Recursion relations for the generic Hylleraas three-electron integral are obtained in a closed form by using integration by parts identities. Numerically fast algorithms suitable for high precision calculations of the integral with high powers of interelectronic coordinates are presented.

We observed a universal phenomenon of the competition among multiple filaments generated during the propagation of intense femtosecond laser pulses in air. We show that the fluorescence signal from the excitation of nitrogen molecules inside the plasma channel contains important information pertaining to the formation and interaction of multiple filaments. The detected backscattered nitrogen fluorescence from inside the filaments yielded irregular changes from shot to shot which cannot be explained by fluctuation arising from the initial laser pulse itself. Numerical simulations reveal a complex dynamics of multiple filament propagation and interaction dynamics that depends strongly on the initial perturbations of the laser beam. The irregular changes of the fluorescence signal are attributed to the interference between adjacent hot spots that evolve into filaments which give rise to new hot spots (filaments) in between, and thus give the appearance of the fusion or branching of filaments.

We have observed and located more than 60 magnetic field-induced Feshbach resonances in ultracold collisions of ground-state ${}^{133}\mathrm{Cs}$ atoms. Multiple extremely weak Feshbach resonances associated with $g$-wave molecular states are detected through variations in the radiative collision cross sections. The Feshbach spectroscopy allows us to determine the interactions between ultracold cesium atoms and the molecular energy structure near the dissociation continuum with unprecedented precision. Our work not only represents a very successful collaboration of experimental and theoretical efforts, but also provides essential information for cesium Bose-Einstein condensation, ${\mathrm{Cs}}_2$ molecules, and atomic clock experiments.

We consider a pair of identical two-level atoms interacting with a scalar field in one dimension, separated by a distance $x_{21}$. We obtain collective decaying states, belonging to a complex spectral representation of the Hamiltonian. The imaginary parts of the eigenvalues give the decay rates, and the real parts give the average energy of the collective states. In one dimension there is strong interference between the fields emitted by the atoms, producing cooperative effects even when the atoms are far apart. The decay rates and the energy oscillate with the distance $x_{21}$. Depending on $x_{21}$, the decay rates will either decrease, vanish, or increase as compared with the one-atom decay rate. We have sub- and superradiance at periodic intervals. Our model may be used to study two-cavity electron waveguides. The vanishing of the collective decay rates then suggests the possibility of obtaining stable configurations, where an electron is trapped inside the two cavities.

We have determined the temperature and heating rate of laser-cooled ions in a Penning trap using Doppler laser spectroscopy. Between and ions are trapped in a Penning trap and Doppler laser cooled to temperatures of a few millikelvin, where they form ion crystals. This system is an example of a strongly coupled one-component plasma. The ion temperature was measured as a function of time after turning off the laser-cooling. In the solid phase, we measured a heating rate of . Information about possible heating mechanisms was obtained directly from temperature measurements, and also from measurements of the rate of radial expansion of the ion plasma. We determined that the observed heating is due to collisions with the residual gas of our vacuum system.

Single and double ionization processes for helium under the impact of B, O, and F anions were studied in the $1.1–1.9\mathrm{a.u.}$ velocity range. Coincidence cross sections were measured for direct ionization (DI), i.e., no projectile electron loss, and single (SL) and double projectile electron loss. The results show that DI is dominated by large impact parameters and SL is essentially the elastic scattering of the extra electron by the target. The cross section ratios taken between double and single helium ionization for single and double loss are projectile independent and grow almost linearly with the velocity.

We propose a semiclassical version of Shor’s quantum algorithm to factorize integer numbers, based on spin-$\frac{1}{2}$ SU(2) generalized coherent states. Surprisingly, we find evidence that the algorithm’s success probability is not too severely modified by our semiclassical approximation. This suggests that it is worth pursuing practical implementations of the algorithm on semiclassical devices.

We discuss practical schemes for using entangled Bose-Einstein condensates to detect phase shifts with a resolution better than the shot-noise limit. We begin by outlining a procedure for demonstrating how squeezed matter waves can be used to make measurements by simply lowering and raising a potential barrier between two condensates. The phase shift is read out by a scheme which involves releasing the condensates and studying the collapses and revivals of the visibility of the observed interference fringes. Finally we show how this scheme could be extended to measurements of other quantities such as gravity. All the steps of this process are attainable with current technology and so may provide a practical route for achieving enhanced resolution measurements with matter waves.

We establish the general equations of motion for the modes of a vortex lattice in a rapidly rotating Bose-Einstein condensate in three dimensions, taking into account the elastic energy of the lattice and the vortex line bending energy. As in two dimensions, the vortex lattice supports Tkachenko and gapped sound modes. In contrast, in three dimensions the Tkachenko mode frequency at long wavelengths becomes linear in the wave vector for any propagation direction out of the transverse plane. We compute the correlation functions of the vortex displacements and the superfluid order parameter for a homogeneous Bose gas of bounded extent in the axial direction. At zero temperature the vortex displacement correlations are convergent at large separation, but at finite temperatures, they grow with separation. The growth of the vortex displacements should lead to observable melting of vortex lattices at higher temperatures and somewhat lower particle number and faster rotation than in current experiments. At zero temperature a system of large extent in the axial direction maintains long range order-parameter correlations for large separation, but at finite temperatures the correlations decay with separation.

