Using a modulated crossed-beam method, we have measured absolute differential cross sections for the excitation of atomic hydrogen to its $n=3\mathrm{}$ $(3\mathrm{}{}^{2}S+3\mathrm{}{}^{2}P+3\mathrm{}{}^{2}D)$ and $4(4{}^{2}S+4\mathrm{}{}^{2}P+4\mathrm{}{}^{2}D+4\mathrm{}{}^{2}F)$ levels by electron impact. A wide range of scattering angles was covered, while the impact energies employed were 20 and 30 eV. Absolute integrated excitation cross sections were calculated from the differential ones. Our results are compared with those of others.

Complex coordinate scaling (CCS) is used to calculate resonance eigenvalues and eigenstates for a system consisting of an inverted Gaussian potential and a monochromatic driving field. Floquet eigenvalues and Husimi distributions of resonance eigenfunctions are calculated using two different versions of CCS. The number of resonance states in this system increases as the strength of the driving field is increased, indicating that this system might have increased stability against ionization when the field strength is very high. We find that the newly created resonance states are scarred on unstable periodic orbits of the classical motion. The behavior of these periodic orbits as the field strength is increased may explain why there are more resonance states at high field strengths than at low field strengths. Close examination of an avoided crossing between resonance states shows that the two states exchange their structure, as in bound systems. This phenomenon might lead to interesting effects at certain field strengths.

Laser cooling by coherent scattering inside an optical cavity, a method proposed for cooling the motion of arbitrary particles that scatter light, is analyzed in terms of the modified emission spectrum. In contrast to conventional Doppler cooling, this method invokes the two-photon Doppler effect along the direction of the momentum transferred in the scattering process. Three-dimensional cooling can therefore be achieved with a single optical cavity. Both in the free-particle regime (cavity Doppler cooling) and in the strong-confiment regime (cavity sideband cooling) the minimum temperature is determined by the resonator linewidth and independent of the atomic level structure. The cooling efficiency and volume are significantly enhanced in resonators with transverse-mode degeneracy, such as the confocal resonator.

Using a comparison equation method rooted in the Landau-Zener model, we report results for the probability of transition and survival in two-state models for a crossing of levels having some width, to account for dissipation. The theory allows arbitrary forms for the state energies, their rate of decay, and coupling, subject only to the limitation inherent in the Landau-Zener class (coupling with infinite “pulse area”). We show how the strong decay result of adiabatic elimination can be recovered, but with important restrictions as to its usability. We also confirm the validity of the well-known Dykhne formula for crossings of real energy levels, and use the new theory to extend the Dykhne result to a class of dissipative crossings we call pseudoreal. Finally, we examine the overall probability for transition at two successive crossings, as occurs in atomic collisions. Here, interference of the crossing states leads to oscillations in the transition probability with collision time. For slow collisions we find that even a modest level of dissipation heavily damps these oscillations, but at the same time enhances the average probability of transition.

We describe the role of first non-Markovian corrections to resonance fluorescence in photonic crystals, using a perturbative expansion of the Heisenberg equations of motion in powers of the atom-field reservoir coupling strength. Non-Markovian effects arise from the rapid variation of the photonic density of states with frequency. Our method recaptures the physics of the photon-atom bound state in the presence of a full photonic band gap. For the anisotropic three-dimensional photonic band gap, it predicts remarkable features in the resonance fluorescence, such as atomic population inversion and switching behavior in a two-level atom for moderate values of the applied laser field. The magnitude of the switching effect depends sensitively on the external laser intensity and its detuning frequency from the atomic transition. The robustness of this effect against nonradiative decay and dephasing mechanisms is also investigated.

We demonstrate that changing the reduced mass in scattering calculations is equivalent to changing the potential. We explore how small changes in the mass alter the scattering length of hydrogen atoms when they interact via the $X{}^1{\Sigma }_g^{+}$ and $b{}^3{\Sigma }_u^{+}$ molecular states. We show how the variation of scattering length with mass depends on the asymptotic potential.

The inclusive yield distribution of ${\mathrm{C}}_n^{+}$ fragments from 45 keV ${\mathrm{C}}_{60}^{-}$ collisions with Ar gas, exhibits comparable yields for fragments with n in the 10–25 range and for fullerene fragments with n in the 40–58 range. Single-collision two-fragment coincidence measurements show a high probablity for formation of two fragments with similar size in the $n=15\mathrm{}–25$ range. Three ${\mathrm{C}}_n^{+}$ fragments each with $n>\mathrm{}2,$ have been observed in triple coincidence measurements. An enhancement of the yield of the lightest fragments with an odd number of carbons is observed.

