We have measured absolute dissociative electron attachment cross sections for $\mathrm{H}X$ and $\mathrm{D}X$ ($X=\mathrm{Cl}$ and Br) using a trochoidal electron spectrometer equipped with a total ion collection collision chamber, operated both in a field-free passive ion collection mode, and an active ion collection mode, with an extracting electric field. Our results for ${\mathrm{Br}}^{-}$ from HBr are in an excellent quantitative agreement with recent predictions of the nonlocal resonance model, but the cross sections for ${\mathrm{Cl}}^{-}$ from HCl and DCl are, respectively, 2.2 times and 2.8 times smaller than the theoretical predictions. Cross sections for the production of ${\mathrm{H}}^{-}$ and ${\mathrm{D}}^{-}$ in the $6–10\mathrm{eV}$ range are much smaller than those for $X^{-}$ and the isotope effect is much weaker, consistent with the assignment to core-excited Feshbach resonances. There is one exception, however, the $9\mathrm{eV}$ band in HCl has a large isotope effect.

Large positron annihilation cross sections have been observed for a variety of molecules at various energies below the threshold for positronium formation. These large values are due to vibrational Feshbach resonances (VFRs), in which the positron attaches to the molecule while exciting a vibration. This leads to rates of annihilation far greater than those expected for a simple collision. The dependence of the annihilation rate on incident positron energy can be used to deduce positron-molecule binding energies. Presented here is a comprehensive study of resonant annihilation in small molecules (e.g., hydrocarbons with one or two carbon atoms). In some cases, only fundamental vibrations are important, and theory correctly predicts the annihilation rates as a function of incident positron energy. In other cases, combination and overtone vibrations are shown to support Feshbach resonances. In the subset of these cases where the positron-molecule coupling strengths can be determined for these combination modes, theoretical predictions are in agreement with the measurements. Finally, there are species that do not exhibit VFRs, such as carbon dioxide. This is interpreted as evidence that positrons bind very weakly or not at all to these targets. Several of these molecules exhibit a variety of behaviors that are presently unexplained. The implications of the results presented here for more comprehensive theories of positron annihilation on molecules are discussed.

We study static properties of attractively interacting Bose-Fermi mixtures of uniform atomic gases at zero temperature. Using the Green’s function formalism, we calculate the boson-fermion scattering amplitude and the fermion self-energy in the medium to lowest order of the hole-line expansion. We study the ground-state energy and pressure as a function of the scattering length for a few values of the boson-fermion mass ratio $m_b∕m_f$ and the number ratio $N_b∕N_f$. We find that the attractive contribution to the energy is greatly enhanced for small values of the mass ratio. We study the role of Bose-Fermi pair correlations in the mixture by calculating the pole of the boson-fermion scattering amplitude in the medium. The pole shows a standard quasiparticle dispersion for a Bose-Fermi pair. In addition, we also study the fermion dispersion relation. We find two dispersion branches with the possibility of avoided crossings. This strongly depends on the number ratio $N_b∕N_f$.

We propose a two-photon beating experiment based upon biphotons generated from a resonant pumping two-level system operating in a backward geometry. On the one hand, the linear optical-response leads biphotons produced from two sidebands in the Mollow triplet to propagate with tunable refractive indices, while the central-component propagates with unity refractive index. The relative phase difference due to different refractive indices is analogous to the pathway-length difference between long-long and short-short pathways in the original Franson interferometer. By subtracting the linear Rayleigh scattering of the pump, the visibility in the center part of the two-photon beating interference can be ideally manipulated among [0, 100%] by varying the pump power, the material length, and the atomic density, which indicates a Bell-type inequality violation. On the other hand, the proposed experiment may be an interesting way of probing the quantum nature of the detection process. The interference will disappear when the separation of the Mollow peaks approaches the fundamental time scales for photon absorption in the detector.

We achieve impulsive alignment in a $400\mathrm{K}$ sample of diatomic iodine. This alignment results in an ensemble of coherent rotational wave packets with revival structures at 220 and $440\mathrm{ps}$. The revivals contain many more oscillations than are typically seen in rotational wave packets. The high-temperature sample contains a very large distribution in $J$, with strong centrifugal distortions. We find that the high initial temperature, rather than the strength of the laser impulse, gives rise to the centrifugally distorted revival oscillations. We present polarization measurements of this rotational wave packet together with semiclassical simulations showing the importance of the thermal distribution of population in both rotational and vibrational states. Our results show that excitation of coherent rotations is possible even in a system where the thermal energy is large compared to the energy exchanged with the laser field.

