We apply quantum-defect theory to study low-energy ground-state atomic collisions, including aligned dipole interactions such as those induced by an electric field. Our results show that coupled even-$l$ relative orbital angular momentum partial-wave channels exhibit shape resonance structures while odd-$l$ channels do not. We analyze and interpret these resonances within the framework of multichannel quantum defect theory.

In this paper, we present results on the energy loss of ${\mathrm{H}}_3$ molecules in ${\mathrm{SiO}}_2$ films with thickness ranging from 2.5 to 50 nm. For this purpose, we have used the resonant ${}^{18}\mathrm{O}(p,\alpha {)}^{15}\mathrm{N}$ nuclear reaction at 151.2 keV with atomic and molecular ${\mathrm{H}}_3$ beams. This reaction is particularly suitable in the present study, since the width of the resonance peak is only 50 eV. The experimental results show the maximum values of interference effects so far observed: $R\approx 1.8-2.1$ for the lowest thickness range of 2.5–7.0 nm. Calculations based on the dielectric formalism are in good agreement with the experimental data.

The formalism developed in a previous paper is used to predict the line shape of the $1S-2S$ transition in cold, magnetically trapped hydrogen. The presence of the inhomogeneous trapping magnetic field introduces shifts and broadenings to the spectral line. The understanding of the line shape is important for ultrahigh-precision measurements in trapped hydrogen, particularly for the proposed test of CPT violation through the comparison of hydrogen with antihydrogen.

The case is considered of a weak Gaussian harmonic pulse of frquency $\mathrm{}(2s+1)\mathrm{}\omega$ passed through an atomic medium collinearly with an intense Gaussian laser pulse of frequency $\omega .$ The harmonic beam may be amplified or deamplified according to the balance between stimulated emission and absorption. A simple analytic expression for the gain is derived in the tunneling limit of ionization. It predicts a positive (negative) gain for positive (negative) delay of the harmonic pulse with respect to the laser pump pulse. The gain may be significant and proportional to the delay for delays of a few laser periods, much shorter than the pulse envelopes. Possibilities for experimental observations are briefly discussed.

Coherent control of a physical or chemical process can be achieved by using phase and amplitude modulated femtosecond laser pulses. A self-learning loop, which connects a femtosecond pulse shaper, an optimization algorithm, and an experimental feedback signal, can automatically steer the interaction between system and electric field and allows control even without any knowledge of the Hamiltonian. The dependability of such a loop is essential to the significance of the optimization results, assigning the optimization algorithm an important role within these learning loops. In this paper, an evolutionary strategy is presented in detail that has successfully been applied to femtosecond pulse shaping in optimal control experiments. A general introduction to evolutionary algorithms is given and the specific adaptation for femtosecond pulse shaping is described. The stability and effectiveness of the algorithm is investigated both in experiments and simulations with an emphasis on the influence of steering parameters of the algorithm, number of configurations in search space, and noise. The algorithm optimizes a set of variables parametrizing the electric field. This particular mapping greatly facilitates the dissection of the optimization goal which is demonstrated by three possible parametrizations and associated applications: polynomial phase functions and adaptive femtosecond pulse compression, periodic phase functions and control of nonlinear photon transitions, multiple pulse structures and control of molecular dynamics.

We consider (2+1)-dimensional beams, whose transverse size may be comparable to or smaller than the carrier wavelength, on the basis of an extended version of the nonlinear Schrödinger equation derived from Maxwell’s equations. As this equation is very cumbersome, we also study, in parallel, its simplified version, which keeps the most essential term, namely the term that accounts for the nonlinear diffraction. The full equation additionally includes terms generated by a deviation from the paraxial approximation and by a longitudinal electric-field component in the beam. Solitary-wave stationary solutions to both the full and simplified equations are found, treating the terms that modify the nonlinear Schrödinger equation as perturbations. Within the framework of the perturbative approach, a conserved power of the beam is obtained in an explicit form. It is found that the nonlinear diffraction affects stationary beams much stronger than nonparaxiality and longitudinal field. Stability of the beams is directly tested by simulating the simplified equation, with initial configurations taken as predicted by the perturbation theory. The numerically generated solitary beams are always stable and never start to collapse, although they display periodic internal vibrations, whose amplitude decreases with the increase of the beam power.

We show how group symmetries can be used to reconstruct quantum states. The method we propose is presented in the context of the two-mode SU(1,1) states of the radiation field. In our scheme for SU(1,1) states, the input field passes through a nondegenerate parametric amplifier and one measures the probability of finding the output state with a certain number (usually zero) of photons in each mode. The density matrix in the Fock basis is retrieved from the measured data by the least-squares method after singular value decomposition of the design matrix followed by Tikhonov regularization. Several illustrative examples involving the reconstruction of a pair coherent state, a Perelomov coherent state, and a coherent superposition of pair coherent states are considered.

Maximum-likelihood estimation is applied to the determination of an unknown quantum measurement. The calibrated measuring apparatus carries out measurements on many different quantum states and the positive operator-valued measure governing the measurement statistics is then inferred from the collected data via the maximum-likelihood principle. In contrast to the procedures based on linear inversion, our approach always provides a physically sensible result. We illustrate the method on the case of the Stern-Gerlach apparatus.

We report the results of high-resolution infrared laser photodetachment threshold experiments on the negative ion of bismuth. The hyperfine structure of the neutral and negative-ion ground states are included in the threshold model. The electron affinity of ${}^{209}\mathrm{Bi}$ is determined to be $7600.66\left(10\right)\mathrm{}\hspace{0.5em}{\mathrm{cm}}^{-1}$ [942.362(13) meV].