The general character of nonlinear coherent states (NCS) is considered. A method is introduced by which any pure state of the quantum harmonic oscillator can be represented in a limiting sense as a NCS. The representation of a Fock state as a NCS is discussed in detail. As a physical example we show how to prepare a highly excited Fock state in an ion trap based on the concept of NCS.

We experimentally studied the Faraday rotation of resonant light in an optically thick cloud of laser-cooled rubidium atoms. Measurements yield a large Verdet constant in the range of ${10}^5$°/T mm and a maximal polarization rotation of 150°. A complete analysis of the polarization state of the transmitted light was necessary to account for the role of the probe laser’s spectrum.

We study both experimentally and theoretically the losses induced by parametric excitation in far-off-resonance optical lattices. The atoms confined in a one-dimensional sinusoidal lattice present an excitation spectrum and dynamics substantially different from those expected for a harmonic potential. We develop a model based on the actual atomic Hamiltonian in the lattice and we introduce semiempirically a broadening of the width of lattice energy bands which can physically arise from inhomogeneities and fluctuations of the lattice, and also from atomic collisions. The position and strength of the parametric resonances and the evolution of the number of trapped atoms are satisfactorily described by our model.

A recent improved version of the semiclassical-quantal approach has been applied to the $e^{-}-\mathrm{H}$ near-threshold ionization for ${\theta }_{12}=180\mathrm{}°$ geometry. It is found, that unlike other sophisticated theoretical methods such as distorted wave theory or convergent close-coupling calculation, the present relatively simpler approach produces correct behavior and numerical values for the triple-differential cross sections. We compare our results with recent absolute measurements and accurate numerical calculations at 2 eV and 4 eV above the threshold at constant ${\theta }_{12}$ geometry.

We measured the total destruction cross sections of small $X_n^{-}$ clusters $(X=\mathrm{Si}$ and C; $n=2,$ 3, and 4) in noble gas targets (Y = He, Ne, and Ar), with relative velocities $v$ in the 0.10–0.95 a.u interval for silicon, and in the 0.20–1.20 a.u. interval for carbon. The measured values increase monotonically with target and projectile sizes, as expected on a geometrical basis. In particular the dependence of the cross sections on n is linear for carbon clusters, agreeing with a quantitative model based on the linear structure of these clusters. Ratios of the measured cross sections for the several ${\mathrm{X}}_n^{-}$ clusters, ${\sigma }_{X,n}^{\mathrm{Ne}}\mathrm{}\left(v\right)/{\sigma }_{X,n}^{\mathrm{He}}\mathrm{}\left(v\right),$ ${\sigma }_{X,n}^{\mathrm{Ar}}\mathrm{}\left(v\right)/{\sigma }_{X,n}^{\mathrm{He}}\mathrm{}\left(v\right),$ and ${\sigma }_{X,n}^{\mathrm{Ar}}\mathrm{}\left(v\right)/{\sigma }_{X,n}^{\mathrm{Ne}}\mathrm{}\left(v\right),$ were verified to fall into universal curves, i.e., each cross section is the product of target- and projectile-dependent factors.

We have measured positive fragment ions produced in collisions of 2 MeV ${\mathrm{Si}}^{q+}\hspace{0.5em}(q=0,$ 1, 2, 4) projectiles with a ${\mathrm{C}}_{60}$ molecular target. The measurement was performed with a time-of-flight coincidence method between fragment ions and charge-selected outgoing projectiles. For all the charge-changing collisions investigated here, the mass distribution of small fragment ions ${\mathrm{C}}_n^{+}$ $(n=1\mathrm{}–12)$ can be approximated fairly well by a power-law form of $n^{-\lambda }$ as a function of the cluster size n. The power $\lambda$ derived from each mass distribution is found to change strongly according to different charge-changing collisions. As a remarkable experimental finding, the values of $\lambda \left(\mathrm{loss}\right)$ in electron loss collisions are almost the same for the same final charge states k irrespective of the initial charge q, exhibiting a nearly perfect linear relationship with k. We also performed calculations of the projectile ionization on the basis of the semiclassical approximation and obtained inelastic energy deposition for individual collision processes. The estimated energy deposition is found to have a simple correlation with the experimentally determined values of $\lambda \left(\mathrm{loss}\right).\mathrm{}$

