High-order harmonic pulse durations are measured using a laser and vacuum ultraviolet cross-correlation technique and the results are compared to theory. Harmonic pulses generated using moderate laser intensity are well described by current models and demonstrate that harmonic pulses are temporally broadened when produced at laser intensities sufficiently high to ionize the medium. At even higher generating laser intensity, measured pulse durations are longer than simulated pulse durations. We consider dipole emission from ions and distortion of the spatial laser profile as possible causes for the discrepancy.

Low-intensity white light was used to increase the loading rate of ${}^{87}\mathrm{Rb}$ atoms into a vapor-cell magneto-optic trap by inducing nonthermal desorption of Rb atoms from the stainless-steel walls of the vapor cell. An increased Rb partial pressure reached a new equilibrium value in fewer than 10 s after switching on the broadband light source. After the source was turned off, the partial pressure returned to its previous value in $1/e$ times as short as 10 s.

We describe an experiment in which $3\times {10}^7\hspace{0.5em}\mathrm{Cs}$ atoms are loaded into a $400\hspace{0.5em}\mu \mathrm{m}$ crossed beam far-off-resonant trap (FORT) that is only $2\hspace{0.5em}\mu \mathrm{K}$ deep. A high-density sample is prepared in a magneto-optic trap, cooled in a three-dimensional far-off-resonant lattice (FORL), optically pumped into the lowest-energy state, adiabatically released from the FORL, magnetically levitated, and transferred to the final trap with a phase-space density of ${10}^{-3}.$ Spontaneous emission in the FORT is negligible, and we have compressed the atoms in the FORT to a spatial density of $2\times {10}^{13}\hspace{0.5em}{\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}/\mathrm{c}\mathrm{m}}^3.$ Evaporative cooling under these conditions proceeds rapidly.

We discuss the dynamics of ultracold atoms in an optical potential accelerated by gravity. The positions and widths of the Wannier-Stark ladder of resonances are obtained as metastable states. The metastable Wannier-Bloch states oscillate in a single band with the Bloch period. The width of the resonance gives the rate transition to the continuum.

We construct three-dimensional solutions of Maxwell’s equations that describe Gaussian light beams focused by a strong lens. We investigate the interaction of such beams with single atoms in free space and the interplay between angular and quantum properties of the scattered radiation. We compare the exact results with those obtained with paraxial light beams and from a standard input-output formalism. We put our results in the context of quantum information processing with single atoms.

A scheme for engineering quantum interference in a $\Lambda$-type atom coupled to a frequency-tunable, single-mode cavity field with a preselected polarization at finite temperature is proposed. Interference-assisted population trapping, population inversions, and probe gain at one sideband of the Autler-Townes spectrum are predicted for certain cavity resonant frequencies.

A simple approach is presented for approximating Lamb shifts, the leading quantum electrodynamical (QED) effects, in molecules containing light elements. The Lamb-shift contributions to the electronic energies are estimated from scaled nuclear and electronic Darwin terms. QED effects on the rovibrational states of water are found to be significantly larger than current experimental uncertainties, and only one order of magnitude smaller than current computational uncertainties.

The time-dependent Dirac equation is solved numerically on a space-time grid for an atom in a strong static magnetic field and a laser field. The resonantly induced relativistic motion of the atomic electron leads to a ringlike spatial probability density similar to the features that have been recently predicted [Wagner, Su, and Grobe, Phys. Rev. Lett. 84, 3282 (2000)] based on a phase-space method. We further demonstrate that spin-orbit coupling for a fast-moving electron in such an atom becomes significant and the time dependence of the spin can dephase even if initially aligned parallel to the direction of the static magnetic field.

It is often asserted that quantum effects can be observed in coincidence detection rates or other correlations, but never in the rate of single-photon detection. We observe nonclassical interference in a singles rate, thanks to the intrinsic nonlinearity of photon counters. This is due to a dependence of the effective detection efficiency on the quantum statistics of the light beam. Such measurements of detector response to photon pairs promise to shed light on the microscopic aspects of silicon photodetectors, and on general issues of quantum measurement and decoherence.

