A fully relativistic approach is described for obtaining the resonance contribution to the cross sections for transitions between magnetic sublevels in highly charged ions due to impact with an electron beam. We derive the relativistic distorted-wave cross section for the ion in a lower N-electron magnetic sublevel to capture a directive electron and form a doubly excited $\mathrm{}(N+1\mathrm{})\mathrm{}$-electron magnetic sublevel. Also the autoionization rate from this magnetic sublevel to an N-electron magnetic sublevel is derived. The resonances are then treated as the two-step process of electron capture followed by autoionization to the final sublevel with the effects of autoionization to a different final level or radiative decay of the doubly excited sublevels included. These resonance contributions are added to the relativistic distorted-wave results for the “direct” contribution to give the complete cross section. Numerical results expressed in terms of the collision strengths are calculated and studied for He-like oxygen and iron and for Be-like oxygen. These are of interest for electron beam ion trap experiments and population alignment analysis.

We demonstrate direct loading and cooling of a thermal beam into a cryogenic helium buffer gas. Our test species is rubidium; we observe a thermal beam with $3\times {10}^{13}{\mathrm{s}}^{-1}$ flux entering a cryocell and thermalizing with a 4.2-K buffer gas. There is no evidence of clustering or other spurious loss mechanisms. The cooling technique should be applicable to a wide variety of species, including radicals.

Ultrafast pulse shapes are used to control simultaneously the optimal population transfer coefficients and rotational wave-packet quantum interferences in the $E{}^1{\Sigma }_g^{+}$ state of ${\mathrm{Li}}_2$ $({\nu }_E=9,$ $J_E=27\mathrm{}$ and 29). By dividing the spectral bandwidth of the ultrafast pulses into multiple “control domains” centered on each resonant wavelength, the population transfer coefficients can be manipulated independently of the wave-packet interferences to maximize the ${\mathrm{Li}}_2$ photoionization yield at arbitrary short pump-probe time delays. To investigate the population transfer coefficients with and without wave-packet interferences, respectively, the pump polarization is set to be either parallel to or at the magic angle (∼55°) relative to the probe polarization. A comparison is made between phases that are symmetric and antisymmetric about the resonances. The effects of resonant and nonresonant frequencies are separately established and quantified. It is estimated that up to 90% of the possible nonresonant Rabi oscillations can be brought into phase simultaneously for each rovibrational state in the wave packet, while at the same time a constant phase offset added to one of the control domains establishes the phase of the wave-packet interference.

Intramolecular electronic dynamics and tunnel ionization of ${\mathrm{H}}_2$ in an intense laser field $(I\approx {10}^{14}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ and $\lambda =760\mathrm{}\mathrm{nm})$ are examined with accurate evaluation of three-dimensional two-electron wave-packet dynamics by the dual transformation method. We estimated the ionization probabilities at different values of the internuclear distance R and found that tunnel ionization of ${\mathrm{H}}_2$ is enhanced by field-induced two-electron dynamics. An ionic component characterized by the electronic structure ${\mathrm{H}}^{+}{\mathrm{H}}^{-}$ or ${\mathrm{H}}^{-}{\mathrm{H}}^{+}$ is created near the descending well, where the dipole interaction energy with the laser electric field $\varepsilon \mathrm{}\left(t\right)\mathrm{}$ becomes lower. Ionization proceeds via the formation of a localized ionic component in the descending well, in contrast to the ${\mathrm{H}}_2^{+}$ case, in which the electron is ejected most easily from the ascending well. As R increases, while the population of ${\mathrm{H}}^{-}{\mathrm{H}}^{+}$ (or ${\mathrm{H}}^{+}{\mathrm{H}}^{-})$ decreases, a pure ionic state ${\mathrm{H}}^{-}{\mathrm{H}}^{+}$ becomes easier to ionize in an intense field because of the smallar attractive force of the distant nucleus. As a result, ionization is enhanced at the critical distance $R_c=(4\mathrm{}–{6)a}_0$ ${(a}_0$ is the Bohr radius). Although the rate of direct ionization from a covalent state is much smaller than that from an ionic state, the ionization at large R $(>~{8a}_0)$ mainly proceeds from the remaining covalent component, which outmeasures the created ionic component. Thus, the field-induced intramolecular electron transfer between nuclei, which triggers strong electron-electron correlation, is governed by the molecular structure as well as the field intensity. The mechanism of the ionization enhanced by field-induced intramolecular electron transfer is consistent with the observation of charge-asymmetric dissociation channels of diatomic molecules such as ${\mathrm{N}}^{+}+{\mathrm{N}}^{3+}.$ We also investigated the intramolecular electronic dynamics by analyzing the populations of field-following adiabatic states defined as eigenfunctions of the instantaneous electronic Hamiltonian. An effective instantaneous Hamiltonian for ${\mathrm{H}}_2$ was constructed of three main electronic states, X, $B{}^1{\Sigma }_u^{+}$ and $\mathrm{EF}.\mathrm{}$ We found that the difference in electronic and ionization dynamics between the small R and large R cases originates in the character of the level crossing of the lowest two adiabatic states.

