In this paper is shown an application of Clifford algebras to the construction of computationally universal sets of quantum gates for n-qubit systems. It is based on the well-known application of Lie algebras together with the especially simple commutation law for Clifford algebras, which states that all basic elements either commute or anticommute.

We report results of differential cross sections for elastic scattering, target-elastic Ps excitations, and target-inelastic excitation of hydrogen in a five-state coupled-channel model allowing for $\mathrm{Ps}\mathrm{}\left(1s\right)\mathrm{}\mathrm{H}\mathrm{}(2s,2p)\mathrm{}$ and $\mathrm{Ps}\mathrm{}(2s,2p)\mathrm{}\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ excitations using a recently proposed time-reversal-symmetric regularized electron-exchange model potential. The present model yields a singlet Ps-H S-wave resonance at 4.01 eV of width 0.15 eV and a P-wave resonance at 5.08 eV of width 0.004 eV. We also study the effect of the inclusion of the excited Ps and H states on the convergence of the coupled-channel scheme.

We describe the generation of amplitude- and frequency-modulated light with a modulation frequency equal to the fundamental vibrational frequency of molecular deuterium $\left(2994\mathrm{}{\mathrm{cm}}^{\mathrm{-}1}\approx 90\mathrm{THz}\right).\mathrm{}$ This is a first step toward the synthesis of subfemtosecond pulses with prescribed temporal shape.

The ${5s}^2{}^1{S}_0\to 5s5p{}^3{P}_0$ transition of a single laser-cooled ${}^{115}{\mathrm{In}}^{+}$ ion in a miniature radiofrequency trap is investigated as a possible optical frequency standard. This line at a frequency of 1267 THz (wavelength 236.5 nm) is highly immune to frequency shifts due to external perturbations so that the expected systematic uncertainties can be reduced to the millihertz level. Experimentally, we obtained a fractional resolution $\Delta \nu /\nu =1.3\mathrm{}\times {10}^{-13}$ (linewidth 170 Hz), limited by the frequency instability of the laser used for excitation. The g factor and the lifetime of the metastable ${}^3{P}_0$ level were measured as ${g(}^3{P}_0)=-9.87(5)\mathrm{}\times {10}^{-4}$ and $\tau {(}^3{P}_0)=0.195\mathrm{}(8)\mathrm{}\hspace{0.5em}\mathrm{s}.$ Both values are in good agreement with perturbative calculations, based on hyperfine mixing between the ${}^{1}P$ and ${}^{3}P$ levels.

We obtained coherent states for the hydrogen atom by transforming the problem into four oscillators in the parametric time at a classical level, and quantizing these oscillators by using path integration over their holomorphic coordinates. We showed that for the negative- (positive-) energy coherent states the mean values of the physical position of the electron satisfy the Keplerian ellipses (hyperbolas) and that their dispersions oscillate (increase) in parametric time.

Recent work has extended Bell’s theorem by quantifying the amount of communication required to simulate entangled quantum systems with classical information. The general scenario is that a bipartite measurement is given from a set of possibilities and the goal is to find a classical scheme that reproduces exactly the correlations that arise when an actual quantum system is measured. Previous results have shown that, using local hidden variables, a finite amount of communication suffices to simulate the correlations for a Bell state. We extend this in a number of ways. First, we show that, when the communication is merely required to be finite on average, Bell states can be simulated without any local hidden variables. More generally, we show that arbitrary positive operator valued measurements on systems of n Bell states can be simulated with ${O(n2\mathrm{}}^n)$ bits of communication on average (again, without local hidden variables). On the other hand, when the communication is required to be absolutely bounded, we show that a finite number of bits of local hidden variables is insufficient to simulate a Bell state. This latter result is based on an analysis of the nondeterministic communication complexity of the NOT-EQUAL function, which is constant in the quantum model and logarithmic in the classical model.

The necessary and sufficient condition of the separability of a mixed state of any system is presented, which is practical in judging the separability of a mixed state. This paper also presents a method of finding the disentangled decomposition of a separable mixed state.

We show how a single trapped electron offers the opportunity to realize universal quantum logic gates within the present experimental possibilities. As an example, we propose to implement the Deutsch algorithm by using the quantized cyclotron motion and the electron spin as qubits.

The parameters that determine the nondipole $\left(E1\mathrm{}-E2\right)$ corrections to the photoelectron angular distribution have been investigated for the $s-$ and p-subshells of the noble-gas atoms through comparing results calculated in the Hartree-Fock (HF) approximation and taking into account multielectron correlations, using the random-phase approximation with exchange. Our results cover the photoelectron energy range $\epsilon$ from the photoionization thresholds to 1.6 keV. We find the interesting result that near the photoionization thresholds these parameters are generally characterized by an oscillatory behavior as a function of $\epsilon ,$ exclusive of the parameter for the He $1s$ subshell. These oscillations are sensitive to multielectron correlations, except those of the Ar $3p$ subshell. This finding supports once more that the photoprocesses in these atomic subshells are of a collective character. We conclude that their correct description cannot be achieved within the framework of a one-electron approximation such as the HF approximation. Results are presented and discussed.

The self-energy screening correction is evaluated in a model in which the effect of the screening electron is represented as a first-order perturbation of the self-energy by an effective potential. The effective potential is the Coulomb potential of the spherically averaged charge density of the screening electron. We evaluate the energy shift due to a ${1s}_{1/2},$ ${2s}_{1/2},$ ${2p}_{1/2},$ or ${2p}_{3/2}$ electron screening a ${1s}_{1/2},$ ${2s}_{1/2},$ ${2p}_{1/2},$ or ${2p}_{3/2}$ electron, for nuclear charge Z in the range $5<~Z<~92.$ A detailed comparison with other calculations is made.

