Zhu and Rabitz [J. Chem. Phys. 109, 385 (1998)] presented a rapidly convergent iterative algorithm for optimal control of the expectation value of a positive-definite observable in a pure-state quantum system. In this paper we generalize this algorithm to a quantum-statistical mechanics setting and show that it is both efficient in the mixed-state case and effective in achieving the control objective of maximizing the ensemble average of arbitrary observables in the cases studied.

We consider the interaction of a quantum system (spin-$\frac{1}{2})$ with a macroscopic quantum apparatus (harmonic oscillator) which in turn is coupled to a bath of harmonic oscillators. Exact solutions of the Markovian master equation show that the reduced density matrix of the system-apparatus combination decoheres to a statistical mixture where up and down spins eventually correlate with pointer states of the apparatus (harmonic oscillator), with associated probabilities in accordance with quantum principles. For the zero-temperature bath these pointer states turn out to be coherent states of the harmonic oscillator (apparatus) for arbitrary initial states of the apparatus. Further, we see that the decoherence time is inversely proportional to the square of the separation between the two coherent states with which the spins correlate. For a high-temperature bath, pointer states no longer remain coherent states but are Gaussian distributions (generalized coherent states). Spin up and down states of the system now correlate with nearly diagonal distributions in position of these generalized coherent states. The diagonalization in position increases with the temperature of the bath. The off-diagonal elements in spin space decohere over a time scale which goes inversely as the square of the separation between the peaks of the two position distributions that correlate with the spin states. Zurek’s earlier approximate result for the decoherence time is consistent with our exact results. Our analysis brings out the importance of looking at a measurementlike scenario where definite correlations are established between the system and apparatus to determine the nature of the pointer basis of the apparatus. Further, our exact results demonstrate in an unambiguous way that the pointer states in this measurement model emerge independent of the initial state of the apparatus.

Electroweak radiative corrections to the matrix elements $〈{\mathrm{ns}}_{1/2}|H_{\mathrm{PNC}}|n^{\prime }{p}_{1/2}〉$ are calculated for highly charged hydrogenlike ions. These matrix elements constitute the basis for the description of the most parity-nonconserving processes in atomic physics. The operator $H_{\mathrm{PNC}}$ represents the parity-nonconserving relativistic effective atomic Hamiltonian at the tree level. The deviation of these calculations from the calculations valid for the momentum transfer $q^2=0\mathrm{}$ demonstrates the effect of the strong field, characterized by the momentum transfer $q^2{=m}_e^2\hspace{0.5em}{(m}_e$ is the electron mass). This allows for a test of the standard model in the presence of strong fields in experiments with highly charged ions.

Grover’s quantum algorithm improves any classical search algorithm. We show how random Gaussian noise at each step of the algorithm can be modeled easily because of the exact recursion formulas available for computing the quantum amplitude in Grover’s algorithm. We study the algorithm’s intrinsic robustess when no quantum correction codes are used, and evaluate how much noise the algorithm can bear with, in terms of the size of the phone book and a desired probability of finding the correct result. The algorithm loses efficiency when noise is added, but does not slow down. We also study the maximal noise under which the iterated quantum algorithm is just as slow as the classical algorithm. In all cases, the width of the allowed noise scales with the size of the phone book as $N^{-2/3}.$

Line shapes observed in photoassociation spectroscopy of ultracold $(T<\mathrm{}1\mathrm{}\mathrm{mK})$ atoms are asymmetric and the peak of the line is shifted by a temperature-dependent amount from the zero-temperature threshold. In principle, calculating the line shape requires a full knowledge of both the ground- and excited-state potentials. We demonstrate here that an approximation based on the Wigner threshold law for scattering yields a relatively simple expression which allows one to extract line positions and linewidths directly from the data. The formula contains a few parameters (threshold frequency, linewidth, temperature, height) and does not require a detailed knowledge of the molecular potentials involved. We illustrate the utility of this approach with examples for Na photoassociation at 500 μK and also discuss the limitations of the approach.

We investigate ortho-positronium–lithium-atom (Ps-Li) scattering using static-exchange and three-Ps-state coupled-channel calculations. The present three-Ps-state scheme, while closely agreeing with the resonance and binding energies in the Ps-H system, predicts $S-,$ $P-,$ and $D$-wave resonances at 4.25 eV, 4.9 eV, and 5.25 eV, respectively, in the electronic spin-singlet channel of Ps-Li scattering. The present calculation also yields a Ps-Li binding in this attractive singlet channel with an approximate binding energy of 0.218 eV, which is in adherence with the recent findings of a chemically stable PsLi system using stocastic variational and quantum Monte Carlo calculations. We further report elastic, $\mathrm{Ps}\mathrm{}\left(2s\right)-,$ and $\mathrm{Ps}\mathrm{}\left(2p\right)\mathrm{}$-excitation cross sections at low to medium energies (0.068–30 eV).

