For two kinetically coupled Morse oscillators, we present details of the method of calculation in Ref. 1 of the semiclassical wave function for an Einstein-Brillouin-Keller quantizing torus, using a single trajectory and its stability matrix. This is the “standard” method, contrasted in Ref. 1 with our new “direct” method, which does not require the calculation of the stability matrix.

The effects of environmental decoherence on a mass-center position of a body consisting of many atoms are studied using a kind of linear quantum Boltzmann equation. It is shown that under realistic laboratory conditions these effects can be essentially eliminated for dust particles containing ${10}^{15}$ atoms. However, the initial velocity distribution and certain geometrical conditions make standard interference-type measurements extremally difficult beyond the nanometer scale. The results are illustrated by the analysis of the recent experiments involving fullerenes. Applications of decoherence effects to precise monitoring of environment or to separation of molecules are suggested.

Recent experimental measurements of the excitation of the $4s$ $J=1\mathrm{}$ fine-structure levels of argon by positron impact have prompted us to carry out calculations for this process. We have used the relativistic distorted-wave method with multiconfiguration Dirac-Fock wave functions for atomic states. Distortion potentials with and without a polarization potential were used. Results obtained for distortion potentials without polarization gave good agreement with the experimental measurements for positron impact energies between 20 and 30 eV.

For the Wigner function of a system in N-dimensional Hilbert space, we propose the condition, which ensures that the Wigner function has correct marginal distributions along tilted lines. Under this condition we get the Wigner function without ambiguity if N is odd. If N is even, the Wigner function does not exist.

The method of iterated resolvents is used to obtain an effective Hamiltonian for neighboring qubits in the Kane solid-state quantum computer. In contrast to the adiabatic gate processes inherent in the Kane proposal we show that free evolution of the qubit-qubit system, as generated by this effective Hamiltonian, combined with single-qubit operations, is sufficient to produce a controlled-NOT gate. Thus the usual set of universal gates can be obtained on the Kane quantum computer without the need for adiabatic switching of the controllable parameters as prescribed by Kane [Nature (London) 393, 133 (1998)]. Both the fidelity and the gate time of this nonadiabatic controlled-NOT gate are determined by numerical simulation.

We present a detailed theoretical analysis of Bragg spectroscopy from a Bose-Einstein condensate at $T=0\mathrm{}\hspace{0.5em}\mathrm{K}.$ We demonstrate that within the linear-response regime, both a quantum-field-theory treatment and a mean-field Gross-Pitaevskii treatment lead to the same value for the mean evolution of the quasiparticle operators. The observable for Bragg spectroscopy experiments, which is the spectral response function of the momentum transferred to the condensate, can therefore be calculated in a mean-field formalism. We analyze the behavior of this observable by carrying out numerical simulations in axially symmetric three-dimensional cases and in two dimensions. An approximate analytic expression for the observable is obtained and provides a means for identifying the relative importance of three broadening and shift mechanisms (mean field, Doppler, and finite pulse duration) in different regimes. We show that the suppression of scattering at small values of q observed by Stamper-Kurn et al. [Phys. Rev. Lett. 83, 2876 (1999)] is accounted for by the mean-field treatment, and can be interpreted in terms of the interference of the u and $v$ quasiparticle amplitudes. We also show that, contrary to the assumptions of previous analyses, there is no regime for trapped condensates for which the spectral response function and the dynamic structure factor are equivalent. Our numerical calculations can also be performed outside the linear-response regime, and show that at large laser intensities a significant decrease in the shift of the spectral response function can occur due to depletion of the initial condensate.

The coherent microwave emission from an optically thick atomic ensemble in a cavity under coherent population trapping is analyzed. Transient and continuous operations are theoretically examined within the frame of a closed three-level system in the Dicke regime. The effects related to the atomic density and to the propagation in the active medium are examined with particular reference to the subnatural linewidth, the low group velocity and the shifts of the maser emission profile from the unperturbed atomic transition. The case of alkali-metal atoms submitted to a Λ excitation scheme is addressed in view of applications in the atomic frequency standard field. Experimental observations in agreement with the theoretical predictions are reported for the case of rubidium in a buffer gas. Apparent superluminal propagation is also reported and briefly discussed.

