Finite quantum systems where the position $x$ and the momentum $p$ take values in $\mathbb{Z}\left(d\right)$ are considered. An extended phase space $x-p-X-P$, where $X$ is position increment and $P$ is momentum increment, is introduced. The extended Wigner function $\mathcal{W}\left(x,p,X,P\right)$ and the extended Weyl function $\tilde{\mathcal{W}}\left(x^{\prime },p^{\prime },X^{\prime },P^{\prime }\right)$ are defined and their properties are studied. They quantify fourth-order interference. Several examples are discussed.

Recently, Wildfeuer et al. [Phys. Rev. A 76, 052101 (2007)] studied possible experiments demonstrating nonlocal correlation effects through the violation of various Bell-type inequalities by maximally path-entangled number states of the form $\left(|N⟩|0⟩+e^{i\phi }|0⟩|N⟩\right)/\sqrt{2}$, the so-called $N00N$ states, and some strong violations were found. In this paper, we re-examine the same Bell-type inequalities with respect to maximally path-entangled coherent states of the form $\mathcal{N}\left({|\alpha ⟩}_a{|0⟩}_b+e^{i\Phi }{|0⟩}_a{|\alpha e^{i\theta }⟩}_b\right)$. We find in many cases even stronger violations of the Bell-type inequalities than appear to be possible with the $N00N$ states.

In this contribution we group the operator basis for $d^2$-dimensional Hilbert space in a way that enables us to relate bases of entangled states with single-particle mutually unbiased state bases (MUB), each in dimensionality $d$. We utilize these sets of operators to show that an arbitrary density matrix for this $d^2$-dimensional Hilbert-space system is analyzed via $d^2+d+1$ measurements, $d^2-d$ of which involve those entangled states that we associate with MUB of the $d$-dimensional single-particle constituents. The number $d^2+d+1$ lies in the middle of the number of measurements needed for bipartite state reconstruction with two-particle MUB $\left(d^2+1\right)$ and those needed by single-particle MUB $\left[{\left(d^2+1\right)}^2\right]$.

A two-way protocol for defeating passive eavesdropping is proposed. For each information bit, Alice sends Bob $T$ sec of signal-beam output from a spontaneous parametric down-converter over a pure-loss channel while retaining the idler beam with which it is maximally entangled. Bob imposes a single information bit on the light he receives from Alice via binary phase-shift keying. He then amplifies the modulated beam and sends the resulting light back to Alice over the same pure-loss channel. Even though the loss and amplifier noise destroy any entanglement between the light that Alice receives from Bob and the idler she has retained, she can decode Bob’s bit with an error probability that can be orders of magnitude lower than what is achieved by a passive eavesdropper who receives all the photons that are lost en route from Alice to Bob and from Bob to Alice. In particular, Alice and Bob can communicate at 50 Mbit/s over 50 km of low-loss fiber with an error probability of less than ${10}^{-6}$ while the passive eavesdropper’s error probability must exceed 0.28.

Low-energy electron-exchange collisions with the simple open-shell molecules ${\text{O}}_2$, NO, and ${\text{NO}}_2$ have been investigated by measuring the change in electron-spin polarization after scattering polarized electrons from unpolarized molecules with energies between 8 and 20 eV and scattering angles up to $130°$. Results for elastic collisions with ${\text{O}}_2$ and NO are compared with existing theories where the agreement is fair. Direct observation of spin-exchange collisions is obtained for elastic scattering from ${\text{NO}}_2$ and for electron-impact excitation of ${\text{O}}_2$ (6.1 eV energy loss). It is also shown that the results may be influenced by spin-orbit interaction, which was assumed to be negligible in previous studies.

The multiphoton ionization of neon atoms was studied in the focus of the soft-x-ray free-electron laser FLASH by photoion spectroscopy. The photon energy was chosen in the range of ${\text{Ne}}^{+}2p\to n\ell$ resonances between 41 and 42 eV. The experiments were performed at the PG0 branch of the FLASH monochromator beamline while measuring the spectral distribution of every single FLASH pulse. By correlating the ratio of doubly and singly charged neon ions generated and the measured photon energy distribution, the enhancement of this ratio due to resonant ${\text{Ne}}^{+}$ excitation was found.

Regular and irregular spin-mixing dynamics are studied in a spin-1 atomic Bose-Einstein condensate coupled with a molecular condensate. Based on the experimental photoassociation spectroscopy of ${}^{87}\text{R}\text{b}$ spin-1 atoms, a two-channel model is proposed, in which two zero-spin atoms can be associated with a molecular state via a laser field, and a pair of $+1$- and $-1$-spin atoms can also be associated with the same molecular state via the same laser field. We find that the spin-mixing dynamics can be manipulated by the laser field and a magnetic field. Both regular and irregular oscillations can be observed under different parameters. Using the Fourier transform analysis, the spin-mixing dynamics may be changed from the regular oscillation with localized spectral distributions to irregular oscillation with a broad spectral distribution.