We analyze the influence of an arbitrarily directed uniform magnetic field on the laser sub-Doppler cooling of atoms. The analysis is done for a (3+5)-level atom excited by a ${\sigma }^{+}-{\sigma }^{-}$ laser field configuration. Our analysis shows that the effects of the magnetic field depend strongly on the direction of the magnetic field. In an arbitrarily directed magnetic field the laser cooling configuration produces both the main resonance existing already at zero magnetic field and additional sub-Doppler resonances caused by two-photon and higher-order multiphoton processes. These sub-Doppler resonances are, however, well separated on the velocity scale if the Zeeman shift exceeds the widths of the resonances. This allows one to use the main sub-Doppler resonance for an effective laser cooling of atoms even in the presence of the magnetic field. The effective temperature of the atomic ensemble at the velocity of the main resonance is found to be almost the same as in the absence of the magnetic field. The defined structure of the multiphoton resonances may be of importance for the sub-Doppler laser cooling of atoms, atomic extraction from magneto-optical traps, and applications related to the control of atomic motion.

Using the time-dependent mean-field Gross-Pitaevskii equation we study the dynamics of small repulsive Bose-Einstein condensed vortex states of ${}^{85}\mathrm{Rb}$ atoms in a cylindrical trap with low angular momentum $ħL$ per atom $(L<~6),$ when the atomic interaction is suddenly turned attractive by manipulating the external magnetic field near a Feshbach resonance. Consequently, the condensate collapses and ejects atoms via explosion and a remnant condensate with a smaller number of atoms emerges that survives for a long time. Details of this collapse and explosion are compared critically with a similar experiment performed with zero angular momentum $\mathrm{}(L=0\mathrm{})\mathrm{}$ by Donley et al. [Nature (London) 412, 295 (2001)]. A suggestion for a future experiment with the vortex state is made.

Diffractive optics are used to create low- and high-order Laguerre-Gaussian (LG) beams from the output of a diode laser. We examine the mode purities, conversion efficiencies, extinction ratios, and propagation characteristics. We present detailed analyses of the beam profiles for one low-order $\left({\mathrm{LG}}_0^1\right)$ and one high-order $\left({\mathrm{LG}}_1^2\right)$ Laguerre-Gaussian mode. Modeling the ${\mathrm{LG}}_1^2$ beam as a superposition of LG modes, we find $(99.3\mathrm{}\pm 0.9\%)$ of the laser intensity in the ${\mathrm{LG}}_1^2$ mode, a mode purity greater than for LG beams created by other methods external to the laser cavity. The high mode purity may be useful in making atom traps for precision measurements and for Bose-Einstein condensation.

