An entanglement witness (EW) is an operator that allows the detection of entangled states. We give necessary and sufficient conditions for such operators to be optimal, i.e., to detect entangled states in an optimal way. We show how to optimize general EW, and then we particularize our results to the nondecomposable ones; the latter are those that can detect positive partial transpose entangled states (PPTES’s). We also present a method to systematically construct and optimize this last class of operators based on the existence of “edge” PPTES’s, i.e., states that violate the range separability criterion [Phys. Lett. A 232, 333 (1997)] in an extreme manner. This method also permits a systematic construction of nondecomposable positive maps (PM’s). Our results lead to a sufficient condition for entanglement in terms of nondecomposable EW’s and PM’s. Finally, we illustrate our results by constructing optimal EW acting on $H=C^2\otimes C^4.$ The corresponding PM’s constitute examples of PM’s with minimal “qubit” domains, or—equivalently—minimal Hermitian conjugate codomains.

The density of an atom in a state of well-defined total angular momentum has a specific finite spherical harmonic content, without and with interactions. Approximate single-particle schemes, such as the Hartree, Hartree-Fock, and local density approximations, generally violate this feature. We analyze, by means of perturbation theory, the degree of this violation and argue that it is small. The correct symmetry of the density can be assured by a constrained-search formulation without significantly altering the calculated energies. We compare our procedure to the (different) common practice of spherically averaging the self-consistent potential. Kohn-Sham density functional theory with the exact exchange-correlation potential has the correct finite spherical harmonic content in its density; but the corresponding exact single-particle potential and wave functions contain an infinite number of spherical harmonics.

A procedure is given for calculating transition amplitudes that are equal in the length and velocity forms for transitions in atoms with one valence electron within the framework of relativistic many-body perturbation theory starting from the Dirac-Hartree-Fock approximation. This procedure is applied to obtain form-independent second- and third-order dipole matrix elements for the principal transitions in alkali-metal atoms. Comparisons are made with other calculations and with experiment.

Experimental and theoretical values for the lifetimes of the $5s5p{}^1{P}_1$ and ${}^3{P}_1$ levels in the Cd isoelectronic sequence are examined in the context of a data-based isoelectronic systematization. Lifetime and energy-level data are combined to account for the effects of intermediate coupling, thereby reducing the data to a regular and slowly varying parametric mapping. This empirically characterizes small contributions due to spin-other-orbit interaction, spin dependences of the radial wave functions, and configuration interaction, and yields accurate interpolative and extrapolative predictions. Multiconfiguration Dirac-Hartree-Fock calculations are used to verify the regularity of these trends, and to examine the extent to which they can be extrapolated to high nuclear charge.

The relativistic version of the J-matrix method for a scattering problem on the potential vanishing faster than the Coulomb one is formulated. As in the nonrelativistic case it leads to a finite algebraic eigenvalue problem. The derived expression for the tangent of phase shift is simply related to the nonrelativistic case formula and gives the latter as a limit case. It is due to the fact that the used basis set satisfies the “kinetic balance condition.”

We have measured resonant strengths for $\Delta n>~1$ dielectronic recombinaton in heliumlike ${\mathrm{Ar}}^{16+}.$ The measurements were performed with an electron beam ion trap and include the $\mathrm{KLM}$ through $\mathrm{KLP}$ resonances contributing to $\overrightarrow{n}1\hspace{0.5em}\mathrm{K}$-shell x-ray emission with $n=2\mathrm{}-6.$ The measured values agree within a few percent with relativistic multiconfiguration calculations.

The primary goal of research in “quantum chaos” is to explore the extent to which the methods and natural intuition of classical mechanics can be used to elucidate the complex and often surprising behavior of large quantum systems. Much recent work is based on the deep connections between classical periodic (or closed) orbits and the quantum spectrum revealed by semiclassical “trace formulas.” These ideas have important applications in the analysis of the “recurrence spectrum” of Rydberg atoms in strong static electric fields in which the measured peaks are associated with individual classical periodic orbits. Here we present detailed experimental measurements of the recurrence spectrum for $n=15\mathrm{}–25,$ singlet and triplet, $m=0,$ 1, helium Rydberg atoms and we provide a purely quantum-mechanical explanation for the structure of the recurrence spectrum based on the regularities of the Stark photoabsorption spectrum. This analysis serves to demystify these (still complex) representations of the quantum spectrum; provides new insight into the functional differences between hydrogen and helium Rydberg atoms in strong fields; and reemphasizes the remarkable correpondence between the classical and quantum theory for these systems.

