We present calculations on electric transport properties of small sodium clusters ${\mathrm{Na}}_N$ $(N<~9),$ based on the Landauer formalism combined with an approximate density-functional approach. For a given cluster size N, the resistance depends sensitively on the cluster geometry (isomers). As a function of cluster size, an even-odd oscillation of the minimal resistance is found.

We investigate a Bell-type inequality for probabilities of detected atoms formulated using atom-photon interactions in a cavity. We consider decoherence brought about by both atomic decay and cavity photon loss, and study its quantitative action in diminishing the atom-field and resultant atom-atom secondary correlations. We show that the effects of decoherence on nonlocality can be observed in a controlled manner in actual experiments involving a micromaser and also a microlaser.

We theoretically study the decoherence of a gas of bosonic atoms induced by the interaction with a largely detuned laser beam. It is shown that for a standing laser beam decoherence coincides with the single-particle result. For a running laser beam reabsorption of photons leads to significant nonlocal many-particle modifications.

Quantum process tomography is a procedure by which the unknown dynamical evolution of an open quantum system can be fully experimentally characterized. We demonstrate explicitly how this procedure can be implemented with a nuclear magnetic resonance quantum computer. This allows us to measure the fidelity of a controlled-NOT logic gate and to experimentally investigate the error model for our computer. Based on the latter analysis, we test an important assumption underlying many models of quantum error correction, the independence of errors on different qubits.

Beyond the no-cloning theorem, the universal symmetric quantum cloning machine was first addressed by Bužek and Hillery. Here, we realized the $\overrightarrow{1}$2 qubit Bužek-Hillery cloning machine with linear optical devices. This method relies on the representation of several qubits by a single photon. We showed that the fidelities between the two output qubits and the original qubit are both $\frac{5}{6}$ (which proved to be the optimal fidelity of $\overrightarrow{1}$2 qubit universal cloner) for arbitrary input pure states.

In the present paper, we investigate the saturation mechanism of FDFWM (forward degenerate four-wave-mixing) spectra, observed with different polarizations of the input beams, line coupling, and Doppler effect. Our theoretical approach uses a nonperturbative resolution of the density matrix equations, decomposed on the irreducible tensor basis. This formalism greatly simplifies analytical expressions and allows for a correct treatment of magnetic sublevels structure in a three-J level system. Systematic calculations of the FDFWM signal for specific NO lines are performed to characterize intensities and line shapes as a function of saturation. Relative intensities exhibit strong changes in the intermediate regime of saturation further supporting the necessity for using such a complete model. Under saturating conditions, line coupling is shown to distort the spectra, according to the type of transition and the polarization configuration. This effect is observed in the following paper [V. Krüger et al., paper II, Phys. Rev. A 2001 (to be published)], where saturated experimental spectra of NO are presented and interpreted for two polarization configurations of interest for diagnostic purposes.

The behavior of forward degenerate four-wave-mixing spectra of NO $Ã-\tilde{X}\mathrm{}(0,0)\mathrm{}$ in the presence of strong optical fields is observed for two crossed-polarization arrangements. The NO features in terms of coupled and isolated lines are interpreted with the complete model described in the preceding paper [V. Krüger et al., paper I, Phys. Rev. 63, 012716 (2001)]. In the intermediate regime of saturation, the variation of relative line intensities with input energy is properly reproduced for NO. Thanks to these fits, we have been able to determine saturation threshold with a good accuracy. Important properties of the different polarization schemes are observed and discussed.

