One-electron removal in the $p+\mathrm{Na}$ collision system has been investigated at low energy $(4–25\mathrm{keV})$ by means of recoil ion momentum spectroscopy. The focus will be on the contribution of one-electron capture from the Na $2p$ inner shell into the hydrogen ground state, thereby leaving the ${\mathrm{Na}}^{+}$ target ion in an excited state. This process is observed directly in the ${\mathrm{Na}}^{+}$ recoil spectra because it is well separated from contributions of capturing the outer-shell electron. The final ${\mathrm{Na}}^{+}$ excited state population reveals the role of the outer-shell electron in these inner-shell capture processes. A transition from active participation of the outer-shell electron to a passive role as spectator was found to occur around 1.4 times the orbital velocity of the outer-shell electron.

Previous work has shown that if an attractive $1∕r^2$ potential is regularized at short distances by a spherical square-well potential, renormalization allows multiple solutions for the depth of the square well. The depth can be chosen to be a continuous function of the short-distance cutoff $R$, but it can also be a log-periodic function of $R$ with finite discontinuities, corresponding to a renormalization-group (RG) limit cycle. We consider the regularization with a $\delta$-shell potential. In this case, the coupling constant is uniquely determined to be a log-periodic function of $R$ with infinite discontinuities, and an RG limit cycle is unavoidable. In general, a regularization with an RG limit cycle is selected as the correct renormalization of the $1∕r^2$ potential by the conditions that the cutoff radius $R$ can be made arbitrarily small and that physical observables are reproduced accurately at all energies much less than ${\hslash }^2∕m{R}^2$.

A general relation between the phase time (group delay) and the dwell time is derived for relativistic tunneling particles described by the Dirac equation. It is shown that the phase time equals the dwell time plus a self-interference delay which is a relativistic generalization of previous results.

The effects of dissipation on a holonomic quantum computation scheme are analyzed within the quantum-jump approach. We extend to the non-Abelian case the refocusing strategies formerly introduced for (Abelian) geometric computation. We show how double loop symmetrization schemes allow one to get rid of the unwanted influence of dissipation in the no-jump trajectory.

An improved nonlocal resonance model proposed by Čížek, Horáček, and Domcke [J. Phys. B 31, 2571 (1998)] is used for the calculation of cross sections of electron dissociative attachment and vibrational excitation of molecular hydrogen by the impact of low-energy electrons in the range of ${}^2\Sigma _u^{+}$ resonance. The model is based on ab initio data and takes full account of the nonlocality of the effective potential for the nuclear motion. The dissociative attachment cross sections and rate constants are calculated for all target states $(v,J)$ of relevance and compared with other theoretical and experimental data. It is found that the present dissociative attachment cross section calculated under the conditions of the experiment carried out by Schulz and Asundi reproduces the larger of the two values proposed by them, i.e.–$2.8\times {10}^{-21}{\mathrm{cm}}^2$. A detailed discussion of the dissociative attachment cross section as a function of the vibrational and rotational target states is given. Very narrow peaks, with a width of $1\mathrm{meV}$, are observed in the dissociative attachment cross section for large values of the orbital quantum number $J$. These structures are interpreted as shape resonances in ${\mathrm{H}}^{-}+\mathrm{H}$ collision dynamics. It is shown that for large values of $J$ rotational excitation of the hydrogen molecule enhances the dissociative attachment more efficiently than vibrational excitation. The largest dissociative attachment cross section of $28.3\times {10}^{-16}{\mathrm{cm}}^2$ is obtained for $v=1$ and $J=29$. The process of vibrational excitation will be discussed in a separate paper.

A comparative study of the resonant charge-transfer process of ${\mathrm{H}}^{-}$ in front of plane-model Cu surfaces of symmetries (111) and (100) is performed using a two-dimensional Crank-Nicholson wave-packet propagation approach. Very different electron evolutions near the two surfaces are related to different structures of the respective band gaps and allow for the visualization of electronic interaction mechanisms. It is shown that electrons get localized near the Cu(111) surface due to the reflectivity imposed by the band gap. This enables considerable recapture by the ion. In contrast, ${\mathrm{H}}^{-}$ is neutralized more efficiently near Cu(100), for which the surface state is embedded in the bulk valence band. Image states are found to be important intermediaries for charge transfer at smaller ion-surface distances. As a consequence of all these effects, the dynamics of ion neutralization near (111) and (100) surfaces vastly differ to yield quite dissimilar ion-survival probabilities. It is found that while the ion-surface interaction time becomes important at normal incidence, for near-grazing incidences, the point of closest approach to the surface is a crucial determinant of the ion survival.

We present a complete multiphoton classification of prethreshold structures in measured microwave ionization data of hydrogen Rydberg atoms. We show that fourth-order quasienergy perturbation theory reproduces the locations of prethreshold structures, thus proving that prethreshold structures are a perturbative effect. Additional prethreshold structures are predicted to occur at field and frequency values, to our knowledge, not yet explored experimentally.

We compute the spatial population statistics for one-dimensional Fermi gases and for Bose gases with hard-core repulsions in periodic potentials. We show how the statistics depend on the atomic density in the ground state of the system, and we present calculations for the dynamical turn-on of the potential.

We study two-photon resonant nondegenerate four-wave mixing (NFWM) in a dressed cascade four-level system. In the presence of a strong coupling field, the two-photon resonant NFWM spectrum exhibits Autler-Townes splitting, accompanied by either suppression or enhancement of the NFWM signal. Such phenomena are demonstrated in Ba through inducing of atomic coherence between the ground state $6s^2$ and the doubly excited autoionizing Rydberg state $6pnd$. This technique provides a spectroscopic tool for measuring not only the resonant frequency and dephasing rate but also the transition dipole moment between two highly excited atomic states.