We present a detailed semiclassical study of the propagation of a pair of optical fields in resonant media with and without the adiabatic approximation. In the case of near- and on-resonance excitation, we show detailed calculations, both analytical and numerical, of the extremely slowly propagating probe pulse and the subsequent regeneration of a pulse via a coupling laser. Further discussions of the adiabatic approximation provide much subtle understanding of the process, including the effect on the bandwidth of the regenerated optical field. We show that the adiabatic condition does not generally predict that the regenerated field will have the same bandwidth as that of the original probe pulse. Indeed, we show analytically that for a set of coupling pulses well satisfying the adiabatic conditions, the regenerated field usually has a different bandwidth from the original probe pulse. For very-far-off resonance excitations, we show that the analytical solution is nearly detuning independent, providing a simple condition is satisfied. This surprising result is vigorously tested and compared to numerical calculations with very good agreement.

We develop a multimode theory of direct homodyne measurements of quantum optical quasidistribution functions. We demonstrate that unbalanced homodyning with appropriately shaped auxiliary coherent fields allows one to sample point-by-point different phase-space representations of the electromagnetic field. Our analysis includes practical factors that are likely to affect the outcome of a realistic experiment, such as nonunit detection efficiency, imperfect mode matching, and dark counts. We apply the developed theory to discuss feasibility of observing a loophole-free violation of Bell’s inequalities by measuring joint two-mode quasidistribution functions by photon counting under locality conditions. We determine the range of parameters of the experimental setup that enable violation of Bell’s inequalities for two states exhibiting entanglement in the Fock basis: a one-photon Fock state divided by a 50:50 beam splitter, and a two-mode squeezed vacuum state produced in the process of nondegenerate parametric down-conversion.

We propose a general construction of an observable measuring the time of occurrence of an effect in quantum theory. Time delay in potential scattering theory is computed as a straightforward application.

This Brief Report presents a corollary to Uhlmann’s theorem which provides a simple operational interpretation of the fidelity of mixed states.

Any charged particle moving faster than light through a medium emits Cherenkov radiation. We show that charged particles moving faster than light through the vacuum emit Cherenkov radiation. How can a particle move faster than light? The weak speed of a charged particle can exceed the speed of light. By definition, the weak velocity $〈\mathbf{v}{〉}_w$ is $〈{\Psi }_{\mathrm{fin}}|\mathbf{v}|{\Psi }_{\mathrm{in}}〉/〈{\Psi }_{\mathrm{fin}}|{\Psi }_{\mathrm{in}}〉,$ where $\mathbf{v}$ is the velocity operator and $|{\Psi }_{\mathrm{in}}〉$ and $|{\Psi }_{\mathrm{fin}}〉$ are, respectively, the states of a particle before and after a velocity measurement. We discuss the consistency of weak values and show that superluminal weak speed is consistent with relativistic causality.

A quantum-mechanical investigation of the vibrational deactivation of ${}^{14}{\mathrm{N}}_2(\nu =1,j_{\mathrm{rot}}=j)$ in the ultracold collisions with ${}^3\mathrm{He}$ atoms is presented. Ab initio potential-energy calculations are carried out at BCCD(T) level and a global three-dimensional potential-energy surface is obtained by fitting ab initio points within the reproducing kernel Hilbert space method. Close coupling scattering calculations are performed at collision energy ranging from ${10}^{-6}$ to 2000 ${\mathrm{cm}}^{\mathrm{-}1}$. It is shown that the potential-energy surface supports a series of shape and Feshbach resonances. Their influence on the behavior of elastic and inelastic cross sections and quenching rate coefficients is discussed. It is demonstrated that, similar to the ${\mathrm{H}\mathrm{e}-\mathrm{O}}_2$ system, the rate coefficients exhibit three different regimes: Wigner regime at very low temperatures, van der Waals regime at intermediate temperatures due to series of resonances, and the usual rovibration–translation energy transfer regime at high temperatures.

