Recently two methods have been developed for the quantization of the electromagnetic field in general dispersing and absorbing linear dielectrics. The first is based upon the introduction of a quantum Langevin current in Maxwell’s equations [T. Gruner and D.-G. Welsch, Phys. Rev. A 53, 1818 (1996); Ho Trung Dung, L. Knöll, and D.-G. Welsch, Phys. Rev. A 57, 3931 (1998); S. Scheel, L. Knöll, and D.-G. Welsch, Phys. Rev. A 58, 700 (1998)], whereas the second makes use of a set of auxiliary fields, followed by a canonical quantization procedure [A. Tip, Phys. Rev. A 57, 4818 (1998)]. We show that both approaches are equivalent.

By studying high-precision ion yield measurements in diatomic molecules ${\mathrm{N}}_2$ and NO with 30-fs linearly (LP) and circularly (CP) polarized light, we extend to molecular systems the study of ellipticity effects on both single and double ionization in strong laser fields. Competing ionization rates between LP and CP light, as predicted in the Ammosov-Delone-Krainov model, is observed experimentally by studying singly ionized ${\mathrm{N}}_2$ and NO. We further observe an anomalously high ${\mathrm{NO}}^{2+}$ signal with CP, which shows a nonsequential ionization signature. A hypothesis is given that ties this observation to the influences of electronic structure on ellipticity effects in strong-field ionization.

Classical dynamics is formulated as a Hamiltonian flow in phase space, while quantum mechanics is formulated as unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and classical nonlinear dynamics. Previous solutions have focused on computing quantities associated with a statistical ensemble such as variance or entropy. However a more direct comparison would compare classical predictions to the quantum predictions for continuous simultaneous measurement of position and momentum of a single system. In this paper we give a theory of such measurement and show that chaotic behavior in classical systems can be reproduced by continuously measured quantum systems.

Experimental and theoretical values for the lifetimes of the ${6s6p}^1{P}_1$ and ${}^3{P}_1$ levels in the Hg isoelectronic sequence are examined in the context of a data-based isoelectronic systematization. New beam-foil measurements for lifetimes in Pb III and Bi IV are reported and included in a critical evaluation of the available database. These results are combined with ab initio theoretical calculations and linearizing parametrizations to make predictive extrapolations for ions with $84<~Z<~92.$

Higher-order $(\alpha /\pi {)}^2(Z\alpha {)}^6$ logarithmic corrections to the hydrogen Lamb shift are calculated. The results obtained show the two-loop contribution has a very peculiar behavior and significantly alter the theoretical predictions for low-lying S states.

We introduce an analytical method to investigate radiation trapping problems with Doppler frequency redistribution. The problem is formulated within the framework of the Holstein-Biberman-Payne equation. We interpret the basic integro-differential trapping equation as a generalized wave equation for a four-dimensional (4D) classical system (an associated quasiparticle). We then construct its analytical solution by a semiclassical approach, called the geometrical quantization technique (GQT). Within the GQT, it is shown that the spatial and frequency variables can be separated and that the frequency part of the excited atom distribution function obeys a stationary Schrödinger equation for a perturbed oscillator. We demonstrate that there is a noticeable deviation of the actual spectral emission profile from the Doppler line in the region of small opacities. The problem of calculating the spatial mode structure and the effective radiation trapping factors is reduced to the evaluation of wave functions and quantized energy values of the quasiparticle confined in the vapor cell. We formulate the quantization rules and derive the phase factors, which allow us to obtain analytically the complete spectrum of the trapping factors in 1D geometries (layer, cylinder, sphere) and other (2D and 3D) geometries when the separation of space variables is possible. Finally, we outline a possible extension of our method to treat radiation trapping effects for more general experimental situations including, for instance, a system of cold atoms.

We describe an efficient and robust method for producing an entangled state of a two-spin system, using a sequence of two pulse pairs. We show that the mixing angle of the entangled state has a purely geometrical origin, so it is insensitive to small variations of the time-integrated pulse amplitude.

