Exchange interactions in spin systems can give rise to quantum entanglement in the ground and thermal states of the systems. We consider a spin tetramer, with spins of magnitude $\frac{1}{2}$, in which the spins interact via nearest-neighbor, diagonal, and four-spin interactions of strength $J_1$, $J_2$, and $K$, respectively. The ground- and thermal-state entanglement properties of the tetramer are calculated analytically in the various limiting cases. Both bipartite and multipartite entanglements are considered and a signature of the quantum phase transition (QPT), in terms of the entanglement ratio, is identified. The first-order QPT is accompanied by discontinuities in the nearest-neighbor and diagonal concurrences. The magnetic properties of a $S=\frac{1}{2}$ antiferromagnetic polyoxovanadate compound V12 are well explained by tetramers, with $J_2=0$, $K=0$, in which the spins interact via the isotropic Heisenberg exchange interaction Hamiltonian. Treating the magnetic susceptibility $\chi$ as an entanglement witness (EW), an estimate of the lower bound of the critical entanglement temperature $T_c$ below which entanglement is present in the experimental compound, is determined. Two other cases considered include the symmetric tetramer—i.e., tetrahedron $(J_1=J_2,K=0)$—and the symmetric trimer. In both the cases, there is no entanglement between a pair of spins in the thermal state but multipartite entanglement is present. A second EW based on energy provides an estimate of the entanglement temperature $T_E$ below which the thermal state is definitely entangled. This EW detects bipartite entanglement in the case of the tetramer describing a square of spins (the case of V12 ) and multipartite entanglement in the cases of the tetrahedron and symmetric trimer.

We report first configuration interaction calculations of hyperfine constants $A_{\Vert }$ and the effective electric field $W_d$ acting on the electric-dipole moment of the electron, in two excited electronic states of ${}^{207}\mathrm{Pb}\mathrm{O}$. A combined scheme of correlation calculations is also developed and applied to studying the core properties. The obtained hyperfine constants, $A_{\Vert }=-3826\mathrm{MHz}$ for the $a\left(1\right)$ state and $A_{\Vert }=4887\mathrm{MHz}$ for the $B\left(1\right)$ state, are in very good agreement with the experimental data, $-4113\mathrm{MHz}$ and $5000\pm 200\mathrm{MHz}$, respectively. We find $W_d=-\left({6.1}_{-0.6}^{+1.8}\right)\times {10}^{24}\mathrm{Hz}∕\left(\mathrm{e}\mathrm{cm}\right)$ for $a\left(1\right)$, and $W_d=-(8.0\pm 1.6)\times {10}^{24}\mathrm{Hz}∕\left(\mathrm{e}\mathrm{cm}\right)$ for $B\left(1\right)$.

We calculate the radiative transition rates $np\to 1s+\gamma$ in kaonic hydrogen and kaonic deuterium, induced by strong low-energy interactions and enhanced by Coulomb interactions. The obtained results should be taken into account for the theoretical analysis of the experimental data on the x-ray spectra and yields in kaonic atoms.

Partial cross-sections for photoionization with excitation of ${\mathrm{Li}}^{+}$ leaving the remaining bound electron in the $1s,$ $2s,$ $2p,$ $3s,$ $3p$, and $3d$ states and total cross-sections for double photoionization have been calculated employing the time-dependent close-coupling method. The calculations include both the ground state $1s^2{}^{1}S$ and the two lowest metastable excited states $1s2s{}^{1,3}S$. Photon energies below and up to about 200 eV above the respective thresholds for double ionization are considered. Comparisons are drawn mainly with convergent close-coupling results [A. S. Kheifets and I. Bray, Phys. Rev. A 58, 4501 (1998)] and $B$-spline based $R$-matrix results [H. W. van der Hart and L. Feng, J. Phys. B 34, L601 (2001)].

Using the classical-trajectory Monte Carlo (CTMC) method, the electronic stopping cross sections of hydrogen atoms by protons and antiprotons impact are calculated. The results show that the CTMC method compares fairly well with previous quantum mechanics calculations of the stopping cross sections for the same colliding pairs. It turns out therefore that the CTMC method constitutes a reliable and, computationally speaking, convenient alternative to calculate the stopping of ions in matter. The present results also show that the stopping appears to be particularly sensitive to the angular momentum $\left(L\right)$ of the electron orbit. In the case of protons, the highest sensitivity to $L$ becomes evident around the energy of the maximum stopping. While for antiprotons the largest sensitivity of the stopping to $L$ is observed down at low bombarding energies, i.e., below 10 keV.