We propose a technique for robust and efficient navigation in the Hilbert space of entangled symmetric states of a multiparticle system with externally controllable linear and nonlinear collective interactions. A linearly changing external field applied along the quantization axis creates a network of well separated level crossings in the energy diagram of the collective states.One or more transverse pulsed fields applied at the times of specific level crossings induce adiabatic passage between these states. By choosing the timing of the pulsed field appropriately, one can transfer an initial product state of all N spins into (i) any symmetric state with n spin excitations and (ii) the N-particle analog of the Greenberger-Horne-Zeilinger state. This technique, unlike techniques using pulses of specific area, does not require precise knowledge of the number of particles and is robust against variations in the interaction parameters. We discuss potential applications in two-component Bose condensates and ion-trap systems.

This work considers a generalization of Grover’s search problem, viz., to find any one element in a set of acceptable choices which constitute a fraction f of the total number of choices in an unsorted database. An infinite family of sure-success quantum algorithms are introduced here to solve this problem, each member for a different range of f. The nth member of this family involves n queries of the database, and so the lowest few members of this family should be very convenient algorithms within their ranges of validity. The even member ${\mathcal{A}}_{2n}$ of the family covers an ever larger range of f for larger n, which is expected to become the full range $0<~f<~1$ in the limit $\overrightarrow{n}\infty .$ These algorithms are particularly useful when the cost of failure of a search is very high, and for multistage searches with a different search criterion for each stage.

We report on a theoretical and experimental study of state-selective differential single-electron transfer cross sections between ${\mathrm{Na}}^{+}$ ions and $\mathrm{Rb}\mathrm{}(5s,5p)\mathrm{}$ atoms at collision energies of 2, 5, and 7 keV. A two-center multichannel semiclassical impact parameter close-coupling method with straight-line trajectories was used to obtain single-electron capture amplitudes. By combining with the eikonal approximation, we calculated the angular differential cross sections. These results are compared to the experimental data obtained with Rb targets cooled in a magnetic optical trap. It is shown that there is generally a good agreement between the present calculations and the experiments. In spite of the higher resolution offered from the cold target, the rapid oscillations in the differential cross sections are not resolved by the experiments.

Accurate knowledge of x-ray mass attenuation coefficients is essential for studies as diverse as atomic physics, materials science, and radiation safety. However, a significant discrepancy exists between theoretical tabulated results for air at soft x-ray energies. We outline a precision measurement of the mass attenuation coefficients for air at various energies using two types of detectors and a simple test of detector response. We discuss whether sufficient accuracy can be obtained using this data to distinguish between competing theoretical estimates. In the process, we investigate the intensity response of two common synchrotron x-ray detectors: an x ray to optical charge-coupled device camera using a crystal scintillator and an x-ray sensitive photodiode.

The influence of a high-intensity laser field on the inelastic interactions between a swift molecular ion and a solid target is studied by means of the dielectric theory. Excitations of the electron gas in the solid are described by the linearized hydrodynamic Poisson equations, thus allowing derivation of general expressions for the induced potential in the target and the interaction force among the ions within the molecule, in the presence of the laser field. Based on the numerical solution of the equations of motion for the constituent ions, the Coulomb explosion patterns and the molecular energy losses are discussed for a range of laser parameters.

We demonstrate that the rate constant for the collisional relaxation of $\mathrm{C}{(}^3{P}_1)$ in a buffer gas of He vanishes as the temperature decreases below 1 K. This suggests that the buffer-gas loading technique can be used for trapping excited paramagnetic $\mathrm{C}{(}^3{P}_1)$ atoms at ultracold temperatures.

A fully covariant scheme of renormalization is developed for the evaluation of radiative corrections to the energy levels of atoms and ions in an external magnetic field. Bound-state QED corrections to g factors are calculated for H-like ions in the ground state with nuclear charge numbers $1<~Z<~90$ and for the $\mathrm{ns}$ valence electrons in the atoms Cs, ${\mathrm{Ba}}^{+},$ and Fr. It is shown that these corrections should be taken into account in the comparison with experimental data for neutral atoms.