We present theoretical findings on the spin collective modes of a two-species Fermi liquid, prepared alternatively in a polarized equilibrium or a polarized nonequilibrium state. We explore the effects on these modes of a diverging $s$-wave scattering length, as occurs near a Feshbach resonance in a fermionic atomic gas. We compare these atomic gas modes with those of the conventional ${}^3\mathrm{He}$ system, and we find that they differ from the conventional systems, and that the gap and spin stiffness are tunable via the Feshbach resonance.

We explore the subtle relationships between partial separability and entanglement of subsystems in multiqubit quantum states and give experimentally accessible conditions that distinguish between various classes and levels of partial separability in a hierarchical order. These conditions take the form of bounds on the correlations of locally orthogonal observables. Violations of such inequalities give strong sufficient criteria for various forms of partial inseparability and multiqubit entanglement. The strength of these criteria is illustrated by showing that they are stronger than several other well-known entanglement criteria (the fidelity criterion, violation of Mermin-type separability inequalities, the Laskowski-Żukowski criterion, and the Dür-Cirac criterion) and also by showing their great noise robustness for a variety of multiqubit states, including $N$-qubit Greenberger-Horne-Zeilinger states and Dicke states. Furthermore, for $N⩾3$ they can detect bound entangled states. For all these states, the required number of measurement settings for implementation of the entanglement criteria is shown to be only $N+1$. If one chooses the familiar Pauli matrices as single-qubit observables, the inequalities take the form of bounds on the antidiagonal matrix elements of a state in terms of its diagonal matrix elements.

Fermions play an essential role in many areas of quantum physics and it is desirable to understand the nature of entanglement within systems that consist of fermions. Whereas the issue of separability for bipartite fermions has extensively been studied in the present literature, this paper is concerned with maximally entangled fermions. A complete characterization of maximally entangled quasifree (Gaussian) fermionic states is given in terms of the covariance matrix.

In this paper, we rigorously prove the intuition that in security proofs for the Bennett-Brassard 1984 (BB84) protocol, one may regard an incoming signal to Bob as a qubit state. From this result, it follows that all security proofs for BB84 protocol based on a virtual qubit entanglement distillation protocol, which was originally proposed by Lo and Chau [Science 283, 2050 (1999)] and by Shor and Preskill [Phys. Rev. Lett. 85, 441 (2000)], are all valid even if Bob’s actual apparatus cannot distill a qubit state explicitly. As a consequence, especially, the well-known result that a higher bit error rate of 20% can be tolerated for BB84 protocol by using two-way classical communications is still valid even when Bob uses threshold detectors. Using the same technique, we also prove the security of Bennett-Brassard-Mermin 1992 (BBM92) protocol where Alice and Bob both use threshold detectors.

Entanglement does not correspond to an observable, and its evaluation always corresponds to an estimation procedure where the amount of entanglement is inferred from the measurements of one or more proper observables. Here we address optimal estimation of entanglement in the framework of local quantum estimation theory and derive the optimal observable in terms of the symmetric logarithmic derivative. We evaluate the quantum Fisher information and, in turn, the ultimate bound to precision for several families of bipartite states for either for qubits or continuous-variable systems and for different measures of entanglement. We found that for discrete variables, entanglement may be efficiently estimated when it is large, whereas estimation of weakly entangled states is an inherently inefficient procedure. For continuous-variable Gaussian systems the effectiveness of entanglement estimation strongly depends on the chosen entanglement measure. Our analysis makes an important point of principle and may be relevant in the design of quantum information protocols based on the entanglement content of quantum states.

We give an explicit expression for the geometric measure of entanglement for three-qubit states that are linear combinations of four orthogonal product states. It turns out that the geometric measure for these states has three different expressions depending on the range of definition in parameter space. Each expression of the measure has its own geometrically meaningful interpretation. Such an interpretation allows oneself to take one step toward a complete understanding for the general properties of the entanglement measure. The states that lie on joint surfaces separating different ranges of definition, designated as shared states, seem to have particularly interesting features. The properties of the shared states are fully discussed.

We have investigated the relative triple-photoionization cross section of lithium from near threshold to $650\mathrm{eV}$ photon energy using monochromatized synchrotron radiation. Specifically, we reduced the statistical error bars in the $300\text{to}420\mathrm{eV}$ region and significantly extended the energy range compared to previous measurements. From the measured triple-to-double photoionization ratio, we determine the triple-to-single photoionization ratio and derive the triple-photoionization cross section. We make an estimate for the high-energy limit of that ratio and compare it to theoretical predictions. We also compare the ${\mathrm{Li}}^{3+}$ cross section with theoretical calculations.

