A deep, narrow interference minimum that exists for symmetric noncoplanar $\mathrm{}(e,2e)\mathrm{}$ ionization experiments, first discovered in helium, has now been found in neon. In helium, the $1s$ electron is ionized, whereas in neon, the minimum is observed ionizing the inner $2s$ electron. The depth of the measured minima indicates that a simple, underlying coherent process is occurring in the reaction.

The time-independent Schrödinger problem for the ${\mathrm{H}}^{\mathrm{-}}$ plus ac field system has been solved from first principles via the nonperturbative many-electron, many-photon theory (MEMPT) for a wide range of values of frequency ω and of intensity I of linearly polarized light. The calculations obtained the multiphoton electron detachment rates (MPEDRs) as the imaginary part of a complex eigenvalue and were done for combinations of values of ω and of I defining regimes of “weak” and of “strong” fields. Most of the results cover the cases of two-, three-,…, seven-photon electron detachment, studied as a function of frequency and of intensity. However, special cases, such as the one of $I=2\mathrm{}\times {10}^{11}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ for the ${\mathrm{CO}}_2$ frequency of 0.117 eV, represent detachment processes into various symmetries requiring the absorption of at least 25 photons. The MEMPT results were obtained without any empirical adjustment of energies or of basis sets. The dressed-atom resonance wave function consisted of optimized function spaces for the initial and final states, including the lowest ${}^{1}S,$ ${}^1{P}^o,$ and ${}^{1}D$ doubly excited states (DES). The initial state was represented by a ten-term numerical multiconfigurational Hartree-Fock wave function whose energy, -0.5275 a.u., is very close to the exact one, -0.5277 a.u., and which accounts self-consistently for electron correlation as well as for the proper magnitude of the $1s$ orbital at large values of r. The ${\mathrm{H}}^{\mathrm{-}}\mathrm{\hspace{0.5em}}\mathrm{DES}$ wave functions were correlated, yielding accurate energies. However, their presence does not affect the results at all. The results converged well when 15 photon blocks were used. In spite of the large number of absorbed photons required in cases such as the ${\mathrm{CO}}_2$ frequency, the calculations converged well, within the numerical accuracy of the algorithms, by using free-electron angular momenta with 1 up to 7. The systematic quantitative study of the dependence of the MPEDRs on ω and I has led to conclusions as to the behavior at thresholds and as to the limits of validity of the predictions of the lowest-order perturbation theory. An interesting result is the appearance of intensity-dependent structures in the two-, four-, and six-photon detachment rates, which is caused by the interference of the ${}^{1}S$ and ${}^{1}D$ channels. For a number of $(I,\omega )$ pairs, comparison is possible with published results obtained by earlier large-scale calculations which either started from first principles or used parametrized one-electron models. Overall, there is good agreement. We conclude that the current level of theoretical knowledge of the ${\mathrm{H}}^{\mathrm{-}}\mathrm{MPEDR}$ spectrum is very satisfactory for a large set of experimentally possible laser parameters.