We have measured absolute cross sections for the K-shell ionization of medium- and high-Z targets of Sb, Gd, Yb, Au, and Bi induced by low- to intermediate-velocity F ions having energies between 2.5 and 5.8 MeV/u. Our main interest is to see the effect of the relativistic nature of the K-shell electrons of these target atoms on the ionization cross sections. The information on the degree of relativistic effect has been obtained by comparing the measured data with different theoretical calculations with and without including the relativistic corrections. A comparative study of the two different models such as SCA (semiclassical approximation) and ECPSSR [perturbed stationary state (PSS) including the corrections for energy (E) loss, Coulomb (C) deflection, and relativistic (R) effects] is presented. It is shown that the SCA calculations with the relativistic wave function predict an ionization cross section that is at least an order of magnitude higher compared to that given by the nonrelativistic calculation for Bi target. This factor is reduced to about 2 in the case of Sb. The ECPSSR, however, predicts lower ratios for the relativistic to nonrelativistic calculations. The experimental results, in general, are in good agreement with the SCA calculations using relativistic wave functions as well as with the ECPSSR model. For high-Z targets the SCA gives slightly better agreement with the data compared to the ECPSSR. In addition, it is shown that in the ECPSSR formalism the ionization cross sections of high-Z (with large relativistic effect) as well as low-Z targets (with less relativistic effect) can be scaled approximately to follow a universal curve after including the relativistic correction.

Time-dependent density-functional theory (TDDFT) excitation energies are calculated for ${\mathrm{Zn}}_i{\mathrm{S}}_i$ global minima clusters, $i=1\mathrm{}–9.$ The geometry of the global minima is ringlike for $i=1\mathrm{}–5$ and three-dimensional (3D) spheroidlike for $i=6\mathrm{}–9.$ In general, the calculated excitations happen from nonbonding p orbitals of sulfur. These orbitals are perpendicular to the molecular plane in the case of the rings, and normal to the spheroid surface for 3D clusters. The calculated excitation energies are larger for ringlike clusters as compared to 3D ones, with the excitation energies of the latter structures lying close to the visible spectrum. The difference between Kohn-Sham eigenvalues of the orbitals involved in the electronic excitations studied have also been compared with the TDDFT results of the corresponding excitations for two approximate density functionals, i.e., MPW1PW91 and B3LYP, the latter being more accurate. The B3LYP excitation energies calculated as the difference between Kohn-Sham eigenvalues of the orbitals involved in the excitation have been found to be only 0.30–0.40 eV too high for the smaller 3D-like clusters. Moreover, they approach the TDDFT value as the cluster size increases. Therefore, this might be a practical approach to estimate excitation energies of large ${\mathrm{Zn}}_i{\mathrm{S}}_i$ clusters.

We study the scattering of the quantized electromagnetic field from a linear, dispersive dielectric using the scattering formalism for quantum fields. The medium is modeled as a collection of harmonic oscillators with a number of distinct resonance frequencies. This model corresponds to the Sellmeir expansion, which is widely used to describe experimental data for real dispersive media. The integral equation for the interpolating field in terms of the in field is solved and the solution used to find the out field. The relation between the in and out creation and annihilation operators is found that allows one to calculate the S matrix for this system. In this model, we find that there are absorption bands, but the input-output relations are completely unitary. No additional quantum-noise terms are required.

Propagation of a pulse pair in a nondissipative three-level medium is investigated in the adiabatic-following approximation to a trapped state. The general case of unequal oscillator strengths of two electric dipole transitions in an atom is studied analytically, and the adiabaticity criterion for the matter-field interaction is derived. It is shown that the interaction adiabaticity strongly depends on the relationship between oscillator strengths. A simple expression specifying the critical propagation length at which the stimulated Raman adiabatic passage process is still effective is derived. An estimate of the propagation distance at which a complete energy transfer from the pump pulse into the Stokes pulse occurs is made.

We construct a large number of coherent states satisfying the resolution of unity with a positive weight function, obtained through analytic solutions of the Stieltjes moment problem (coherent states on a plane) and the Hausdorff moment problem (coherent states on a disk). These solutions are obtained through the method of inverse Mellin transform. In addition, these coherent states induce a deformation of the metric that has been calculated analytically.