Normalized experimental differential cross sections for the electron impact excitation of the $1{}^2\overrightarrow{S}2{}^{2}S+2\mathrm{}{}^{2}P$ levels of H at 30, 40, 50, 54.4, and 100 eV incident energies are presented. Ratios of scattering intensities of electrons incident on a target mixture of H and He and having excited the H $\mathrm{}(n=2\mathrm{})\mathrm{}$ and He $\mathrm{}(n=2\mathrm{})\mathrm{}$ levels are measured using electron-energy-loss spectroscopy. These intensity ratios are normalized to available, accurate, experimental excitation differential cross sections for He $\mathrm{}(n=2\mathrm{})\mathrm{}$ [except at 54.4 eV, where theoretical He $\mathrm{}(n=2\mathrm{})\mathrm{}$ differential cross sections are used] to obtain relative differential cross sections for electron impact excitation of the H $\mathrm{}(n=2\mathrm{})\mathrm{}$ manifold. The relative H $\mathrm{}(n=2\mathrm{})\mathrm{}$ differential cross sections are placed on an absolute scale by determining the H/He mixture ratio using energy-loss spectra taken at 200 eV and 25° scattering angle, and normalizing to accurate theoretical H $\mathrm{}(n=2\mathrm{})\mathrm{}$ and He $\mathrm{}(n=2\mathrm{})\mathrm{}$ differential cross sections at this energy and scattering angle. Comparisons with available calculations and measurements are made.

Fragmentation and ionization of ${\mathrm{C}}_{60}$ are studied for electron capture and loss collisions of fast ${\mathrm{Li}}^{q+}$ $(q=0\mathrm{}–3)$ projectiles at a velocity $v=3.38\mathrm{}$ a.u. Production cross sections are measured for all observed ions by a time-of-flight method in coincidence with outgoing projectile charge states k. Multifragmentation as well as multiple ionization are observed strongly even for the neutral projectiles. Total production cross sections, summed over all observed ions, are found to be the same order of magnitude for $q<~2,$ indicating that the fragmentation is induced in close collisions, i.e., by penetration of the incident particles through the ${\mathrm{C}}_{60}$ cage. Also, it is found that the total fragmentation cross sections as a function of k show nearly the same shape as the equilibrium charge state distributions (CSD) measured for other condensed materials. This certainly implies that a memory for the initial charge state q is nearly lost while penetrating the cage, and the final CSD is approximately equilibrated.

We have measured the secondary-electron (SE) yield in coincidence with 1–2-MeV ${\mathrm{He}}^{+,2+}$ ions reflected from a SnTe(001) at grazing incidence. Specific ion trajectories, i.e., true specular reflection and subsurface channeling, can be distinguished in the energy spectrum of the reflected ions. By selecting the specific trajectories, above- and below-surface SE production processes are separately studied. The position-dependent SE production rate for 2-MeV ${\mathrm{He}}^{2+}$ is found to be about four times larger than that for 0.5-MeV ${\mathrm{H}}^{+},$ indicating that the SE production rate at the surface is proportional to $q^2.$ Analyzing the SE number distributions for subsurface channeled ions, the mean free path of SE’s in SnTe is estimated to be 0.6 nm.

In this paper we investigate the quantum and classical dynamics of a single trapped ion subject to nonlinear kicks derived from a periodic sequence of Gaussian laser pulses. We show that the classical system exhibits diffusive growth in the energy, or “heating,” while quantum mechanics suppresses this heating. This system may be realized in current single trapped-ion experiments with the addition of near-field optics to introduce tightly focused laser pulses into the trap.

An adiabatic-Floquet formalism is used to study the suppression of ionization in short laser pulses. In the high-frequency limit the adiabatic equations involve only the pulse envelope where transitions are purely ramp effects. For a short-ranged potential having a single-bound state we show that ionization suppression is caused by the appearance of a laser-induced resonance state, which is coupled by the pulse ramp to the ground state and acts to trap ionizing flux.

A technique for determining the quantum state of electronic wave packets from probability distribution measurements is presented. Specifically, a measurement of the fractional probability in each of a wave packet’s constituent eigenstates can be used in conjunction with a measurement of the wave packet’s time-dependent probability distribution to recover the complex amplitude of each constituent eigenstate. The method is demonstrated for radial Rydberg wave packets using previously measured time-dependent probability distributions in coordinate and momentum space. By exploiting delay imaging techniques, it should be possible to retrieve the quantum state of wave packets in real time.