The Wigner representation of angular-momentum orientation in the classical limit on $J\gg 1$ has been used to derive an equation of angular-momentum motion in the case of a closed two-level system interacting with an arbitrary polarized radiation. This equation enables us to carry out a theoretical analysis of angular-momentum motion and consider final states of the quantum system for all types of dipole transitions. We have found that in the case of a zero magnetic field in the final state of the system with $\overrightarrow{J}J$ or $\overrightarrow{J}J+1\mathrm{}$ optical transition, the angular momentum is directed along or opposite to the wave vector of the radiation depending on the sign of the polarization ellipsity, while for a linear polarization the angular momentum is isotropically distributed on the plane orthogonal to the polarization vector. For the $\overrightarrow{J}J-1$ transition two directions of angular momentum are possible in the final state. These directions are determined by the ellipsity of polarization. The spatial size of the final distribution of the angular momentum has been defined by the quantum uncertainty, $1/\sqrt{J},$ of the angular-momentum orientation. In the case of the $\overrightarrow{J}J-1$ or $\overrightarrow{J}J,$ transition particles come into “dark” states while for the $\overrightarrow{J}J+1\mathrm{}$ transition they occupy the “brightest” state. In the presence of a nonzero magnetic field, particles with $\overrightarrow{J}J$ transition have in the final state only one angular-momentum orientation, i.e., along or opposite to the direction of the magnetic field depending on the polarization ellipsity sign. For the $\overrightarrow{J}J+1\mathrm{}$ transition both directions are possible, i.e., along and opposite to the magnetic field. In the case of the $\overrightarrow{J}J-1$ transition the directions of the angular momentum form a cone around the magnetic field.

A numerical method of calculating the non-Markovian evolution of a driven atom radiating into a structured continuum is developed. The formal solution for the atomic reduced density matrix is written as a Markovian algorithm by introducing a set of additional, virtual density matrices which follow, to the level of approximation of the algorithm, all the possible trajectories of the photons in the electromagnetic field. The technique is perturbative in the sense that more virtual density matrices are required as the product of the effective memory time and the effective coupling strength becomes larger. The number of density matrices required is given by $3^M$ where M is the number of time steps per memory time. The technique is applied to the problem of a driven two-level atom radiating close to a photonic band gap and the steady-state correlation function of the atom is calculated.

We study the linear and nonlinear optical properties of autoionizing systems under the action of a single-laser field. It is found that the group velocity is greatly reduced by the presence of a neighboring autoionizing state. Conditions for self-focusing or defocusing are also derived for the case of an isolated autoionizing system.

We present a setup for quantum secret sharing based on energy-time entanglement. In opposition to known implementations using three particle Greenberger-Horne-Zeilinger (GHZ) states, our idea takes advantage of only two entangled photons created via parametric down conversion. However, the system comprising the pump plus the two down-converted photons bare the same quantum correlation and can be used to mimic three entangled qubits. The relatively high coincidence count rates found in our setup enable for the first time an application of a quantum communication protocol based on more than two qubits.

Total cross sections for single-electron loss of ${\mathrm{N}}^{+}$ ions impinging on Ne, Kr, and Xe were measured in the energy range from 1.5 to 5.0 keV. The measured electron-loss cross sections show a monotonically increasing behavior as a function of energy of the incident beam for all the targets studied. Our results are compared with previous experimental data and are found to be in excellent agreement.

We present a simple method for creating a maximal coherent superposition of N states (a superposition state with equal amplitudes) in a robust way. We show that in the adiabatic limit the robustness of the population transfer out of a single state to the superposition state is equivalent to stimulated Raman adiabatic passage. As is typical for schemes based upon population trapping the method is insensitive to radiative decay from excited states.