The design of surface-electrode ion traps is studied analytically. The classical motion of a single ion in such a trap is described by coupled Mathieu equations. An analytic boundary-value solution for the Laplace equation in three dimensions with a piecewise-constant Dirichlet boundary condition is described. This solution is used to model the electrostatic potential field generated by a series of electrodes lying in a single plane. The model is applied to the problem of designing surface-electrode ion traps, including calculating important trap design parameters such as the center position of the trapped ion, trap depth, and stability parameters. The model is used to determine optimized dimensions for trap electrodes in various cases.

The concept of mutually unbiased bases is studied for $N$ pairs of continuous variables. To find mutually unbiased bases reduces, for specific states related to the Heisenberg-Weyl group, to a problem of symplectic geometry. Given a single pair of continuous variables, three mutually unbiased bases are identified while five such bases are exhibited for two pairs of continuous variables. For $N=2$, the golden ratio occurs in the definition of these mutually unbiased bases suggesting the relevance of number theory not only in the finite-dimensional setting.

We show that the possible ensembles produced when a separable operation acts on a single pure bipartite entangled state are completely characterized by a majorization condition, a collection of inequalities for Schmidt coefficients, which is identical to that already known for the particular case of local operations and classical communication (LOCC). As a consequence, various known results for LOCC, including some involving monotonicity of entanglement, can be extended to the class of all separable operations.

We calculate the low-lying energy spectrum for three trapped identical bosons interacting via a finite-range potential. The spectrum is compared to results from the zero-range model. The thresholds for trimer binding and atom-dimer binding are extracted and related to effective range corrections. Effective range corrections to Efimov physics and Borromean binding are two aspects of the same effect, and we connect these two regions qualitatively. The Borromean window becomes slightly narrower for substantial effective ranges. The structure at the atom-dimer threshold is an atom far away from the dimer and the major energy correction is due to the change of dimer energy with effective range. This structure becomes less pronounced when the effective range increases.

Using model systems we construct exact solutions of the Schrödinger equation for the tunneling effect in terms of the so-called resonant states. Two models of atomic ionization by an electrostatic field $E$ are studied in detail with a special emphasis on strong fields where the decay exponents become proportional to $E^{2∕3}$. The tunneling process, initiated by the field, is presented by an infinite sum of exponentially decaying terms without a usual slow decaying component at longer times. The sum of this series in some cases, including our models, lead to a nonexponential decay. The normalization techniques of the spatially divergent resonant wave functions via regularization of divergent integrals are considered. In particular, we apply an approximate semiclassical cutoff procedure which allows us to place the resonant states on a similar footing as the usual bound states and even use the standard normalization of the probability density. An application of such approach can illuminate and simplify calculation schemes for the study not only of ionization in electrostatic fields but also the multiphoton ionization by low frequency laser beams.

A series of resonant Auger-electron spectra excited at selected photon energies across the O $1s\to \text{Rydberg}$ resonances in ${\mathrm{O}}_2$ has been measured. Applying a spectator-electron shake relaxation model originally introduced for atomic resonant Auger-electron spectra, and using, to a large extent, the assignments for the core-excited resonances available from the literature, many of the observed spectator Auger-electron final states are assigned in terms of cationic Rydberg series. Vice versa the resonant Auger-electron spectra are used for consistency tests of the literature assignments for the core-excited intermediate Rydberg states. For some of the latter, alternative assignments are proposed for reasons discussed.

We present a precise determination of the polarizability and other proton structure-dependent contributions to the hydrogen hyperfine splitting, based heavily on the most recent data on proton spin-dependent structure functions from the EG1 collaboration experiment at the Jefferson Laboratory. As a result, the total calculated hyperfine splitting now has a standard deviation slightly under 1 part per million, and is about one standard deviation away from the measured value. We also present results for muonic hydrogen hyperfine splitting, taking care to ensure the compatibility of the recoil and polarizability terms.

The emission of x rays in atomic transitions from $M$-shell vacancy states of Pb, Bi, Th, and U induced by electron bombardment was studied by means of wavelength dispersive spectroscopy. Relative transition probabilities, characteristic energies, natural linewidths, and x-ray production cross sections were determined through a careful spectral processing based on a parameter refinement method. The experimental data for a number of $M$-shell relative transition probabilities along with values for a large set of atomic parameters are given. Finally, the origin and shape of the satellite bands at the high-energy side of the main lines are discussed.