A two-component condensate situated in a cylindrically symmetric harmonic trap is investigated using the Popov approximation. The thermal clouds are treated semiclassically, which allows studies of big condensates at high temperatures. We study the influence of the thermal parts on the condensate stability properties. The results are compared with zero-temperature calculations obtained by the Gross-Pitaevskii equations. In the strongly interacting situation, the thermal parts were found to play an important role for the stability properties of the condensates.

Spectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absorption and dispersion, field generation by four-wave mixing, population modulation, and Zeeman optical pumping are derived. On all these observables, subnatural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited-state population modulation in the $D_2$ line of Rb vapor are presented in good agreement with the calculations.

We report measurements of the absolute yield of 123.6-nm vacuum ultraviolet (VUV) radiation produced in a resonant four-wave-mixing scheme in krypton enhanced by electromagnetically induced transparency. One of the mixing fields, in the ultraviolet (UV) at 212.55 nm, was in two-photon resonance with the ${4p}^6{}^1{S}_0–{4p}^{5}5p[0,\frac{1}{2}]$ transition of krypton, while a second field (the coupling field) at 759 nm was resonant with the ${4p}^{5}5p[0,\frac{1}{2}]{-4p}^{5}5s[1,\frac{1}{2}]$ transition. Electromagnetically induced transparency has been predicted to be induced by this coupling field and to enhance the efficiency of the generation of the field at 123.6 nm, on the ${4p}^{5}5s[1,\frac{1}{2}]$ to ${4p}^6{}^1{S}_0$ transition. This was confirmed by measurements of the absolute VUV radiation yield using a calibrated photodiode in the limit of a large density-length product. Energies of ∼30 nJ were produced, which gave a conversion efficiency, from the coupling field energy of ∼1%. Higher yields are thought to be achievable by increasing the coupling laser intensity, the path length of the medium, and by the use of a transform-limited UV pulse of the same duration as the coupling field.

Pulse propagation through a two-resonance medium was investigated in nuclear forward scattering (NFS) of synchrotron radiation (SR). The SR pulse was coherently transmitted through a target system exhibiting two equivalent resonances, the energy separation of which was varied via the Doppler effect. This allowed a continuous change from a single-resonance medium to a two-resonance system with adjustable splitting. For increasing splitting, the observed time evolutions of NFS changed from a dynamical beat (DB) via hybrid forms of beating into a DB-modulated quantum beat. The experimental results were consistently fitted using a dynamical theory for NFS of SR.

We propose for the experimental verification of an inequality concerning wave-particle duality by Englert [Phys. Rev. Lett. 77, 2154 (1996)] relating (or setting) an upper limit on distinguishability and visibility in a two-way interferometer. The inequality, quantifies the concept of wave-particle duality. The considered two-way interferometer is a Young’s double-slit experiment involving two four-level atoms and is a slightly modified version of that of the recent experiment by Eichmann et al. [Phys. Rev. Lett. 70, 2359 (1993)]. The fringe visibility depends on the detected polarization direction of the scattered light and a read out of the internal state of one of the two atoms provides a partial which-way information.

It is shown that the Schrödinger nonrelativistic equation of a system of interacting particles is not a rigorously nonrelativistic equation since it is based on the implicit assumption of finiteness of the interaction propagation velocity. For a system of interacting particles, a fully nonrelativistic nonlinear system of integro-differential equations is proposed. In the case where the size of the system of particles is of the same order as the Compton wavelength associated with particles, certain essential differences are shown to exist as compared with traditional consequences of the nonrelativistic Schrödinger equation.

We study the Bose-Einstein condensation for a cloud of ${}^7\mathrm{Li}$ atoms with attractive nonlocal (finite-range) interaction in a harmonic trap. In addition to the low-density metastable branch, which is present also in the case of local interaction, a new stable branch appears at higher densities. For a large number of atoms, the size of the cloud in the stable high-density branch is independent of the trap size and the atoms are in a macroscopic quantum self-trapped configuration. We analyze the macroscopic quantum tunneling between the low-density metastable branch and the high-density one by using the instanton technique. Moreover, we consider the decay rate of the Bose condensate due to inelastic two- and three-body collisions.

The trapped Bose system can be regarded as two-dimensional if the thermal fluctuation energy is less than the lowest energy in the perpendicular direction. Under this assumption, we derive an expression for the maximum thickness of an effective two-dimensional trapped Bose system.