We have computed multiphoton ionization rates for He irradiated by a dichromatic ac field consisting of the fundamental wavelength $\lambda =248\mathrm{}\mathrm{nm}$ and its second-, third-, and fourth-higher harmonics. The intensities are in the range $1.0\times {10}^{12}–3.5\times {10}^{14}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2,$ with the intensity of the harmonics being 1–2 orders of magnitude smaller. The calculations incorporated systematically electronic structure and electron correlation effects in the discrete and in the continuous spectrum, for ${}^{1}S,$ ${}^{1}P,$ ${}^{1}D,$ ${}^{1}F,$ ${}^{1}G,$ and ${}^{1}H$ two-electron states of even and odd parity. They were done by implementing a time-independent, nonperturbative many-electron, many-photon theory which obtains cycle-averaged complex eigenvalues, whose real part gives the field-induced energy shift, $\Delta ({\omega }_1{,F}_1;{\omega }_2{,F}_2,{\phi }_2),$ and the imaginary part is the multiphoton ionization rate, $\Gamma ({\omega }_1{,F}_1;{\omega }_2{,F}_2,{\phi }_2),$ where ω is the frequency, F is the field strength, and ${\phi }_2$ is the phase difference. Through analysis and computation we show that, provided the intensities are weak, the dependence of $\Gamma ({\omega }_1{,F}_1;{\omega }_2{,F}_2,{\phi }_2)$ on ${\phi }_2$ is simple. Specifically, for odd higher harmonics, Γ varies linearly with $\cos \left({\phi }_2\right)$ whilst for even higher harmonics it varies linearly with $\cos \left(2\mathrm{}{\phi }_2\right).\mathrm{}$ These relations may turn out to be applicable to other atomic systems as well, and to provide a definition of the weak-field regime in the dichromatic case. When the combination of $\left({\omega }_1{,F}_1\right)$ and $\left({\omega }_2{,F}_2\right)$ is such that higher powers of $\cos \left({\phi }_2\right)$ and $\cos \left(2\mathrm{}{\phi }_2\right)$ become important, these rules break down and we reach the strong-field regime.

Enhancement of the production of cold molecules via photoassociation is considered for the ${\mathrm{Cs}}_2$ system. The employment of chirped picosecond pulses is proposed and studied theoretically. The analysis is based on the ability to achieve impulsive excitation which is given by the ultracold initial conditions where the nuclei are effectively stationary during the interaction with a field. The appropriate theoretical framework is the coordinate-dependent two-level system. Matching the pulse parameters to the potentials and initial conditions results in full Rabi cycling between the electronic potentials. By chirping the laser pulse, adiabatic transfer leading to the population inversion from the ground to the excited state is possible in a broad and tunable range of internuclear distance. Numerical simulations based on solving the time-dependent Schrödinger equation (TDSE) were performed. The simulation of the photoassociation of ${\mathrm{Cs}}_2$ from the ground ${}^3{\Sigma }_u^{+}$ to the excited $0_g^{-}$ state under ultracold conditions verifies the qualitative picture. The ability to control the population transfer is employed to optimize molecular formation. Transfer of population to the excited $0_g^{-}$ surface leaves a void in the nuclear density of the ground ${}^3{\Sigma }_u^{+}$ surface. This void is either filled by thermal motion or by quantum “pressure” and it is the rate-determining step in the photoassociation. The spontaneous-emission process leading to cold-molecules is simulated by including an optical potential in the TDSE. Consequently, the rate of cold molecule formation in a pulsed mode is found to be larger than that obtained in a continuous-wave mode.

We investigate the hydrodynamic low-frequency oscillations of highly degenerate Fermi gases trapped in anisotropic harmonic potentials. Despite the lack of an obvious spatial symmetry the wave equation turns out to be separable in elliptical coordinates, similar to a corresponding result established earlier for Bose condensates. This result is used to give an analytical solution of the anisotropic wave equation for the hydrodynamic modes.

We have formulated a kinetic theory for a condensed atomic gas in a trap, i.e., a generalized Gross-Pitaevskii equation, as well as a quantum-Boltzmann equation for the normal and anomalous fluctuations [R. Walser et al., Phys. Rev. A 59, 3878 (1999)]. In this paper, the theory is applied to the case of an isotropic configuration and we present numerical and analytical results for the reversible real-time propagation, as well as irreversible evolution towards equilibrium.

We theoretically investigate the use of red-detuned Laguerre-Gaussian (LG) laser beams of varying azimuthal mode index for producing toroidal optical dipole traps in two-dimensional atomic Bose-Einstein condensates. Higher-order LG beams provide deeper potential wells and tighter confinement for a fixed toroid radius and laser power. Numerical simulations of the loading of the toroidal trap from a variety of initial conditions are also given.