We exploit the analogy with the quantum Hall (QH) system to study weakly interacting bosons in a harmonic trap. For a $\delta$-function interaction potential the “yrast” states with $L>~N\left(N-1\right)$ are degenerate, and we show how this can be understood in terms of Haldane exclusion statistics. We present spectra for four and eight particles obtained by numerical and algebraic methods, and demonstrate how a more general hard-core potential lifts the degeneracies on the yrast line. The exact wave functions for $N=4\mathrm{}$ are compared with trial states constructed from composite fermions (CF), and the possibility of using CF states to study the low L region at high N is discussed.

We study the mechanical stability of the weakly interacting Bose gas with attractive interactions, and construct a unified picture of the collapse valid from the low-temperature condensed regime to the high temperature classical regime. As we show, the noncondensed particles play a crucial role in determining the region of stability, including providing a mechanism for collapse in the noncondensed cloud. Furthermore, we demonstrate that the mechanical instability prevents BCS-type “pairing” in the attractive Bose gas. We extend our results to describe domain formation in spinor condensates.

Line-broadening effects in the coupled mode spectrum of optical cavities and microcavities are included explicitly by (i) the interaction of the electromagnetic mode with a continuum of electromagnetic modes and (ii) the coupling of the electronic excitations to a dissipative source. The effects of interaction with an electromagnetic continuum are treated within a Fano model, and the electronic excitations are represented by harmonic oscillators. The coupled mode frequencies and their emission spectra are given explicitly in terms of the parameters of these line-broadening mechanisms, with particular attention given to expressions for semiconductor microcavities.

We present results from an experimental study of the decoherence and decay of quantum states of a trapped atomic ion’s harmonic motion interacting with several types of engineered reservoirs. We experimentally simulate three types of reservoirs: a high-temperature amplitude reservoir, a zero-temperature amplitude reservoir, and a high-temperature phase reservoir. Interaction with these environments causes the ion’s motional state to decay or heat, and in the case of superposition states, to lose coherence. We report measurements of the decoherence of superpositions of coherent states and two-Fock-state superpositions into these reservoirs, as well as the decay and heating of Fock states. We confirm the theoretically well-known scaling laws that predict that the decoherence rate of superposition states scales with the square of the “size” of the state.

Slow light generated by electromagnetically induced transparency is extremely susceptible with respect to Doppler detuning. Consequently, slow-light gyroscopes should have ultrahigh sensitivity.

We consider the transmission of classical information over a quantum channel by two senders. The channel capacity region is shown to be a convex hull bound by the Von Neumann entropy and the conditional Von Neumann entropy. We discuss some possible applications of our result. We also show that our scheme allows a reasonable distribution of channel capacity over two senders.

A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground-state energy analytically using our method provided certain consistency relations are satisfied. Analytic expressions for the exact-ground-state energy have also been derived specifically for a large class of the one-dimensional oscillator with cubic-quartic anharmonic terms. Our analytical results can be used to check the accuracy of existing numerical methods, for instance the method of state-dependent diagonalization. Our results also agree with the asymptotic behavior in the divergent pertubative expansion of the quartic harmonic oscillator.

The states of the physical algebra, namely the algebra generated by the operators involved in encoding and processing qubits, are considered instead of those of the whole-system algebra. If the physical algebra commutes with the interaction Hamiltonian, and the system Hamiltonian is the sum of arbitrary terms either commuting with or belonging to the physical algebra, then its states are decoherence free. One of the examples considered shows that, for a uniform collective coupling to the environment, the smallest number of physical qubits encoding a decoherence-free logical qubit is reduced from four to three.

A highly stripped cerium $\mathrm{}(Z=58\mathrm{})\mathrm{}$ plasma is produced by irradiating a solid cerium target with a short pulse laser. The x-ray spectrum emitted from the plasma is recorded in the limited wavelength range 9.0–9.3 Å using a high-resolution curved mica crystal spectrometer. The high-resolution spectrum, which corresponds to the $3d-5f$ transitions in Ni-, Cu-, and Zn-like cerium ions, is analyzed by means of a detailed collisional-radiative model that includes autoionization and dielectronic capture processes. The intensity ratio of the Ni-like $3d-5f$ resonant line at 9.045 Å to the features emitted from satellite transitions of Cu-like ions provides an estimate for the mean electron temperature and density of 230 eV and ${10}^{22}\hspace{0.5em}{\mathrm{cm}}^{\mathrm{-}3},$ respectively. The deduced mean electron temperature is higher than that obtained in a similar experiment on laser-produced barium plasma. The origin of the higher mean electron temperature deduced in the present experiment is explained by the different type of transition employed for the temperature diagnostics, which might reflect a different phase of the plasma evolution.