The interaction of He atoms with intense vacuum-ultraviolet light of a free-electron laser is investigated using time-of-flight mass spectroscopy and photoelectron spectroscopy. The atoms were irradiated with $100\mathrm{fs}$ pulses at $95\mathrm{nm}$ wavelength, which corresponds to $\sim 13\mathrm{eV}$ photon energy. The ionization of He atoms is observed at a peak intensity of ${10}^{10}–{10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$, which is due both to nonlinear multiphoton ionization with the fundamental wavelength and single-photon ionization with third harmonic radiation of the free-electron laser. The observation of two sharp photoelectron peaks in the kinetic energy spectra, that are separated by the photon energy, is in agreement with the numerical solution of the time-dependent Schrödinger equation. The calculation was done using the fully quantized field and a limited but representative set of basis states. The ionization rate dependence on the laser peak intensity indicates that: (a) The low-energy peak in the photoelectron spectra is mainly due to two-photon absorption of the fundamental, but (b) the high-energy peak at $15.4\mathrm{eV}$ is probably due to third harmonic FEL radiation. The theoretically predicted contribution from three-photon absorption of the fundamental is of about the same order of magnitude and could not be separated from the third harmonic background signal. Particularly, the photoelectron spectra and ${\mathrm{He}}^{+}$ time-of-flight data give evidence that the intensity of third harmonic light is high enough to perform single-shot spectroscopy on gas phase samples.

We consider the problem of a helium atom under the radiation field of the DESY vacuum ultraviolet (VUV) free electron laser (FEL) (Phase I, $\hslash \cong 13\mathrm{eV}$). We find by solving numerically the time-dependent Schrödinger equation, that there is a large probability for resonant two-photon excitation from the ground state into a low kinetic energy state just above the first He ionization threshold. From this it is possible to go into another quasi-free state higher up, by resonant absorption of an additional photon. There is no double ionization of He. These results are in general agreement with the He photoelectron and time-of-flight (TOF) spectra recorded on March 2002, in the last week of the DESY VUV FEL Phase I operation. A detailed report on the experiments is given in a companion paper.

Loading of atoms contained in a magneto-optic trap into an optical trap formed with the focused laser beam from a $\mathrm{C}{\mathrm{O}}_2$ laser is examined. We show that while the loading efficiency is very sensitive to the volume of the optical trap, it is insensitive to the total laser power once a certain threshold is reached. Based on these observations a time-averaged optical atom trap is realized to compensate for the small capture volume of tight traps which are required for efficient evaporative cooling. Up to a 100% increase in the trap population is observed for the time-averaged traps. We also study the effect on temperature and trap population of changing a time-averaged optical trap back to a static trap. Our results provide a basis for increasing the number of atoms in Bose-Einstein condensates produced using all-optical techniques and show that a high-power laser is not a prerequisite for such an increase.

A peak in the static structure factor of a Bose-Einstein condensate is computed, both near and far from a Feshbach resonance. A low-density approximation is made, allowing for an analytic result. A Monte Carlo calculation shows that the peak is larger than predicted by the low-density approximation, for the upper range of densities considered here. The peak could be measured by a probe beam of cold atoms.

We present a numerical study of the high-quality modes in two-dimensional dielectric stadium microcavities. Although the classical ray mechanics is fully chaotic in a stadium billiard, all of the high-quality modes show a ‘‘strong scar’’ around unstable periodic orbits. When the deformation (ratio of the length of the straight segments over the diameter of the half circles) is small, the high-quality modes correspond to whispering-gallery-type trajectories and their quality factors decrease monotonically with increasing deformation. At large deformation, each high-quality mode is associated with multiple unstable periodic orbits. Its quality factor changes nonmonotonically with the deformation, and there exists an optimal deformation for each mode at which its quality factor reaches a local maximum. This unusual behavior is attributed to the interference of waves propagating along different constituent orbits that could minimize light leakage out of the cavity.

We study an ultracold trapped Fermi gas of atoms in two hyperfine states with unequal populations. In this situation the usual BCS pairing is suppressed and nonstandard pairing mechanisms become important. These are treated by solving the Bogoliubov–de Gennes equations, which at the same time correctly take into account the finite size of the trapped system. We find results which can be viewed as generalization of the LOFF (Larkin-Ovchinnikov-Fulde-Ferrel) phase to finite systems.

The rate of spontaneous electromagnetic emission in a cavity is the normalized output radiation rate in the classical electrodynamics and the Einstein $A$ coefficient in a quantum theory. We reveal the difference and similarity between the quantum and classical rates by calculations of the relative output power of the resonant spontaneous electric-dipole emission as a function of light absorption in a high-$Q$ cavity. We show that the relative resonant output power is equal to the relative width of a morphology-dependent resonance in the spectral dependence of the Einstein $A$ coefficient. The validity of the theory is demonstrated by numerical verification of an experimental result on a microsphere.