We show that atomic-tunneling oscillations between two Bose-Einstein condensates can be increased as well as decreased by preparing the appropriate initial conditions and the nonlinear self-interaction. There is a trade-off relation between the oscillation amplitudes and the frequencies: smaller the oscillation amplitudes, higher the oscillation frequencies. The trajectory of the state vector on the Bloch sphere gives us an intuitive understanding of the increase of the tunneling oscillations. Similar effect predicted in this paper is expected for other nonlinear systems such as in the coupled quantum dots and waveguide coupling, in which the on-site energy and the self-phase-modulation, respectively, give rise to the nonlinear interactions.

Using a second-order perturbative model for a “fast” incident projectile, together with a convergent R matrix with pseudostates close-coupling model for the initial bound state and the scattering of a “slow” ejected electron in the field of the ion, we found a substantial effect of autoionizing resonances in simultaneous ionization-excitation of the $n=2\mathrm{}$ states in ${\mathrm{He}}^{+}.$ Although widely ignored to date, we show that the effect must be accounted for in a meaningful comparison between theoretical predictions and the available experimental data.

We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to be of exponential complexity into one of polynomial complexity. The key to our demonstration is the spin-particle connection (or generalized Jordan-Wigner transformation) that allows exact algebraic invertible mappings of operators with different statistical properties. We give an explicit implementation of a simple problem using a quantum computer based on standard qubits.

There has recently been much discussion regarding entanglement transformations in terms of local filtering operations and whether the optimal entanglement for an arbitrary two-qubit state could be realized. We introduce an experimentally realizable scheme for manipulating the entanglement of an arbitrary state of two polarization-entangled qubits. This scheme is then used to provide some perspective to the mathematical concepts inherent in this field with respect to a laboratory environment. Specifically, we look at how to extract enhanced entanglement from systems with a fixed rank, and, in the case where the rank of the density operator for the state can be reduced, show how the state can be made arbitrarily close to a maximally entangled pure state. In this context we also discuss bounds on entanglement in mixed states.

By considering the utilization of a classical channel without quantum entanglement, fidelity $F_{\mathrm{classical}}=\frac{1}{2}$ has been established as setting the boundary between classical and quantum domains in the teleportation of coherent states of the electromagnetic field [S. L. Braunstein, C. A. Fuchs, and H. J. Kimble, J. Mod. Opt. $47,$ 267 (2000)]. We further examine the quantum-classical boundary by investigating questions of entanglement and Bell-inequality violations for the Einstein-Podolsky-Rosen states relevant to continuous variable teleportation. The threshold fidelity for employing entanglement as a quantum resource in teleportation of coherent states is again found to be $F_{\mathrm{classical}}=\frac{1}{2}.$ Likewise, violations of local realism onset at this same threshold, with the added requirement of overall efficiency $\eta >\frac{2}{3}$ in the unconditional case. By contrast, recently proposed criteria adapted from the literature on quantum-nondemolition detection are shown to be largely unrelated to the questions of entanglement and Bell-inequality violations.

The $\delta$ function gauge of the electromagnetic potential allows semiclassical formulas to be obtained for the probability of exciting a single electron out of the ground state in an ultrarelativistic heavy-ion reaction. Exact formulas have been obtained in the limits of zero impact parameter and large, perturbative, impact parameter. The perturbative impact parameter result can be exploited to obtain a semiempirical cross section formula of the form $\sigma =A\ln \gamma +B$ for single-electron ionization. A and B can be evaluated for any combination of target and projectile, and the resulting simple formula is good at all ultrarelativistic energies. The analytical form of A and B elucidates a result previously found in numerical calculations: scaled ionization cross sections decrease with increasing charge of the nucleus being ionized. The cross section values obtained from the present formula are in good agreement with recent CERN SPS data from a Pb beam on various nuclear targets.

We present a numerical method for solving the Holstein-Biberman-Payne equation with Doppler frequency redistribution. The method is based on direct time propagation of the initial distribution of excited atoms, employing the split-propagation technique. It allows a precise study of various aspects of radiation transfer phenomena occurring in an arbitrary convex three-dimensional spatial region, driven by external conditions with arbitrary time dependencies. We present some results obtained for slab and spherically shaped geometries and compare them to results from other evaluation methods. The efficiency of the method is demonstrated by determining the intensity of radiation escaping the gas cell in afterglow experiments.