It is important to study the behavior of a t-error-correcting quantum code when the number of errors is greater than t because it is likely that there are also small errors besides t large correctable errors. We estimate the fidelity of a t-error-correcting stabilizer code over a general memoryless channel, allowing more than t errors. We also show that the fidelity can be made arbitrary close to $1$ by increasing the code length.

The fidelity of quantum cloning is very often limited by the accompanying unwanted transitions. We show how the fidelity can be improved by using a coherent cycling field to inhibit the unwanted transitions. We demonstrate this explicitly in the context of the model of Simon et al. [J. Mod. Opt. 47, 233 (2000); Phys. Rev. Lett. 84, 2993 (2000)]. We also investigate the effects of the number of atoms on the quality of quantum cloning. We show the state dependence of the scheme, however all the input states of the qubit can be cloned equally well by choosing the cycling field accordingly.

The photoionization cross section of Be from ${1s}^2{2s2p}^1{P}^o$ is studied with the saddle-point complex-rotation method for photon energies from 23 to 117 eV. A full-core plus correlation wave function is used for the initial states. In the continuum, the energy and width for the singly core-excited Be-like ${1s2s2p}^2{}^{1}S,{}^{1}P,$ and ${}^{1}D$ states are calculated to high precision for systems with $Z=4\mathrm{}–10.$ The Auger decay branching ratios of these states are studied to check the spin alignment theory recently proposed by Chung. These results are compared with the available experimental data in the literature.

We consider the nondistortion quantum interrogation of an atom prepared in a quantum superposition. By manipulating the polarization of the probe photon and making connections to interaction-free measurements of opaque objects, we show that nondistortion interrogation of an atom in a quantum superposition can be done with efficiency approaching unity. However, if any component of the atom’s superposition is completely transparent to the probe wave function, a nondistortion interrogation of the atom is impossible.

We present an ab initio three-dimensional quantum study of the coherent control of high-order harmonic generation (HHG) processes in intense pulsed laser fields by means of the genetic algorithm optimization of the laser-pulse amplitude and phase. Accurate time-dependent wavefunction and HHG power spectrum are obtained by the time-dependent generalized pseudospectral method and wavelet transform is used to obtain the dynamical phase associated with the dipole-emission time profile. It is shown that “intra-atomic” dynamical phase matching on the sub-optical cycle, attosecond, time scale can be achieved, leading to nearly perfect constructive interference between different returning electronic wave packets and marked improvement in both emission intensity and purity of a given harmonic order.

Choosing four entangled states to form an orthogonal and complete basis for a two-particle system, we argue that a local hidden variable model should give the probability of each entangled state if the two-particle system is described by a mixed state. Under these conditions, a Bell inequality is derived for the Werner states, and a nonlocality proof can be given for nonsequential measurements.

Unambiguously distinguishing between nonorthogonal but linearly independent quantum states is a challenging problem in quantum information processing. In principle, the problem can be solved by mapping the set of nonorthogonal quantum states onto a set of orthogonal ones, which then can be distinguished without error. Such nonunitary transformations can be performed conditionally on quantum systems; a unitary transformation is carried out on a larger system of which the system of interest is a subsytem, a measurement is performed, and if the proper result is obtained the desired nonunitary transformation has been performed on the subsystem. We show how to construct generalized interferometers (multiports), which when combined with measurements on some of the output ports, implement nonunitary transformations of this type. The input states are single-photon states in which the photon is divided among several modes. A number of explicit examples of distinguishing among three nonorthogonal states are discussed, and the networks that optimally distinguish among these states are presented.

In many candidate designs of solid-state quantum computers, interactions between qubits are limited to a small number of neighboring qubits. Taking into account this limitation we describe how quantum algorithms can be executed efficiently on these designs. We illustrate our results with the quantum Fourier transform for which linear depth networks are obtained. The concepts presented in this work can be applied to all quantum algorithms to reduce considerably the coherence time needed for their execution.

When a superposition $\left(|\alpha 〉-|-\alpha 〉\right)$ of two coherent states with opposite phase falls upon a 50-50 beam splitter, the resulting state is entangled. Remarkably, the amount of entanglement is exactly 1 ebit, irrespective of α, as was recently discovered by Hirota and Sasaki [LANL e-print quant-ph/0101018]. Here we discuss decoherence properties of such states and give a simple protocol that teleports one qubit encoded in Schrödinger cat states.

A partial-differential eigenvalue equation for the density displacement fields associated with electronic excitations is derived in the framework of density-functional theory. Our quantum fluid-dynamical approach is based on a variational principle and the Kohn-Sham ground-state energy functional, using only the occupied Kohn-Sham orbitals. It allows for an intuitive interpretation of electronic excitations in terms of intrinsic local currents that obey a continuity equation. We demonstrate the capabilities of this nonempirical approach by calculating the photoabsorption spectra of small sodium clusters. The quantitative agreement between theoretical and experimental spectra shows that even for the smallest clusters, the resonances observed experimentally at low temperatures can be interpreted in terms of density vibrations.

Measurements of the photoelectron angular-distribution asymmetry parameter $\beta$ for Xe $5s$ photoionization have been performed in the 80–200 eV photon-energy region. The results show a substantial deviation from the nonrelativistic value of $\beta =2\mathrm{}$ and provide a clear signature of significant relativistic effects in interchannel coupling.