The accuracy and effectiveness of various kinetic-energy functionals in providing total noninteracting kinetic energies, atomization kinetic energies, and equilibrium properties is evaluated. Employing converged Kohn-Sham densities, we assess various kinetic-energy functionals in a non-self-consistent manner. It is found that the gradient expansion, the Pearson-Gordon local truncation scheme, and the [4/3]-Padé approximant of DePristo and Kress provide reliable estimates for the total noninteracting kinetic energy. The estimates for the atomization kinetic energy and equilibrium geometries are, however, far from being reliable for chemical applications

The results and main steps of an analytic calculation of radiative-recoil corrections of order $\alpha \left(Z\alpha {)}^5\mathrm{}\right(m/M)m$ to the Lamb shift in hydrogen are presented. The calculations are performed in the infrared safe Yennie gauge. The discrepancy between two previous numerical calculations of these corrections existing in the literature is resolved. Our result eliminates the largest source of the theoretical uncertainty in the magnitude of the deuterium-hydrogen isotope shift.

Using high-precision wave functions describing the ground and excited states of the ${\mathrm{H}}^{-}$ ion, He atom, and heliumlike ions, the cross sections of single- and double-electron photoionization are calculated. The dependence of the ratio R of the double- and single-ionization cross sections on the nuclear charge Z and the principal quantum number of excitation n is studied and compared with the predictions of the high-$Z$ expansion and the high-n shake-off mechanisms.

We report on trapping of fermionic ${}^{40}\mathrm{K}$ atoms in a red-detuned standing-wave optical trap, loaded from a magneto-optical trap. Typically, unpolarized samples of ${10}^6$ atoms are loaded at a density of ${10}^{12}{\mathrm{cm}}^{-3}$ and a temperature of $65\mu \mathrm{K},$ and trapped for more than 1 s. The optical trap appears to be the proper environment for performing collisional measurements on the cold atomic sample. In particular, we measure the spherically averaged elastic collision rate by detecting the rethermalization following an intentional parametric heating of the atoms. We also measure spherically averaged inelastic two-body collision rates for atoms in the ground hyperfine states, through detection of trap losses.

Nonadiabatic transitions between asymptotically degenerate potential curves are discussed. Both crossing and noncrossing two-coupled-Morse-potential systems are studied semiclassically as well as quantum mechanically. Conditions for the appearance of a nonadiabatic transition are clarified. The case of inverse power potentials at infinity is also analyzed. Expressions of nonadiabatic transition probability are obtained.

We analyze the neutralization of low-energy ${\mathrm{He}}^{+}\mathrm{}\left(1s\right)\mathrm{}$ ions interacting with an Al surface under grazing incidence. First, we calculate transition rates for the surface plasmon-assisted mode of ion neutralization. A comparison of these transition rates with Auger rates recently reported in the literature indicates that the collective process is dominant from large to intermediate ion-surface distances. Inclusion of these transition rates into a set of rate equations relevant to the ${\mathrm{He}}^{+}\mathrm{}\left(1s\right)/\mathrm{Al}\mathrm{}\left(111\right)\mathrm{}$ interacting system allows us to compute neutralized fractions and angular distributions of the scattered neutral atoms. Comparison of our results with recent experimental data seems to indicate that proper inclusion of both the Auger and collective surface plasmon rates is essential to explain the experimental results. Finally, a phenomenological rate for transitions into the ground state of He was extracted from experimental angular distributions.

In this paper, we study Stark splitting of a three-level atom in a circularly polarized electromagnetic wave. We calculate energies of splitting levels. Under some special tuning ways and approximation conditions, these energies have simpler forms and display the following general picture of Stark splitting: the levels of a $\Lambda$- or V-type atom are split into six sublevels, while that of a $\Sigma$-type atom is split into nine sublevels. We discuss also the occupation probabilities of splitting levels; they are dependent on initial condition. Under the same tuning ways and approximation conditions, some of them may become zero. Therefore under different initial conditions, practical pictures of Stark splitting are not the same. For example, if the atom is initially in its state 1, the practical picture of Stark splitting is the following: the levels of a $\Lambda$- or V-type atom are split into four sublevels; that of a $\Sigma$-type atom is split into six sublevels. If the atom is initially in its state 2, the practical picture of Stark splitting is the following: the levels of a $\Lambda$- or V-type atom are split into five sublevels, while that of a $\Sigma$-type atom is split into eight sublevels.

A collinear laser-ion beam apparatus has been used to investigate resonance structure in the $\mathrm{Li}{\mathrm{}\left(3s\right)+e}^{-}\mathrm{}\left(\mathrm{kp}\right)\mathrm{}$ partial photodetachment cross section below the $\mathrm{Li}\mathrm{}\left(6p\right)\mathrm{}$ threshold. A complex rotation calculation was used to identify the strongly correlated, doubly excited states of the quasi-two-electron ion ${\mathrm{Li}}^{-}$ that are responsible for the observed resonances. These represent the most highly excited states of ${\mathrm{Li}}^{-}$ observed thus far. Several members of a strong $“+”$ type series were observed as well as at least one resonance with $“-”$ type character. In particular, we report on an observation of a resonance that violates the $\Delta \nu =0\mathrm{}$ propensity rule.

The preparation of SU(2) states as dark states of the motion of a trapped ion is considered. The difficulty in preparing these states is shown to arise from the degeneracy of eigenvalues of the Hamiltonian. This degeneracy is removed by making use of the nonlinearities appearing in the dynamics of an ion that is not well localized. The mechanism of approaching the dark state of interest is analyzed by using the quantum trajectory method.