/0404577 [3] Guthrie B. Partridge, Wenhui Li, Ramsey I. Kamar, Yean-an Liao, Randall G. Hulet, cond-mat/0511752   

First and second sound in the BCS-BEC crossover in uniform Fermi superfluid gases

. The Landau two-fluid hydrodynamic equations are valid in the BCS-BEC crossover when the scattering length is very large. The frequencies of the in-phase and out-phase hydrodynamic modes at finite temperatures are determined by the equilibrium thermodynamic functions, including the temperature-dependent superfluid density. In turn , these depend on the Fermionic and Bosonic thermal excitations. We have calculated all these functions at finite temperatures in a uniform superfluid Fermi gas, including the particle--particle fluctuations using the well-known Nozieres-Schmitt-Rink approximation. These results will be extended to calculate the analogous hydrodynamic modes in a trapped superfluid gas, working within the LDA.   

Light scattering of degenerate fermions

We report on progress in measuring the suppression of resonant light scattering in a gas of degenerate fermions. A gas of trapped degenerate fermions is expected to exhibit narrower optical linewidths and longer excited state lifetimes than single atoms when the Fermi energy is larger than the photon recoil energy [1-3]. In this case, the number of available states into which a scattered atom can recoil is significantly reduced due to the filling of the Fermi sea. We produce a degenerate gas of 4$\times $10$^{4}$ ultra-cold fermionic $^{40}$K atoms by sympathetic cooling with bosonic $^{87}$Rb in a micro-magnetic chip trap. The atoms can then be loaded into a tight dipole trap just above the surface of the chip and probed with a near resonance laser pulse. [1] Th. Busch, J. R. Anglin, J. I. Cirac, and P. Zoller, \textit{Europhys. Lett.} \textbf{44}, 1 (1998). [2] B. DeMarco and D. S. Jin, \textit{Phys. Rev. A} \textbf{58}, R4267 (1998). [3] J. Javanainen and J. Ruostekosky, \textit{Phys. Rev. A} \textbf{52}, 3033 (1995). Work supported by NSERC, CFI, OIT, Research Corporation, and PRO.   

Interaction Energy in a Paired Two-Component Degenerate Fermi Gas in the BEC-BCS Crossover

We have measured the interaction energy of the ground-state of a paired Fermi gas in the BEC-BCS crossover. The crossover describes the smooth transition from a BEC of tightly bound dimers to that of a paired BCS superfluid. A Feshbach resonance is used to tune the atomic scattering length \textit{a}. The interaction energy is extracted from \textit{in-situ} images of a trapped two component gas of $^{6}$Li atoms near $T=0$. Near the peak of the Feshbach resonance the interaction energy is expected to be parameterized by a single universal parameter $\beta$ describing a strongly interacting, paired superfluid. We find that $\beta = -0.54$ $\pm$ $0.05$ in good agreement with recent Monte Carlo calculations giving $\beta = -0.58$. On the BEC side of resonance, we find that the molecular scattering length is $0.6 a$, in agreement with recent theory, but only for fields not too close or too far from resonance.   

Superfluid Expansion of a Rotating Fermi Gas

Pairing and superfluidity in strongly interacting Fermi gases are pure many-body effects: Fermion pairs exist only due to the stabilizing presence of the surrounding atoms. The pairs are thus dependent on density and can break as the density is decreased. In contrast to a Bose-Einstein Condensate (BEC) an expanding superfluid Fermi gas therefore eventually undergoes the phase transition to the normal state. Here we observe the expansion of a rotating, superfluid Fermi gas. As superfluids can contain angular momentum only in the form of vortices, the presence and absence of vortices in the gas is used to distinguish superfluid and normal parts of the expanding cloud. We find that superfluid Fermion pairs survive during expansion. Breakdown of superfluid flow is observed as the density, and hence the binding energy, decreases below a critical value.   

Session Z4: Rydberg Atoms and Coherent Control

Time Dependence of Many-Body Interactions in Ultra-cold Rydberg Atom Samples of Different Geometries

Ultra-cold highly-excited atoms in a magneto-optical trap are strongly coupled by the dipole-dipole interaction. We have investigated the importance of many-body effects by controlling the dimensionality and density of the excited sample and by varying the time during which the atoms are allowed to interact. We excited Rydberg atoms in two different geometries: a nearly one dimensional column with a diameter on the order of the typical interatomic spacing and a more three dimensional column with a diameter a few times larger than the typical spacing. In each volume, the interaction time was varied from 0 to 8~$\mu$s. Many-body effects are seen to be important in the time development of the three-dimensional system, while they are suppressed in the one dimensional case. This work was supported by the National Science Foundation under Grant No. 0134676.   