We show that errors are not generated correlatedly provided that quantum bits do not directly interact with (or couple to) each other. Generally, this no-qubit-interaction condition is assumed except for the case where two-qubit gate operation is being performed. In particular, the no-qubit-interaction condition is satisfied in the collective decoherence models. Thus, errors are not correlated in the collective decoherence. Consequently, we can say that current quantum error correcting codes that correct single-qubit errors will work in most cases including the collective decoherence.

The concept of the “generalized transition moment” is extended beyond the region of applicability of the first Born approximation and is used in the analysis of electron energy-loss spectra for ${\mathrm{O}}_2,$ presented here, which have been measured at intermediate impact energies. A coupled-channel theoretical treatment of the strongly mixed Rydberg and valence states that dominate the optically allowed spectrum is used to explain the relative intensities of many unusual features occurring in the 7–11.2-eV energy-loss region. For these electronically excited states of ${}^3{\Sigma }_u^{-}$ and ${}^3{\Pi }_u$ symmetry, the evolution of the shape of the corresponding electron energy-loss spectrum as the scattering conditions are changed is controlled essentially by one parameter: the ratio of the diabatic generalized transition moments into the Rydberg and valence components of the mixed electronic states. The generalized Rydberg transition moment is found to decrease much faster than the valence moment as the momentum transferred in the collision increases. The results of the coupled-channel analysis also indicate that the more diffuse spectral features are generally asymmetric, those in the 7–9.8-eV region changing slightly in position as the scattering conditions are altered. Thus, the Gaussian–line-shape-based models that have been employed previously in attempts to decompose the diffuse part of the electron energy-loss spectrum for ${\mathrm{O}}_2,$ into contributions from different electronic states, are unlikely to have given meaningful results. As a consequence of the Rydberg-valence interactions, it is found that some vibrational levels of the mixed states give rise to features in the electron energy-loss spectrum which are anomalously strong at the low impact energies and large scattering angles for which normal optically allowed transitions are expected to decline in relative strength. These “persistent lines” are easily confused with those from the optically forbidden transitions which increase in relative intensity under such conditions. Thus, the coupled-channel technique is found to be a valuable aid to the assignment of features in the electron energy-loss spectrum.

The vortex configurations in the Bose-Einstein condensate of a mixture of two different spin states $|{F=1,m}_f=-1〉$ and $|2,1〉$ of ${}^{87}\mathrm{Rb}$ atoms corresponding to the recent experiments by Matthews et al. [Phys. Rev. Lett. 83, 2498 (1999)] are considered in the framework of the Thomas-Fermi approximation as functions of $N_2{/N}_1,$ where $N_1$ is the number of atoms in the state $|1,-1〉$ and $N_2$ in the state $|2,1〉.$ Ranges of this ratio are determined within which the various configurations of the binary condensate are stable.

We present a numerically tractable method to solve exactly the evolution of a N boson system with binary interactions. The density operator of the system $\rho$ is obtained as the stochastic average of particular operators $|{\Psi }_1〉〈{\Psi }_2|$ of the system. The states $|{\Psi }_{1,2}〉$ are either Fock states $|N:{\phi }_{1,2}〉$ or coherent states $|\mathrm{coh}:{\phi }_{1,2}〉$ with each particle in the state ${\phi }_{1,2}\mathrm{}\left(x\right).$ We determine the conditions on the evolution of ${\phi }_{1,2},$ which involves a stochastic element, under which we recover the exact evolution of $\rho .$ We discuss various possible implementations of these conditions. The well known positive P representation arises as a particular case of the coherent state ansatz. We treat numerically two examples: a two-mode system and a one-dimensional harmonically confined gas. These examples, together with an analytical estimate of the noise, show that the Fock state ansatz is the most promising one in terms of precision and stability of the numerical solution.