We have experimentally investigated laser diffraction on electromagnetically induced gratings in a degenerate open two-level system. The experiment employs the standard backward four-wave mixing configuration and the open ${6S}_{1/2}\mathrm{}(F=4\mathrm{})\mathrm{}\to {6P}_{3/2}{(F}^{\prime }=4)$ transition of cold cesium atoms. Population and coherence gratings are accessed for different relative polarizations of the incident laser beams. Natural and subnatural linewidths are observed depending on which frequency of the incident beams is scanned and reveal the effect of the atomic motion on the diffraction spectra. A simple theoretical model using a three-level $\Lambda$ system is in reasonable agreement with the observed results and allowed us to make a close connection with the phenomenon of electromagnetically induced transparency.

According to the theoretical results, the quantum searching algorithm can be generalized by replacing the Walsh-Hadamard transform by almost any quantum-mechanical operation. We have implemented the generalized algorithm using nuclear magnetic resonance techniques with a solution of chloroform molecules. Experimental results show a good agreement between the theory and experiment.

The authors call attention to previous work with related result, a quantum-key-distribution scheme based on partial unknown entanglement with Wigner’s inequality to establish the security of the quantum channel. The sender chooses any entangled state from a certain set or its equivalent state randomly, and sends a sequence of particles out of each pair to the receiver. The two users each choose between two measurements along the fixed axes. In fact, this is a quantum cryptosystem based on mixed entanglement. The main paper was published in Phys. Rev. A 64, 032305 (2001).

The high flux of the gas-phase beamline at the Elettra storage ring, Trieste (Italy), and the efficiency of a multicoincidence end station have been combined to measure the triple-differential cross section (TDCS) for the double photoionization (DPI) of He at excess energies $E=20\mathrm{}$ and 80 eV. The TDCS has been measured in the equal-energy-sharing kinematics, in which the kinetic energies of the two photoelectrons are equal ${(E}_1{=E}_2=E/2).\mathrm{}$ The experiments are compared with the predictions of a many-body Coulomb wave method and a convergent close-coupling calculation. The symmetrized gerade amplitudes of the He (DPI) extracted by the experiments as well as by the two calculations have been fitted by a Gaussian function. The results support the validity of the parametrization of the gerade amplitude via only one parameter, the full width at half maximum ${\vartheta }_{1/2},$ of the Gaussian function, up to 80 eV above threshold.

A theoretical quantum key distribution scheme using Einstein-Podolsky-Rosen (EPR) pairs is presented. This scheme is efficient in that it uses all EPR pairs in distributing the key except those chosen for checking eavesdroppers. The high capacity is achieved because each EPR pair carries 2 bits of key code.

We consider the effects of plasmas on dielectronic-recombination (DR) rates. Effects of plasmas electric fields on DR rates are analyzed in detail in the space of parabolic quantum numbers. A quasiclassical approach is used to obtain general analytical expressions for DR rates in the parabolic basis for arbitrary types of ions having transitions without change of core principal quantum numbers $(\Delta n=0\mathrm{}$ transitions) responsible for the main contribution to DR rates. The approach makes it possible to investigate scaling laws for dependences of both total and differential DR rates on atomic parameters. Effects of electron collisions and ionization are taken into account with the help of cutoff procedures. Numerical data are presented for Li- and Na-like ions under typical plasma conditions. A comparison with numerical calculations for specific ions is presented.