Different quantum mechanical operators can correspond to the same classical quantity. Hermitian operators differing only by operator ordering of the canonical coordinates and momenta at one moment of time are the most familiar example. Classical spacetime alternatives that extend over time can also be represented by different quantum operators. For example, operators representing a particular value of the time average of a dynamical variable can be constructed in two ways: first, as a projection onto the value of the time-averaged Heisenberg picture operator for the dynamical variable and, second, as the class operator defined by a sum over those histories of the dynamical variable that have the specified time-averaged value. We show by both explicit example and general argument that the predictions of these different representations agree in the classical limit and that sets of histories represented by them decohere in that limit.

For entangled states of light both the amount of entanglement and the sensitivity to noise generally increase with the number of photons in the state. The entanglement-sensitivity tradeoff is investigated for a particular set of states, multidimensional entangled coherent states. Those states possess an arbitrarily large amount of entanglement $E$ provided the number of photons is at least of order $2^{2E}$. We calculate how fast that entanglement decays due to photon absorption losses and how much entanglement is left. We find that for very small losses the amount of entanglement lost is equal to $2∕\ln \left(2\right)\approx 2.89$ ebits per absorbed photon, irrespective of the amount of pure-state entanglement $E$ one started with. In contrast, for larger losses it tends to be the remaining amount of entanglement that is independent of $E$. This may provide a useful strategy for creating states with a fixed amount of entanglement.

We provide an easily computable formula for a bipartite mixed-state entanglement measure. Our formula can be applied to readily calculate the entanglement for any rank-2 mixed state of a bipartite system. We use this formula to provide a tight upper bound for the entanglement of formation for rank-2 states of a qubit and a qudit. We also outline situations where our formula could be applied to study the entanglement properties of complex quantum systems.

We present a unifying approach to the quantification of entanglement based on entanglement witnesses, which includes several already established entanglement measures such as the negativity, the concurrence, and the robustness of entanglement. We then introduce an infinite family of new entanglement quantifiers, having as its limits the best separable approximation measure and the generalized robustness. Gaussian states, states with symmetry, states constrained to super-selection rules, and states composed of indistinguishable particles are studied under the view of the witnessed entanglement. We derive new bounds to the fidelity of teleportation $d_{\mathit{min}}$, for the distillable entanglement $E_D$ and for the entanglement of formation. A particular measure, the PPT-generalized robustness, stands out due to its easy calculability and provides sharper bounds to $d_{\mathit{min}}$ and $E_D$ than the negativity in most of the states. We illustrate our approach studying thermodynamical properties of entanglement in the Heisenberg XXX and dimerized models.

The reduction criterion is a well-known necessary condition for separable states, and states violating this condition are entangled and also 1-distillable. In this paper we introduce a set of necessary conditions for separability of multipartite states, obtained from a set of positive but not completely positive maps. These conditions can be thought of as generalizations of the reduction criterion to multipartite systems. We use tripartite Werner states as an example to investigate the entanglement detecting powers of some of these conditions, and we also look at what these conditions mean in terms of distillation. Finally, we show that these maps can be used to give a partial solution to the subsystem problem, as described by Butterley et al.

Considering the dynamics of a two-qubit entangled system in the decoherence environment, we investigate the stability of pairwise entanglement under decoherence. We find that for different decoherence models, there exists some special class of entangled states of which the pairwise entanglement is the most stable. The lifetime of the entanglement in these states is larger than other states with the same initial entanglement. In addition, we also investigate the dynamics of pairwise entanglement in the ground state of spin models such as Heisenberg and $XXY$ models.

High-field negative-muon spin precession experiments have been performed using a backward-muon beam with substantial transverse spin polarization, facilitating high-precision measurements of the magnetogyric ratio of negative muons bound to nuclei in the ground states of muonic atoms. These results may provide a testing ground for quantum electrodynamics in very strong electromagnetic fields.

The present results report a computational analysis of the effects of symmetric bond stretching during positron scattering from polyatomic hydrocarbon molecules in the gas phase. The collisions are considered at very low energies where the behavior of the $s$-wave scattering length can be analyzed and where signatures of virtual state formation appear for all the three systems considered (${\mathrm{C}}_2{\mathrm{H}}_2$, ${\mathrm{C}}_2{\mathrm{H}}_4$, and ${\mathrm{C}}_2{\mathrm{H}}_6$). Furthermore, the present calculations show that the stretching of the CH bonds in all molecules causes the moving of the existing virtual state closer to threshold and further makes it become a bound state whenever highly distorted molecules are involved. The effects of these changes are further seen to cause a marked enhancing of the corresponding annihilation parameters $Z_{\mathit{eff}}$ at low collision energies, in line with what is experimentally observed for such gases. The significance of such model calculations is discussed in some detail.