We study the effect of decoherence on dynamical phase diffusion in the two-site Bose-Hubbard model. Starting with an odd parity excited coherent state, the initial loss of single-particle coherence varies from small bound oscillations in the Rabi regime, through hyperbolic depletion in the Josephson regime, to a Gaussian decay in the Fock regime. The inclusion of local-site noise, measuring the relative number difference between the modes, is shown to enhance phase diffusion. In comparison, site-indiscriminate noise measuring the population imbalance between the two quasimomentum modes slows down the loss of single-particle coherence. Decoherence thus either enhances or suppresses phase diffusion, depending on the details of system-bath coupling and the overlap of decoherence pointer states with collisional-entanglement pointer states. The deceleration of phase diffusion due to the coupling with the environment may be viewed as a many-body quantum Zeno effect. The extended effective decay times in the presence of projective measurement are further enhanced with increasing number of particles $N$ by a bosonic factor of $\sqrt{N}$ in the Fock regime and $N/\text{log}N$ in the Josephson regime.

The rotational properties are studied for a unitary superfluid gas of fermions at zero temperature. Using a hydrodynamic approach, the conditions for the formation of a giant vortex are discussed. It is found that in the present approximation, an anharmonic addition to the usual harmonic-oscillator type of trap potential is necessary for the energetic stability of a giant vortex. To determine the conditions quantitatively, a Thomas-Fermi approach is compared with numerical solutions in three dimensions.

Regular arrays of electromagnetic resonators, in turn coupled coherently to individual quantum two-level systems, exhibit a quantum phase transition of polaritons from a superfluid phase to a Mott-insulating phase. The critical behavior of such a Jaynes-Cummings lattice thus resembles the physics of the Bose-Hubbard model. We explore this analogy by elaborating on the mean-field theory of the phase transition and by presenting several useful mappings which pinpoint both similarities and differences of the two models. We show that a field-theory approach can be applied to prove the existence of multicritical curves analogous to the multicritical points of the Bose-Hubbard model, and we provide analytical expressions for the position of these curves.

Following Crisp’s method based on neoclassical theory for a radiating electron, we have derived the nonrelativistic Lorentz-Dirac equation from quantum mechanics by means of Ehrenfest’s theorem. It is found that the dipole approximation is essential to obtain the correct form of the equation of motion.

We demonstrate the realization of a two-dimensional (2D) quantum gas in a smooth optical surface trap. Using a combination of evanescent wave, standing wave, and magnetic potentials, we create a long-lived quantum gas deep in the 2D regime at a distance of a few microns from a glass surface. To realize a system suitable for many-body quantum simulation, we introduce methods such as broadband “white” light to create evanescent and standing waves to realize a smooth potential with a trap frequency aspect ratio of 300:1:1. We are able to detect phase fluctuations and vortices, and we demonstrate cooling to degeneracy and low disorder in the 2D configuration.

Local effective potential theory of electronic structure is the mapping from a system of electrons in an external field to one of noninteracting fermions or bosons with the same electronic density. The energy and ionization potential are also thereby determined. The mappings may be achieved via either quantal density-functional theory (QDFT) or Hohenberg-Kohn-Sham density-functional theory (HKS-DFT). The wave function for the model fermionic system is a Slater determinant of spin orbitals, whereas that for the model bosons is the density amplitude. In the QDFT mappings, the contributions of the electron correlations due to the Pauli exclusion principle, Coulomb repulsion and correlation-kinetic effects are separately delineated. It has been proved via QDFT that the contribution of Pauli and Coulomb correlations to these model systems is the same; the difference lies solely in their correlation-kinetic component. In this paper, we apply the QDFT of the density amplitude to study the mapping to the bosonic model. The application is to atoms and performed at the Hartree-Fock theory level of electron correlations. A principal conclusion is that correlation-kinetic effects play a significant role in the mapping to the bosonic model, whereas they are negligible in the mapping to the model fermions. For the bosonic model, this contribution increases with electron number, becoming nearly as significant as those due to the corresponding electron-interaction (the sum of the Hartree and Pauli) term. The significance of the correlation-kinetic effects will be further enhanced on the inclusion of Coulomb correlations and the corresponding correlation-kinetic contributions. The consequences of these conclusions for the HKS-DFT of the density amplitude are discussed, as are directions for future work.

Direct calculation of the ground-state two-electron reduced density matrix (2-RDM) and its energy has recently been achieved for many-electron atoms and molecules by solving the anti-Hermitian part of the contracted Schrödinger equation (ACSE) [D. A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)]. In this paper the ACSE method is extended to computing the 2-RDMs and energies of excited states without the many-electron wave function. The contracted Schrödinger equation (CSE) is an important ingredient for excited-state 2-RDM methods because it is a stationary-state condition for both ground and excited states. We develop the theoretical framework for the ACSE as a stationary-state condition through its connections to the CSE and the Schrödinger equation. As in previous ground-state calculations, the indeterminacy of the ACSE is removed by reconstructing its 3-RDM as a functional of its 2-RDM through a cumulant theory for RDMs [D. A. Mazziotti, Chem. Phys. Lett. 289, 419 (1998)]. We calculate the initial 2-RDM from a multiconfiguration self-consistent-field calculation that includes multireference electron correlation, which can be especially important for excited states. The excited-state ACSE method is applied to computing absolute excited-state energies and vertical excitation energies of the molecules HF, ${\text{H}}_2\text{O}$, and ${\text{N}}_2$ as well as ground and excited potential-energy curves of HF. Comparisons are made to traditional multireference methods as well as full configuration interaction. Computed excited-state 2-RDMs nearly satisfy necessary $N$-representability conditions.