Vacuum polarization, an effect originally predicted nearly 70 years ago, is still yet to be directly detected despite significant experimental effort. Previous attempts have made use of large liquid-helium cooled electromagnets which inadvertently generate spurious signals that mask the desired signal. We present an approach for the ultrasensitive detection of optical birefringence that can be usefully applied to a laboratory detection of vacuum polarization. The technique has a predicted birefringence measurement sensitivity of $\Delta n\sim {10}^{-20}$ in a 1 s measurement. When combined with the extreme polarizing fields achievable in this design we predict that a vacuum polarization signal will be seen in a measurement of just a few days in duration.

We describe in detail a theoretical scheme to trap and manipulate an arbitrary number of electrons in vacuum for universal quantum computation. The particles are confined in a linear array of Penning traps by means of a combination of static electric and magnetic fields. Two-electron operations are realized by controlling the Coulomb interaction between neighboring particles. The performances of such a device are evaluated in terms of clock speed, fidelity, and decoherence rates.

We propose a way to make arrays of optical frequency dipole-force microtraps for cold atoms above a dielectric substrate. Traps are nodes in the evanescent wave fields above an optical waveguide resulting from interference of different waveguide modes. The traps have features sought in developing neutral atom based architectures for quantum computing: $\sim 1\mathrm{mW}$ of laser power yields very tight traps $150\mathrm{nm}$ above a waveguide with trap vibrational frequencies $\sim 1\mathrm{MHz}$ and vibrational ground state sizes $\sim 10\mathrm{nm}$. The arrays are scalable and allow addressing of individual sites for quantum logic operations.

We measure the chirp rate of harmonics 13 to 23 in argon by cross correlation with a 12 femtosecond probe pulse. Under low ionization conditions, we directly measure the negative chirp due to the atomic dipole phase, and show that an additional chirp on the pump pulse is transferred to the $q\mathrm{th}$ harmonic as $q$ times the fundamental chirp. Our results are in accord with simulations using the experimentally measured $815\mathrm{nm}$ pump and probe pulses. The ability to measure and manipulate the harmonic chirp rate is essential for the characterization and optimization of attosecond pulse trains.

The macroscopic electromagnetic field is quantized in a linear isotropic permeable-dielectric medium by associating a proper damped quantum-mechanical harmonic oscillator with each mode of the radiation field. We introduce a particular form of the Langevin equation with two memory functions and two random impulses to describe the motion of a damped oscillator. A fully canonical approach is used to quantize the damped oscillator, the conjugate momentum is defined and the quantum-mechanical Hamiltonian is introduced. This brings forth a direct method for the quantization of the radiation field and at the same time introduces an effective Hamiltonian operator. Special attention is paid to the vacuum field fluctuation in permeable dielectrics.

A method of creating pseudopure spin states in large clusters of coupled spins is described. It is based on filtering multiple-quantum coherence of the highest order, followed by a time-reversal period and partial saturation. Experimental demonstration is presented for a cluster of six dipolar-coupled proton spins of a benzene molecule in a liquid crystalline matrix, and the details of spin dynamics are studied numerically.

Observed intensity distribution in the high resolution synchrotron radiation excited $4d$ photoelectron spectrum of $\mathrm{In}$ is compared with the predictions based on the relativistic single configuration (SC) Dirac-Fock calculations. Many-electron effects beyond the SC approximation were found to cause additional fine structures in some of the photoelectron lines.

We have measured the polarization of the heliumlike sulfur resonance line $1s2p{}^{1}P_1\to 1s^2{}^{1}S_0$ and of the blend of the lithiumlike sulfur resonance lines $1s2s2p{}^{2}P_{3∕2}\to 1s^{2}2s{}^{2}S_{1∕2}$ and $1s2s2p{}^{2}P_{1∕2}\to 1s^{2}2s{}^{2}S_{1∕2}$ as a function of electron beam energy from near threshold to $144\mathrm{keV}$. These lines were excited with the LLNL high-energy electron beam ion trap and measured using a newly modified two-crystal technique. Our results test polarization predictions in an energy regime where few empirical results have been reported. We also present calculations of the polarization using two different methods, and good agreement is obtained.

Angular and charge-state distributions are measured for $5–15\text{‐}\mathrm{keV}$. ${\mathrm{Ar}}^0$ and ${\mathrm{Ar}}^{+}$ ions reflected from a KCl(001) surface under glazing angle incidence. The ionization of ${\mathrm{Ar}}^0$ is almost completely suppressed at incident angles smaller than a critical angle ($11–22\mathrm{mrad}$, depending on the ion energy), while a considerable fraction of incident ${\mathrm{Ar}}^{+}$ ions are neutralized. It is demonstrated that a position-dependent Auger neutralization rate can be derived from the observed result without any assumption except for the surface continuum potential. The obtained Auger neutralization rate shows a simple exponential dependence as is usually assumed.

In spectroscopy, the fingerprint of a substance is usually comprised of a sequence of spectral lines with characteristic frequencies and strengths. Identification of substances often involves postprocessing, where the measured spectrum is compared with tabulated fingerprint spectra. Here we suggest a scheme for nonlinear spectroscopy, where, through coherent control of the nonlinear process, the information from the entire spectrum can be practically collected into a single coherent entity. We apply this for all-optical analysis of coherent Raman spectra and demonstrate enhanced detection and effective background suppression using coherent processing.