Coherence conditions for groups of Rydberg atoms

We investigate the excitation of a collection of cold atoms to Rydberg states. By direct numerical solution of Schr\"odinger's equation, we are able to compute various interesting properties of the many body wave function. The high polarizability of Rydberg atoms allows them to support large dipole moments which in turn can interact over long ranges. If the interaction energy between two excited atoms is large enough the resultant energy shift will move the two excitation state out of resonance, thus effectively blocking a two excitation state form occurring. One particular topic investigated is the quantum phase gate, where both groups of atoms are within a blockade radius and subjected to a $\pi -2\pi -\pi$ sequence of pulses. We examine the regime where the groups are neither totally within nor totally outside the blockade radius. Testing the conditions for coherence will help establish constraints for quantum information. If time permits, counting statistics as related to the Mandel $Q$ parameter will be used to measure blockade effectiveness.   

Many-body effects in strongly interacting systems of Rydberg atoms

We investigate the effects of strong interactions in ultracold Rydberg gases. Strong Rydberg-Rydberg interactions have been proposed to entangle large numbers of atoms, which can be used to implement fast quantum gates. The laser excitation of a macroscopic sample of ultracold atoms to high-lying Rydberg states can be dramatically suppressed by their strong long-range interactions. This leads to a local blockade effect, where a single excited Rydberg atom prevents excitation of its neighbors. Recently, large inhibitions of Rydberg excitations due to van der Waals interactions have been observed. We explore the dynamics of strongly interacting systems with many excited atoms. Including many-body correlations is essential for such systems. Besides the inhibition of Rydberg excitation, we are particularly interested in the conditions for collective oscillations. These oscillations should be much faster than the ordinary Rabi flopping for isolated atoms and should depend on the number of atoms in the sample. We discuss different analytical and numerical techniques used for solving the many-body Hamiltonian.   

Ionic Dipole and Quadrupole Matrix Elements from Non Adiabatic Core Polarization

The radial matrix elements connecting the ionic Ba$^+$ state to low lying excited $6p$ and $5d$ states can be extracted from the K splittings of the bound $6sn\ell$ states. We develop an expression for the K splitting by a pair of expansions. Comparison of the contributions from different ionic states confirms that all but the lowest two may be safely ignored. Finally we extract the radial Ba$^+$ matrix elements $\left<6s|r|6p\right>$ and $\left<6s|r^2|5d\right>$.   

Weak signal detection using quantum interference

We demonstrate a powerful technique for detecting weak atomic or molecular transitions that is based on homodyning two atomic transition amplitudes. The scheme is tested on a weak Stark-induced transition in cesium by exciting its ground 6s $^{2}$S$_{1/2}$ state to the 8s $^{2}$S$_{1/2}$ excited state by a 411 nm laser field. The strong local oscillator signal is a two-photon transition excited by an 822 nm laser field that connects the same ground and exited states. The Stark-induced transition can be regulated by controlling a DC field across a Cs cell. The simultaneous excitation of the two pathways results in a quantum interference that can be controlled by phase modulating either of the driving laser fields. The change in the relative phase between the laser fields results in a change in the relative phase between the transition amplitudes of the two paths. Thus, phase modulating one of the beams gives rise to an amplitude modulation of the net excitation rate. The amplitude of this modulation allows a quantitative measure of the weak transition rate.   

Observation of channel phase lag in asymmetric photoelectron angular distributions in the vicinity of autoionizing resonances

We report the results of channel phase lag measurements in the photoionization of atomic barium. We ionize the 6s6p $^{1}$P$_{1}$ excited state via a coherent laser field consisting of two frequencies, $\omega $ and 2$\omega $, to excite the atom to an autoionizing resonance in the series converging on the 5d$_{5/2}$ threshold. We present the channel phase lag observed for the asymmetric angular distribution for different ionization product states at different locations of the autoionizing resonances.   

Measurement of the phase difference between even and odd continuum waves in photoionization of atomic rubidium.

We report improved measurements of asymmetric photoelectron angular distributions resulting from photoionization of atomic rubidium through coherent one-photon and two-photon interactions. Analysis of the asymmetry allows us to determine the phase difference between even- and odd-parity continuum wavefunctions. We discuss calibration of the phase, including field propagation phase shifts and the phase shift upon frequency doubling in a nonlinear crystal.   