We discuss the mechanisms of decoherence of a confined Bose-Einstein condensate at finite temperatures under the explicit condition of conservation of the total number of bosons, N, in the trap. A criterion for the irreversible decay of the condensate two-time correlator is formulated in terms of the orthogonality catastrophe (OC) for the exact N-body eigenstates, so that no irreversible decay occurs without the OC. If an infinite external bath contacts a finite condensate, the OC should practically always occur as long as the bath degrees of freedom are interacting with each other. We find that, if no external bath is present and the role of the bath is played by the normal component, no irreversible decay occurs. We discuss the role of the effect of level repulsion in eliminating the OC. At finite temperatures, the time correlations of the condensate isolated from the environment are dominated by reversible dephasing which results from the thermal ensemble averaging over realizations of the normal component. Accordingly, the correlator exhibits Gaussian decay with a certain decay time ${\tau }_d$ which depends on the temperature as well as on the intensity of the shot noise determined by the statistical uncertainty in the number of bosons, N, in the trap.

We present experimental evidence that the outputs in two unidirectionally coupled semiconductor lasers with an external cavity, when operated in the regime of low-frequency fluctuations, are synchronized in their dropout events but remain uncorrelated in the process of power recovery. We characterize such synchronized cyclic motions by measuring the difference of their Hilbert phases and entropy index. Our analysis of the coupled Lang-Kobayashi equations in a master-slave configuration attributes the observed phenomenon to the different dynamical behavior of the slave laser in the buildup and plateau regions in phase space; the local unstable orbits are robust against coupling in the former but more susceptible to intervention in the latter.

Previous studies on five-wave mixing processes based on Gaussian pulses were restricted to dephasing times shorter than any light pulse duration of the pump and probe beams. Therefore, they do not allow an analysis of the dephasing processes taking place on the bonding mode of the molecular adsorbates. Here we give a description of time-resolved profiles obtained from pumped sum-frequency generation spectroscopy which is valid over the full range of the dephasing times. This enables a detailed analysis of the dephasing processes acting on the adsorbate bonding mode. In particular, we show that pure dephasing processes acting on different vibrational transitions can be analyzed by adopting different resonant conditions for the infrared probe beam. Also, the high sensitivity of the sum-frequency generation signal intensity to the dephasing constants and to the relative values of the field amplitudes is stressed. The model correctly reproduces the experimental data obtained on the C-H stretching modes of hydrogen-terminated $\mathrm{F}/\mathrm{C}\mathrm{}\left(111\right)-(1\mathrm{}\times 1).$

The notion of the Trojan state of a Rydberg electron, introduced by I. Bialynicki-Birula, M. Kaliński, and J. H. Eberly [Phys. Rev. Lett. 73, 1777 (1994)] is extended to the case of an electromagnetic field quantized in a cavity. The shape of the electronic wave packet describing the Trojan state is practically the same as in the previously studied externally driven system. The fluctuations of the quantized electromagnetic field around its classical value exhibit strong squeezing. The emergence of Trojan states in the cylindrically symmetrical system is attributed to spontaneous symmetry breaking.

We unitarily transform the Hamiltonian of a trapped ion, situated at any position of a standing-wave laser field, to that for the normal Jaynes-Cummings model in the bare ionic basis, and we obtain the general evolution operator of the trapped ion system. We show the existence of super-revivals of the ionic inversion if the trapped ion is not located at a node of the standing wave, and we examine the degree of entanglement between the vibrational phonons and the trapped ion. For some parameter values, we find chaotic behavior.

It is well known that the result of any phase measurement on an optical mode made using linear optics has an introduced uncertainty in addition to the intrinsic quantum phase uncertainty of the state of the mode. The best previously published technique [H. M. Wiseman and R. B. Killip, Phys. Rev. A 57, 2169 (1998)] is an adaptive technique that introduces a phase variance that scales as $n^{-1.5},$ where $\mathrm{n̄}$ is the mean photon number of the state. This is far above the minimum intrinsic quantum phase variance of the state, which scales as $n^{-2}.$ It has been shown that a lower limit to the phase variance that is introduced scales as $\ln \left(\mathrm{n̄}\right)/n^2.$ Here we introduce an adaptive technique that attains this theoretical lower limit.