We study one-dimensional (1D) sideband cooling of cesium atoms strongly confined in a far-detuned optical lattice. The Lamb-Dicke regime is achieved in the lattice direction whereas the transverse confinement is much weaker. The employed sideband cooling method, first studied by Vuletić et al., uses Raman transitions between Zeeman levels and produces a spin-polarized sample. We present a detailed study of this cooling method and investigate the role of elastic collisions in the system. We accumulate 83(5)% of the atoms in the vibrational ground state of the strongly confined motion, and elastic collisions cool the transverse motion to a temperature of $2.8\mu \mathrm{K}=0.7\mathrm{}ħ{\omega }_{\mathrm{osc}}{/k}_B,$ where ${\omega }_{\mathrm{osc}}$ is the oscillation frequency in the strongly confined direction. The sample then approaches the regime of a quasi-2D cold gas. We analyze the limits of this cooling method and propose a dynamical change of the trapping potential as a mean of cooling the atomic sample to still lower temperatures. Measurements of the rate of thermalization between the weakly and strongly confined degrees of freedom are compatible with the zero-energy scattering resonance observed previously in weak 3D traps. For the explored temperature range the measurements agree with recent calculations of quasi-2D collisions. Transparent analytical models reproduce the expected behavior for $k_{B}T\gg ħ{\omega }_{\mathrm{osc}}$ and also for $k_{B}T\ll ħ{\omega }_{\mathrm{osc}}$ where the 2D features are prominent.

We investigate the dynamics of a one-dimensional ${\mathrm{H}}_2$ model molecule in strong laser fields by numerical integration of the time-dependent Schrödinger equation without the use of the Born–Oppenheimer approximation. Ionization typically occurs at internuclear separations close to the ground-state equilibrium distance. This is contrary to the case of ${\mathrm{H}}_2^{+},$ which ionizes at larger internuclear distances where charge-resonance-enhanced ionization is possible. Similar to the case of atoms, we find considerable nonsequential double ionization.

We derive quantum evolution equations for the dynamics of dilute condensed Bose gases. The approach contains, at different orders of approximation, for cases close to equilibrium, the Gross-Pitaevskii equation and the first-order Hartree-Fock-Bogoliubov theory. The proposed approach is also suited for the description of the dynamics of condensed gases that are far away from equilibrium. As an example the scattering of two Bose condensates is discussed.

We investigate the self-phase modulation of intense femtosecond laser pulses propagating in an ionizing gas and its effects on collective properties of high-order harmonics generated in the medium. Plasmas produced in the medium are shown to induce a positive frequency chirp on the leading edge of the propagating laser pulse, which subsequently drives high harmonics to become positively chirped. In certain parameter regimes, the plasma-induced positive chirp can help to generate sharply peaked high harmonics, by compensating for the dynamically induced negative chirp that is caused by the steep intensity profile of intense short laser pulses.

The expansion of a Bose-Einstein condensate in an atomic waveguide is analyzed. We study different regimes of expansion, and identify a transient regime between one-dimensional and three-dimensional dynamics, in which the properties of the condensate and its further expansion can be well explained by reducing the transversal dynamics to a two-level system. The relevance of this regime in current experiments is discussed.

Optical pumping of an atomic sample with narrow-band light can create sub-Doppler features, known as Bennett structures, in the velocity distribution of state populations. In the presence of static magnetic or electric fields, the corresponding sub-Doppler features in the index of refraction can cause nonlinear optical rotation and induced ellipticity of resonant light propagating through the atomic medium. Physical mechanisms causing Bennett-structure-related nonlinear electro- and magneto-optical effects are discussed in detail for transitions involving states with low angular momenta. Measurements of Bennett-structure-related nonlinear magneto-optical rotation and electric-field-induced ellipticity for the Rb $D2\mathrm{}$ line are performed and compared to density-matrix calculations. The latter effect can be used for measuring electric fields applied to atoms.

We propose a simple method to generate in practice the most general two-mode states with maximum entanglement. The method is based on energy-conserving dispersive interactions that can be easily implemented in different context such as quantum optical fields, quantum motion of trapped ions, or in Bose-Einstein condensates.