Observation of high-order quantum resonances in the delta kicked rotor

Quantum resonances in the delta kicked rotor\footnote{F.L. Moore, J.C. Robinson, C.F. Bharucha, B. Sundaram, M.G. Raizen, {\it Phys. Rev. Lett.} \textbf{75} 4598 (1995). } are characterized by a dramatically increased energy absorption rate in direct contradiction to the momentum localization generally observed. These resonances exist where the scaled Planck's constant $\tilde{\hbar}=\frac{r}{s}\cdot4\pi$, for integers $r$ and $s$. However only the $\tilde{\hbar}=r\cdot2\pi$ resonances are easily observable. We report on the observation of high-order quantum resonances ($s>2$) utilizing a sample of low temperature, non-condensed atoms and a pulsed optical standing wave. Resonances are observed for $\tilde{\hbar}=\frac{r}{16}\cdot4\pi$ for integers $r=2-6$. The behavior of the resonances with variation of kick number and kick strength is examined. Quantum numerical simulations suggest that our observation of high-order resonances indicates a much longer spatial coherence than expected from an initially thermal atomic sample.   

Coherent Control of Strong Field Dynamics.

We present experimental results on coherent control of multi-photon transitions in the strong field limit. A learning algorithm is capable of discovering shaped laser pulses which can compensate for dynamic Stark shifts and greatly outperform an unshaped laser pulse. We provide a comparison between experiments that use a spontaneous emission signal as feedback for the learning algorithm and ones that make use of a stimulated emission signal. Our experimental results are compared with calculations of the strong field dynamics.   

Session Z5: Quantum Information and Cavity QED

Cavity QED with atom chips and micro-resonators

Cavity QED provides a rich experimental setting for quantum information processing, both in the implementation of quantum logic gates and in the development of quantum networks. Moreover, studies of cavity QED will help elucidate the dynamics of continuously observed open quantum systems with quantum- limited feedback. To achieve these goals in cavity QED, a neutral atom must be tightly confined inside a high-finesse cavity with small mode volume for long periods of time. Microfabricated wires on a substrate---known as an atom chip---can create sufficiently high-curvature magnetic potentials to trap atoms in the Lamb- Dicke regime. The integration of micro-resonators, such as microdisks and photonic bandgap cavities, with atom chips forms a robust and scalable system capable of probing the strong- coupling regime of cavity QED with magnetically trapped atoms. We have recently built an atom-cavity chip utilizing a fiber taper coupled microdisk resonator. This device combines laser cooling and trapping of neutral atoms with magnetic microtraps and waveguides to deliver cold atoms to the small mode volume of the high-Q cavity. We will relate our progress toward detecting single atoms with this device.   

Optical beams with embedded vortices: building blocks for atom optics and quantum information

Laser beams with embedded vortices, Bessel or Laguerre-Gaussian modes, provide a unique opportunity for creating elements for atom optics, entangling photons and, potentially, mediating novel quantum interconnects between photons and matter. High-order Bessel modes, for example, contain intensity voids and propagate nearly diffraction-free for tens of meters. These vortices can be exploited to produce dark channels oriented longitudinally (hollow beams) or transversely to the laser propagation direction. Such channels are ideal for generating networks or circuits to guide and manipulate cold neutral atoms, an essential requirement for realizing future applications associated with atom interferometry, atom lithography and even some neutral atom-based quantum computing architectures. Recently, we divided a thermal cloud of neutral atoms moving within a blue-detuned beam into two clouds with two different momenta by crossing two hollow beams. In this presentation, we will describe these results and discuss the prospects for extending the process to coherent ensembles of matter.   

Two-Dimensional Control of Trapped Ions in a T-junction Array of Ion Traps

One proposal for a scalable quantum computer involves shuttling trapped atomic ions between interaction zones where ions can be entangled and storage zones where ions can be sent to store quantum information [1]. We have performed a proof of principle experiment where ions were shuttled throughout an array of linear traps arranged to make a T-junction with 11 trapping zones. These experiments were guided by simulations of the electric potential in the ion trap array, where time-varying potentials are efficiently modeled with electrode ``basis'' functions that exploit the potential of each individual electrode. In order to arbitrarily control trapped ions in two- dimensions, it may be necessary to implement four key shuttling protocols that have all been experimentally demonstrated in the T-junction array [2]: linearly shuttling ions along channels and through junctions, shuttling ions around corners, and separating and recombining two ions that are in the same trapping zone. By combining these protocols, we demonstrated the controllable swapping of the positions of two ions in the same trapping zone. [1]. D. Kielpinski et al, Nature 417, 709 (2002); M. Rowe et al., Quant. Inf. Comp. 2, 257 (2002). [2]. W. K. Hensinger et al. Appl. Phys. Lett. 88, 034101; *University of Michigan,**University of Sussex,***Western Illinois University; Work supported by the DTO and the NSF ITR program.   