We show that a qubit chosen from equatorial or polar great circles on a Bloch sphere can be remotely prepared with one cbit from Alice to Bob if they share one ebit of entanglement. Also we show that any single-particle measurement on an arbitrary qubit can be remotely simulated with one ebit of shared entanglement and communication of one cbit.

A model of three-level laser, in which the pumping excites the atoms from the lower lasing level, is considered. The statistical properties of the field are calculated using full quantum treatment. It is shown that apart from threshold there is additional critical value of the pump rate, at which the laser field behaves in a phase-transition-like manner: the photon number drops down, the Fano factor has a strong peak, the relative photon number variance grows enormously, and the second-order coherence function jumps to 2, which is typical for thermal light.

Dielectronic recombination (DR) of ${\mathrm{Li}}^{+}$ ions in the metastable $1s2s{}^{3}S$ state has been calculated by using the close-coupling R-matrix method and perturbation theory, and compared with the high-resolution experiment. Good agreement has been shown. The occurrence of the experimental double peak structure at energies of 0.1–0.2 eV can be surprisingly attributed to relativistic effects. A very strong radiation damping effect on the resonances in the second peak position was discovered. Furthermore, in the ${1s2p(}^{1}P)nl$ $(n=5\mathrm{}-7)$ resonance energy region, our calculations have displayed that the contribution to DR from high-angular-momentum $\mathrm{}(l>\mathrm{}3\mathrm{})\mathrm{}$ configurations is very small. This point is markedly different from the result of Saghiri et al. [Phys. Rev. A 60, R3350 (1999)].

A quantum theory of ultrahigh-order harmonic generation is presented that generalizes the Lewenstein model into the relativistic regime. Various effects appear in the harmonic spectrum: a multiplateau structure in the weakly relativistic case; for stronger fields, the interference pattern familiar from the nonrelativistic case disappears, the height of the plateau decreases towards high harmonic orders, and the cutoff is lower compared to the nonrelativistic case. All of these features are explained in terms of relativistic quantum trajectories.

We study the valence electron of an alkaline atom or a general charged particle with arbitrary spin and with magnetic moment moving in a rotating magnetic field. By using a time-dependent unitary transformation, the Schrödinger equation with the time-dependent Hamiltonian can be reduced to a Schrödinger-like equation with a time-independent effective Hamiltonian. Eigenstates of the effective Hamiltonian correspond to cyclic solutions of the original Schrödinger equation. The nonadiabatic geometric phase of a cyclic solution can be expressed in terms of the expectation value of the component of the total angular momentum along the rotating axis, regardless of whether the solution is explicitly available. For the alkaline atomic electron and a strong magnetic field, the eigenvalue problem of the effective Hamiltonian is completely solved, and the geometric phase turns out to be a linear combination of two solid angles. For a weak magnetic field, the same problem is solved partly. For a general charged particle, the problem is solved approximately in a slowly rotating magnetic field, and the geometric phases are also calculated.

We describe and analyze numerically schemes (i) for entangling orthogonal motional modes of one or a few harmonically trapped atoms or ions and (ii) for transferring the entanglement from one of these local modes to a distant trapped atom (or atoms) via a light-mediated quantum-state transfer procedure proposed in previous work [A.S. Parkins and H.J. Kimble, J. Opt. B: Quantum Semiclass. Opt. $1,$ 496 (1999)]. Possibilities arising from these schemes include the generation of an Einstein-Podolsky-Rosen state in the positions and momenta of distantly separated trapped atoms and the preparation of delocalized mesoscopic vibrational states.

A single-particle entangled state can be generated by illuminating a beam splitter with a single photon. Quantum teleportation utilizing such a single-particle entangled state can be successfully achieved with a simple setup consisting only of linear optical devices such as beam splitters and phase shifters. Application of the locality assumption to a single-particle entangled state leads to Bell’s inequality, a violation of which signifies the nonlocal nature of a single particle.