Using x-ray diffraction and beam-foil spectroscopy, we have determined precise wavelengths for Lyman ${\alpha }_1$ and Lyman ${\alpha }_2$ in hydrogenic germanium of $1.1669938\pm 33\pm 169$ and $1.1724336\pm 39\pm 170\mathrm{\AA }$. Hydrogenic germanium ${\mathrm{Ge}}^{31+}$ $1s\text{−}2p_{3∕2}$ and $1s\text{−}2p_{1∕2}$ Lamb shifts are measured to be $66080\pm 237\pm 1121$ and $67169\pm 281\pm 1237{\mathrm{cm}}^{-1}$, respectively. This $14\mathrm{ppm}$ measurement of the wavelengths thus provides a 1.8% measurement of the $2p\text{−}1s$ Lamb shift and is an improvement by a factor of 3 over previous work. Fitting the full two-dimensional dispersion relation, including Balmer and Lyman series, limits random and systematic correlation of parameters. Dominant systematics are due to diffraction parameters including crystal thickness and alignment, differential Doppler shifts due to the variable location of spectral emission downstream of the beam-foil target, and dielectronic, $2s\text{−}1s$, and $4f\text{−}2p$ satellites. Models developed are applicable to all relativistic plasma modeling in beam-foil spectroscopy at accelerators. The technique also reports the germanium $2p_{3∕2}\text{−}2p_{1∕2}$ fine structure as $397617\pm 251\pm 512{\mathrm{cm}}^{-1}$, representing a 0.14% measurement of the fine structure and a 71% measurement of the QED contribution to the hydrogenic germanium fine structure, an improvement of a factor of 6 over previous work. We also report a precise measurement of heliumlike resonances and fine structure.

A theoretical study on double-resonance optical pumping for the transitions $5S_{1/2}\text{−}5P_{3/2}\text{−}4D_{3/2,5/2}$ of ${}^{87}\text{R}\text{b}$ atoms is presented. The full-density-matrix equations in the presence the probe and the coupling laser beams for all relevant magnetic sublevels of the hyperfine levels were solved numerically, and the absorption of a probe beam was calculated as a function of the detuning of the coupling beam. The calculated results were compared with experimental data, and they showed an excellent agreement. The results were also compared with the approximate results calculated when the coherence between the ground and the highest excited levels was neglected. We found that the dominant operating mechanism for double-resonance signals was the optical pumping rather than the two-photon coherence, although the latter affected the signals significantly.

The Uehling correction to the energy levels is presented in terms of the hypergeometric functions ${{}_{2}F}_1$. This presentation allows to derive various asymptotics and approximations. Further applications of this method to other atomic characteristics are also considered.

We report a theoretical study on electron collisions with the sulfur monoxide radical. More specifically, differential, integral, and momentum-transfer cross sections are calculated and reported in the 1–500 eV energy range. Calculations are performed at the static-exchange-polarization-absorption level of approximation. A combination of the iterative Schwinger variational method and the distorted-wave approximation is used to solve the scattering equations. Our study reveals shape resonances in both the doublet and quartet spin-specific scattering channels. The occurrence of such resonances may enhance the spin-flip effects. In addition, the comparison of our calculated total absorption cross sections with existing experimental total ionization cross sections is encouraging.

The dependences of absolute differential bremsstrahlung cross sections on 0.4–2-keV electron scattering by supersonic gas jets of Ar, Kr, and Xe versus electron energy as well as the atom number $Z$ were studied experimentally. The bremsstrahlung photons have been detected at an angle $97°$ to the incident electron beam in the ultrasoft x-ray spectral region 70–200 eV. It is found that as the electron energy is increased from 0.4 to 2 keV, the absolute bremsstrahlung cross section for Xe increases throughout the whole electron energy range and the energy dependencies of cross sections for Ar and Kr displayed maxima at electron energies of $\sim 0.7\text{keV}$ (Ar) and $\sim 1\text{keV}$ (Kr). These experimental results cannot be explained in the framework of Bethe and Heitler and Sauter theory, based on the first Born approximation. The experimental absolute differential bremsstrahlung cross sections for Ar, Kr, and Xe are considerably larger then the tabulated values of ordinary bremsstrahlung. The obtained $Z$ dependence of bremsstrahlung cross section differs with calculated one, particularly for large atomic number $Z$.