Using prior information for continuous measurement quantum state reconstruction.

Density matrices representing quantum states must be positive.~ This restriction can provide crucial information for a quantum state-tomography procedure, allowing one to reconstruct states for which there is otherwise insufficient information.~ We explain the use of semidefinite programming techniques to enforce the positivity constraint and present an example of its use in the course of quantum state reconstruction by continuous weak measurement.~ Both simulated and experimental results for the reconstruction will be discussed for a variety of states~of a spin F=3 system in cesium, measured through polarization spectroscopy.   

Unitary Integration and Fiber Bundle Geometry of N-level Quantum Systems.

Geometric properties of quantum systems, such as Berry's geometric phase and later generalizations, bring out important characteristics of quantum physics. They are now central to the field of quantum computation as a possible route to fault tolerant operation. We use fiber bundle technique to describe SU(N) quantum dynamics of N-level system as a fiber bundle over a 2(N-1)-dimensional projective space and (N-1)$^{2}$-dimensional SU(N-1)$\times $U(1) fiber. This provides a hierarchical route to a higher SU(N) groups in terms of lower dimensional ones.   

Decoherence-free subspaces and spontaneous emission cancellation: necessity of Dicke limit

Decoherence-free subspaces (DFS) of an open quantum system are states for which the coupling to the environment is canceled by destructive interference. DFS are usually studied for states involving two or more particles and are considered a prominent candidate for quantum memory and quantum information processing. Experiments with ions indicate that partial cancellation is possible, but a demonstration of significant cancellation is challenging. \\ We prove that a perfect physical DFS requires co-located particles, i.e., the Dicke limit. The assumptions made are very general and invoke a homogeneous environment with energy-conserving coupling to the particles. We indicate when a DFS outside the Dicke limit may be possible; this includes molecular and confined systems. Furthermore, we establish a connection between DFS and spontaneous emission cancelation and refine the conditions for one of the important theorems on DFS to hold.   

Detectability of dissipative motion in quantum vacuum via superradiance

We report on a feasibility study for the detection of vacuum-induced dissipative motion, also known as the dynamical Casimir effect. Casimir photons are generated using high frequency mechanical resonators currently available through FBAR technology. The corresponding weak radio-frequency signal will stimulate population-inverted alkali atoms to generate an intense superradiant pulse detectable with conventional electronics.   

Analysis of photon-atom entanglement generated by AC Stark shifts in a cavity

AC Stark shifts provide a mechanism to entangle polarization states of photons and atoms. We examine a situation in which an off-resonant light with two polarizations interacts with a collection of 4-levels atoms in a cavity. As the frequency shift in each polarization is conditioned by the number of atoms at the corresponding sub-levels, any imbalance of atom numbers would lead to a rotation of Stokes parameters of light. The quantum entanglement generated in this process is analyzed by the Schmidt decomposition method. We derive the time-dependence of entanglement entropy and the effective Schmidt number for Gaussian amplitudes. In addition, we indicate how the rate of change of entanglement is controlled by the initial fluctuations of atoms and photons.   

Toward Cavity QED on an atom chip

We describe the construction and operation of microfabricated atom chips containing optical cavities suitable for cavity QED. The silicon or sapphire chips support microfabricated magnetic traps and guides for ultracold atoms, as well as Fabry- Perot optical cavities with axes perpendicular to the chips' surface. In the case of the sapphire chip, the cavities are half planar with the flat mirrors deposited directly on the surface of the chip, and curved macroscopic mirrors mounted above the chip. The silicon chip has micromachined holes through which the modes of externally mounted Fabry-Perot cavities pass. The cavities have small enough mode volume and high enough finesse to be useful as atom number detectors in a variety of on-chip experiments. Also this technology may be used in a number of cavity QED based quantum optics schemes, which would benefit from controllable magnetic loading of cold atoms into optical cavities.