For an ion in a Paul trap, the effect of the micromotion on the heating by stray electric fields is studied analytically. A sequence of unitary transformations, set up from the solutions to the classical dynamics, leads to the exact quantum time propagator for each realization of the random classical field; subsequently, a statistical average is performed to obtain the fidelity of the motional ground state. In this nonperturbative approach, the role of the micromotion in the depopulation is understood as an effective change in the time dependence of the external field and an intrinsic modulation of the heating rate; it is shown that the consequent enhanced complexity of the dynamics can result in a reduction of the heating time.

We present a simple Fokker-Planck model for the evolution of the number of atoms and the spatial distribution in a ${\mathrm{CO}}_2$ laser trap which is loaded from a magneto-optical trap (MOT). Deep ${\mathrm{CO}}_2$ laser traps can achieve very high densities, but reach equilibrium slowly compared to shallow traps. Equilibrium times range from milliseconds for shallow traps to seconds in traps which are deep compared to the thermal energy. A universal function for the maximum number of trapped atoms is given, assuming that the optical dipole trap reaches thermal equilibrium with the MOT.

The quasidegeneracy approximation [V. A. Yurovsky, A. Ben-Reuven, P. S. Julienne, and Y. B. Band, J. Phys. B 32, 1845 (1999)] is used here to evaluate transition amplitudes for the problem of curve crossing in linear potential grids involving two sets of parallel potentials. The approximation describes phenomena, such as counterintuitive transitions and saturation (incomplete population transfer), not predictable by the assumption of independent crossings. Also, a new kind of oscillations due to quantum interference (different from the well-known Stückelberg oscillations) is disclosed, and its nature discussed. The approximation can find applications in many fields of physics, where multistate curve crossing problems occur.

In this paper we study the properties of Bose-Einstein condensates in shallow traps. We discuss the case of a Gaussian potential, but many of our results also apply to the traps having a small quadratic anharmonicity. We show the errors introduced when a Gaussian potential is approximated with a parabolic potential; these errors can be quite large for realistic optical trap parameter values. We study the behavior of the condensate fraction as a function of trap depth and temperature and calculate the chemical potential of the condensate in a Gaussian trap. Finally we calculate the frequencies of the collective excitations in shallow spherically symmetric and one-dimensional traps.

The correlation effects of sixth order on cascade three-level polarization beats are investigated using chaotic field, phase-diffusion, and Gaussian-amplitude models. The polarization beat signal is shown to be particularly sensitive to the statistical properties of the Markovian stochastic light fields with arbitrary bandwidth. Different stochastic models of the laser field only affect the sixth- and fourth-order coherence functions. The constant background of the beat signal originates from the amplitude fluctuation of the Markovian stochastic fields. The Gaussian-amplitude field shows fluctuations larger than the chaotic field, which again exhibits fluctuations much larger than for the phase-diffusion field with pure phase fluctuations caused by spontaneous emission. The cases that the pump beams have either narrowband or broadband linewidth are considered and it has been found that for both cases a Doppler-free precision in the measurement of the energy-level difference of the excited states can be achieved. The sixth-order coherence function theory is of vital importance in cascade three-level polarization beats.

We show how a control of the dynamics of a decay process can be achieved by the application of a series of $2\pi$ pulses on an auxiliary transition. The $2\pi$ pulse changes the phase of the ground state by $\pi$ while leaving the phase of the excited state unaltered. This produces quantum interferences between the transition amplitudes for evolution in the short interval, just before and after the $2\pi$ pulse. Such an interference under suitable tailoring of the density-of-states of the bath and the time $\tau$ leads to accelerated decay.

The propensity of molecules to spatially align along the polarization vector of intense, pulsed light fields is related to readily accessible parameters (molecular polarizability, moment of inertia, peak intensity, and pulse duration of the light). It is possible to predict which molecules can be spatially aligned, and under what circumstances, upon exposure to intense light. Accounting for both enhanced ionization and hyperpolarizability, it is shown that all molecules can be aligned, even those with the smallest static polarizability, when subjected to ultrashort pulses of sufficient intensity.