In this paper we derive the intensity and phase noise spectra of a single-mode semiconductor laser on the basis of an operatorial Langevin set of equations that includes the dynamics of the microscopic variables, i.e., the carrier polarization and their distribution over the k states. In particular we take into account the fact that the carriers pumped into the active layer are subject to the blocking determined by Pauli exclusion principle. We demonstrate that, due to the fastness of the carrier scattering and polarization dephasing processes, the noise spectra can be determined on the basis of a macroscopic linearized set of three equations for the two quadrature components of the laser intensity and the total carrier number. A formal comparison with the paradigmatic results of [Yamamoto et al. Phys. Rev. A 34, 4025 (1986)] allows to deduce that the only essential difference arises from Pauli-induced pump blocking, which has the effect of increasing the low-frequency branch of the intensity noise spectrum. We demonstrate that, even for very small amounts of pump blocking, the low-frequency intensity noise steeply rises with the stationary value of the carrier density in the active layer, which depends on a great number of parameters. This result can explain the erratic behavior of the experimental findings and their discrepancy with the standard theoretical predictions.

Spontaneous emission of an atom with two close upper levels and one lower level in a multilayer dielectric medium, and quantum interference between transitions from the upper levels to the lower one, are considered. Since the medium is inhomogeneous along the direction normal to the interfaces of the dielectric layers, the vacuum has an anisotropic spatial structure, and quantum intereference between the two decay channels can appear even if the two dipole matrix elements are orthogonal to each other. If the atom is placed in a three-layer dielectric plate cavity, a strong quantum interference similar to that for an atom with two nearly parallel dipole moments in free space arises due to the influence of anisotropic vacuum. Putting the atom in a three-layer dielectric waveguide and a one-dimensional photonic crystal, there appears a strong quantum interference similar to that for an atom with nearly antiparallel dipole moments.

In the strong-field regime a single multiphoton resonance can enhance many harmonics of the fundamental laser frequency simultaneously. We demonstrate that an alkali-metal atom driven by an intense, ultrafast midinfrared pulse is an ideal system for observing this effect by calculating the response of potassium atoms to radiation that is nearly three or five photon resonant with the $4s-4p$ transition. We find that all the harmonics through at least the 17th are enhanced over a wide range of intensities, and that the resonance width of the enhanced harmonics is governed by the lifetime of the multiphoton resonance.

We state a quantum version of the Bayes rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state of the N copies is exchangeable. As an illustration, we apply the rule to N qubits. Finally, we show that quantum state estimates derived via the principle of maximum entropy are fundamentally different from those obtained via the quantum Bayes rule.

We discuss the criteria presently used for evaluating the efficiency of quantum teleportation schemes for continuous variables. Using an argument based upon the difference between 1-to-2 quantum cloning (quantum duplication) and 1-to-infinity cloning (classical measurement), we show that a fidelity value larger than 2/3 warrants that the teleported state is the best possible remaining copy of the input state. This value has not been reached experimentally so far.

We show that the highly excited rovibrational spectra of a diatomic molecule and the closely related slow atomic collision processes contain more systematics and require less parameters to characterize than the Rydberg spectrum of an atom. In the case of a single channel, e.g., we show that a single short-range parameter gives a complete description of slow collisions for practically all angular momenta, and covers an energy range of hundreds of millikelvins. The same parameter also describes the highly excited rovibrational spectra in the threshold region, including states of different angular momenta. Sample applications and predictions of the theory are presented, including comparisons with experiment.

We consider the possibility of enhanced cooling of hydrogen atoms by a buffer gas of alkali-metal atoms Na, K, Rb, and Cs. Ultracold elastic collision cross sections for the Na-H and Rb-H purely spin-polarized pairs are found to be 640 and 860 times larger than that for the H-H pair, respectively. From an analysis of the techniques of production of ultracold sodium and rubidium samples, it seems feasible that the critical conditions for Bose-Einstein condensation of hydrogen could be achieved already at the stage of optical cooling of the sodium or rubidium buffer gas.

We derive a direct reconstruction algorithm for the discrete Wigner function through different types of measurements. For a system described in a Hilbert space of dimension ${N=N}_1\dots N_p,$ where the numbers $N_i$ are prime, the reconstruction is accomplished with ${(N}_1+1)\dots {(N}_p+1)$ factorable (local) von Neumann measurements. For the special case where the dimension is a power of a prime, the reconstruction can be performed in a much more efficient way using $N+1\mathrm{}$ complementary measurements. If the system is composed of a number of smaller subsystems, these measurements will then in general be nonseparable.