Dilute rubidium gases at submicrokelvin temperatures offer the possibility of exceptionally small and negative group velocities. We devise an experimental scheme in which nearly dispersionless and highly superluminal pulse propagation at optical frequencies can be observed. Comparisons with other schemes and potential applications are briefly discussed.

A new physical scheme for femtosecond x-ray lasers, where the upper lasing level ${(L}_{23}$ innershell vacancy level) is pumped by x-ray photons and the lower lasing level ${(M}_1$ innershell vacancy level) is depopulated via a Coster–Kronig radiationless transition, is analyzed for Ca. The transition wavelength is 4.1 nm, which is inside the water window (the wavelength range between the K absorption edges of oxygen and carbon). The peak spectral brightness of the x-ray laser output at 4.1 nm is predicted to be as large as $5\times {10}^{25}{\mathrm{p}\mathrm{h}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{n}\mathrm{s}/\mathrm{s}/(\mathrm{m}\mathrm{m}}^2{\mathrm{}\mathrm{mrad}}^2\mathrm{}0.1\%\mathrm{}\mathrm{bandwidth}),$ which is 4 to 5 orders of magnitude brighter than a typical undulator radiation in the similar spectral region. In addition to the high flux, the expected duration of x-ray lasing of ∼3 fs will be useful for the study of fast dynamics in physical and biological sciences.

We study the collinear propagation of two weak sideband fields in a far-off-resonance Raman medium driven by a strong field. We show the existence of two sideband-field superpositions called normal modes that propagate independently at different group velocities, one at the vacuum speed of light and one at a reduced velocity and with an induced relative phase shift. We find that the effect of slow group velocity on nonlinear conversion occurs via the relative group delay as well as the relative phase shift.

Pattern formation in cavity nonlinear optical systems subjected to a periodic modulation of frequency detuning is studied analytically and numerically with particular reference to the models of optical parametric oscillator and two-level laser. Owing to the nonautonomous dynamics, a new mechanism for pattern formation as a result of a primary instability, rather distinct from the most common tilted-wave mechanism found in autonomous systems, is predicted and explained in detail by means of a phase integral (WKB) analysis of the underlying field equations. This mechanism for pattern formation can be traced back to the existence of coherent field oscillations in the two-field dynamics and associated to the existence of turning points in the WKB expansion, which break the adiabatic following. In particular, it is shown that nonadiabatic effects are likely when the decay rates of interacting fields are equal, corresponding to the existence of real turning points. For different relaxation rates of interacting fields, the turning points are complex and nonadiabatic effects vanish at low modulation frequencies. Above threshold, weakly nonlinear analysis and numerical simulations indicate that traveling waves are selected by the nonlinearity.

We demonstrate that the classical helium atom exhibits algebraic decay of the survival probability in the autoionizing $\mathrm{eZe}$ configuration. Excitation towards asymptotic orbits of marginal stability is identified as the cause of the nonexponential decay. Since one electron travels along a bound Kepler trajectory of infinite excitation in these orbits, we argue that the classical decay law will prevail in the quantum dynamics of a wave packet launched along the $\mathrm{eZe}$ configuration.

The population transfer in a $\Lambda$-like system, with intermediate states belonging to the continuous spectrum, is investigated in the case in which continuum-continuum and nonresonant transitions must be taken into account. The two phenomena are shown to essentially influence the dynamics of the system, in particular the final populations of the discrete states. The transfer probability can be increased if the two components of the pulse are shifted in time in a counterintuitive way, but unlike in the typical case of STIRAP, it is an oscillating function of the time delay.

In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for nondissipative quantum systems imposes kinematical bounds on the optimization of arbitrary observables. We summarize our previous results on kinematical bounds and show that these bounds are dynamically realizable for completely controllable systems. Moreover, we establish improved bounds for certain partially controllable systems. Finally, the question of dynamical realizability of the bounds for arbitrary partially controllable systems is shown to depend on the accessible sets of the associated control system on the unitary group $U\left(N\right)\mathrm{}$ and the results of a few control computations are discussed briefly.