A single-photon Fock state has been generated by means of conditional preparation from a two-photon state emitted in the process of spontaneous parametric down-conversion. A recently developed high-frequency homodyne tomography technique has been used to completely characterize the Fock state by means of a pulse-to-pulse analysis of the detectors' difference photocurrent. The density matrix elements of the generated state have been retrieved with a final detection efficiency of about 57%. A comparison has been performed between the phase-averaged tomographic reconstructions of the Wigner function as obtained from the measured density-matrix elements and from a direct Abel transform of the homodyne data. The ability of our system to work at the full repetition rate of the pulsed laser $\left(82\mathrm{MHz}\right)$ substantially simplifies the detection scheme, allowing for more “exotic” quantum states to be generated and analyzed.

We show the possible stable soliton generation for the dark-state polaritons in an electromagnetically induced transparency medium composed of $\Lambda$-type atoms. Whether the solitons are dark or bright can be controlled by the coupling field intensity and the one-photon detuning of the probe field. The velocity, spatial, and time widths of the solitons can also be adjusted by the coupling light.

We present, and analyze thoroughly, a highly symmetric and efficient scheme for the determination of a single-qubit state, such as the polarization properties of photons emitted by a single-photon source. In our scheme there are only four measured probabilities, just enough for the determination of the three parameters that specify the qubit state, whereas the standard procedure would measure six probabilities.

We show that efficient quantum computation is possible using a disordered Heisenberg spin-chain with “always-on” couplings. Such disorder occurs naturally in nanofabricated systems. Considering a simple chain setup, we show that an arbitrary two-qubit gate can be implemented using just three relaxations of a controlled qubit, which amounts to switching the on-site energy terms at most 21 times.

We report a value for the $D_2$-line frequency of ${}^{39}\mathrm{K}$ with $0.28\mathrm{ppb}$ uncertainty. The frequency is measured using an evacuated ring-cavity resonator whose length is calibrated against a reference laser. The $D_2$ line presents a problem in identifying the line center because the closely spaced energy levels of the excited state are not resolved. We use computer modeling of the measured spectrum to extract the line center and obtain a value of $391015578.040\left(110\right)\mathrm{MHz}$. In conjunction with our previous measurement of the $D_1$ line, we determine the fine-structure interval in the $4P$ state to be $1729997.132\left(120\right)\mathrm{MHz}$. The results represent significant improvement over previous values.

We propose a trap for confining cold neutral atoms in a microscopic ring using a magnetoelectrostatic potential. The trapping potential is derived from a combination of a repulsive magnetic field from a hard drive atom mirror and the attractive potential produced by a charged disk patterned on the hard drive surface. We calculate a trap frequency of $[29.7,42.6,62.8]\mathrm{kHz}$ and a depth of $[16.1,21.8,21.8]\mathrm{MHz}$ for [${}^{133}\mathrm{Cs}$, ${}^{87}\mathrm{Rb}$, ${}^{40}\mathrm{K}$], and discuss a simple loading scheme and a method for fabrication. This device provides a one-dimensional potential in a ring geometry that may be of interest to the study of trapped quantum degenerate one-dimensional gases.

We theoretically investigate the dynamics of a matter-wave soliton created in a harmonic potential, which is attractive in the transverse direction but expulsive in the longitudinal direction. This Bose-Einstein-condensate (BEC) bright soliton made of ${}^7\mathrm{Li}$ atoms has been observed in a recent experiment [Khaykovich et al., Science 296, 1290 (2002)]. We show that the nonpolynomial Schrödinger equation, an effective one-dimensional equation we derived from the three-dimensional Gross-Pitaevskii equation, is able to reproduce the main experimental features of this BEC soliton in an expulsive potential.

We argue that a full account of the set of quantum states prevents one from applying the rigorous definition of complete positivity. However, we give three equivalent proofs that any quantum evolution of a finite system always admits a Kraus-type decomposition, i.e., a Kraus decomposition but with Kraus matrices dependent on the initial state upon which they apply.

We perform an analysis of recent experimental measurements and improve the lithium interaction potentials. For ${}^6\mathrm{Li}$ a consistent description can be given. We discuss theoretical uncertainties for the position of the wide ${}^6\mathrm{Li}$ Feshbach resonance, and we present an analytic scattering model for this resonance, based on the inclusion of a field-dependent virtual open-channel state. We predict new Feshbach resonances for the ${}^6\mathrm{Li}\text{−}{}^7\mathrm{Li}$ system, and their importance for different types of crossover superfluidity models is discussed.

Linear maps of matrices describing the evolution of density matrices for a quantum system initially entangled with another are identified and found to be not always completely positive. They can even map a positive matrix to a matrix that is not positive, unless we restrict the domain on which the map acts. Nevertheless, their form is similar to that of completely positive maps. Only some minus signs are inserted in the operator-sum representation. Each map is the difference of two completely positive maps. The maps are first obtained as maps of mean values and then as maps of basis matrices. These forms also prove to be useful. An example for two entangled qubits is worked out in detail. The relation to earlier work is discussed.

Systematic errors in quantum operations can be the dominating source of imperfection in achieving control over quantum systems. This problem, which has been well studied in nuclear magnetic resonance, can be addressed by replacing single operations with composite sequences of pulsed operations, which cause errors to cancel by symmetry. Remarkably, this can be achieved without knowledge of the amount of error $ϵ$. Independent of the initial state of the system, current techniques allow the error to be reduced to $O\left({ϵ}^3\right)$. Here, we extend the composite pulse technique to cancel errors to $O\left({ϵ}^n\right)$, for arbitrary $n$.