Extending the Feynman-Kleinert variational approach, we calculate the temperature-dependent effective classical potential governing the quantum statistics of a hydrogen atom in a uniform magnetic field at all temperatures. The zero-temperature limit yields the binding energy of the electron, which is quite accurate for all magnetic-field strengths, and exhibits, in particular, correct logarithmic growth at large fields.

We study a bound system of N identical bosons interacting by model pair potentials of the form $V\left(r\right)=\lambda \mathrm{sgn}{\mathrm{}\left(p\right)r}^p+\mu {/r}^2,$ $\lambda >0,$ $\mu >~0.$ By using a variational trial function and the “equivalent two-body method,” we find explicit upper and lower bound formulas for the N-particle ground-state energy in arbitrary spatial dimensions $d>~3$ for the two cases $p=2\mathrm{}$ and $p=-1.$ It is demonstrated that the upper bound can be systematically improved with the aid of a special large-N limit in collective field theory.

Formulas for the total ionization cross section by electron impact based on the binary-encounter-dipole (BED) model and its simpler version, the binary-encounter-Bethe (BEB) model are extended to relativistic incident electron energies. Total ionization cross sections for the hydrogen and helium atoms from the new relativistic formulas are compared to experimental data. Relativistic effects double the total ionization cross section of H and He at incident electron energy $\approx 300\hspace{0.5em}\mathrm{keV}$ and dominate the cross section thereafter. A simple modification of the original BED-BEB formulas is proposed for applications to ion targets and inner-shell electrons of neutral atoms and molecules. The relativistic and nonrelativistic BEB cross sections are compared to the K-shell ionization cross sections by electron impact for the carbon, argon, nickel, niobium, and silver atoms. For carbon and argon, the relativistic effects are small, and both forms of the BEB cross sections agree well with available experimental data. For the nickel and heavier atoms, the relativistic increase of cross sections becomes noticeable from about 100 keV and higher in the incident electron energy. The empirical formula by Casnati et al. [J. Phys. B 15, 155 (1982)] after correcting for relativistic effects as shown by Quarles [Phys. Rev. A 13, 1278 (1976)] agrees well with the BEB cross sections for light atoms. However, the peak values of the Casnati cross sections become higher than the relativistic BEB peak cross sections as the atomic number increases. The BEB model is also applied to the total ionization cross section of the xenon atom, and the theory agrees well with experiments at low incident electron energies, but disagrees with experiment at relativistic incident energies.

Storage-ring measurements of the dissociative recombination cross section of ${\mathrm{CD}}^{+}$ and ${\mathrm{CH}}^{+}$ molecular ions have revealed prominent resonances at low energy. They were assigned tentatively to capture into core-excited bound Rydberg states, electronically coupled both to the electronic initial continuum and to the dissociative final channel. We present here the result of calculations based on the multichannel quantum defect theory, using molecular data (quantum defects and electronic couplings) extracted from ab initio structure computations. In addition to the Rydberg states converging to the initial ground state $X{}^1{\Sigma }^{+}$ of the ion, we calculated Rydberg series converging to the first two excited electronic states $a{}^3\Pi$ and $A{}^1\Pi .$ The cross section convoluted with the experimental anisotropic Maxwell distribution presents a resonant structure very close to the experimental one, when the ion is assumed to be initially in the lowest rovibrational level of the ground state. We can thus assign the resonances observed near 0.3 and 0.9 eV to low vibrational levels of the ${}^2\Pi$ core-excited Rydberg states $\left(a{}^3\Pi \right)5s\sigma$ and $\left(A{}^1\Pi \right)3p\sigma ,$ respectively. We also give a theoretical estimate of the branching ratio for dissociation to various asymptotic limits, obtained by solving coupled equations for the nuclear wave functions of interacting ${}^2\Pi$ states of CH.