The modulational instability of the nonlinear Schrödinger (NLS) equation is examined in the case with a quadratic external potential. This study is motivated by recent experimental results in the context of matter waves in Bose-Einstein condensates (BECs). The theoretical analysis invokes a lens-type transformation that converts the Gross-Pitaevskii into a modified NLS equation without explicit spatial dependence. This analysis suggests the particular interest of a specific time-varying potential $\left[\sim {(t+t}^{*}{)}^{-2}\right].$ We examine both this potential, as well as the time-independent one numerically and conclude by suggesting experiments for the production of solitonic wave trains in BECs.

We investigate the decoherence of a superposition of symmetric collective internal states of an atomic ensemble due to inhomogeneous coupling to external control fields. For asymptotically large system, we find $\sqrt{N}$ as the characteristic decoherence rate scale with N being the total number of atoms. Our results shed new light on attempts for realizing quantum information processing and storage with atomic ensembles.

We study the local implementation of positive-operator-valued measures (POVMs) when we require only the faithful reproduction of the statistics of the measurement outcomes for all initial states. We first demonstrate that any POVM with separable elements can be implemented by a separable superoperator, and develop techniques for calculating the extreme points of POVMs under a certain class of constraint that includes separability and positive partial transposition. As examples we consider measurements that are invariant under various symmetry groups (Werner, isotropic, Bell diagonal, local orthogonal), and demonstrate that in these cases separability of the POVM elements is equivalent to implementability via local operations and classical communication (LOCC). We also calculate the extrema of these classes of measurement under the groups that we consider, and give explicit LOCC protocols for attaining them. These protocols are hence optimal methods for locally discriminating between states of these symmetries. One of many interesting consequences is that the best way to locally discriminate Bell-diagonal mixed states is to perform a two-outcome POVM using local von Neumann projections. This is true regardless of the cost function, the number of states being discriminated, or the prior probabilities. Our results give the first cases of local mixed-state discrimination that can be analyzed quantitatively in full, and may have application to other problems such as demonstrations of nonlocality, experimental entanglement witnesses, and perhaps even entanglement distillation.

A quantum cryptography implementation is presented that uses entanglement to combine one-way operation with an autocompensating feature that has hitherto only been available in implementations that require the signal to make a round trip between the users. Using the concept of advanced waves, it is shown that this proposed implementation is related to the round-trip implementation in the same way that Ekert’s two-particle scheme is related to the original one-particle scheme of Bennett and Brassard. The practical advantages and disadvantages of the proposed implementation are discussed in the context of existing schemes.

Alkaline-earth-metal atoms in their lowest $\mathrm{}\left(\mathrm{nsnp}\right)\mathrm{}$ ${}^3{P}_2$ state are exceptionally long lived and can be trapped magnetically. The nonspherical atomic structure leads to anisotropic long-range interactions between two metastable alkaline-earth-metal atoms. The anisotropy affects the rotational motion of the diatomic system and couples states of different rotational quantum numbers. This paper develops a tensorial decomposition of the most important long-range interaction operators, and a systematic inclusion of molecular rotations, in the presence of an external magnetic field. This analysis illuminates the nature of the coupling between the various degrees of freedom. The consequences are illustrated by application to a system of practical interest: metastable ${}^{88}\mathrm{Sr}.$ Using atomic parameters determined in a nearly ab initio calculation, we compute adiabatic potential-energy curves. The anisotropic interatomic interaction, in combination with the applied magnetic field, is demonstrated to induce the formation of a long-range molecular potential well. This curve correlates to two fully polarized, low-field seeking atoms in a rotational s-wave state. The coupling among molecular rotational states controls the existence of the potential well, and its properties vary as a function of magnetic-field strength, thus allowing the scattering length in this state to be tuned. The scattering length of metastable ${}^{88}\mathrm{Sr}$ displays a resonance at a field of 339 G.

It is found that dipole-quadrupole photoelectron angular distribution parameters in regions of $n\overrightarrow{p}\mathrm{nd}$ giant dipole resonances in $3d\mathrm{}(n=3\mathrm{})\mathrm{}$ and $4d\mathrm{}(n=4\mathrm{})\mathrm{}$ transition-metal atoms are resonantly increased to such an extent that they can dominate the effects of dipole transitions on the asymmetry of the photoelectron angular distribution. This is illustrated for $3d$ photoionization of Cr and Mn, as well as for $4d$ photoionization of Mo and Tc, where the “spin-polarized” random-phase approximation with exchange calculations are performed with allowance for correlations in both dipole and quadrupole channels.

We have measured the kinetic energy release for the decay ${\mathrm{C}}_{60}^{q+}\to {\mathrm{C}}_{60-2m}^{\left(q-1\right)+}+{\mathrm{C}}_{2m}^{+}$ for charge states $q=4\mathrm{}–8$ and $m=1\mathrm{}$ and 2. The measured kinetic-energy release increases linearly with the fullerene charge state. The estimates of the barrier heights, deduced from the kinetic-energy releases, agree well with the observations regarding the stability and the competition between charge separation $({\mathrm{C}}_2^{+}$ emission) and neutral ${\mathrm{C}}_2$ emission of highly charged fullerenes.

The time evolution of a dilute atomic boson-fermion mixture is studied at zero temperature, when the external magnetic field is brought close to an interspecies Feshbach resonance. On short time scales we find that before a collapse or phase separation of the mixture can occur, oscillations between fermionic atoms and heteronuclear molecules dominate the dynamics. Applying the model presented here to a trapped mixture of ${}^{40}\mathrm{K}{-}^{87}\mathrm{Rb}$ atoms, we find that the predicted oscillations can be revealed in degenerate mixtures of these atoms.

The nuclear spin-dependent parity-nonconserving (PNC) interaction arising from a combination of the hyperfine interaction and the coherent, spin-independent, PNC interaction from Z exchange is evaluated using many-body perturbation theory. For the ${6s}_{1/2}-{7s}_{1/2}$ transition in ${}^{133}\mathrm{Cs},$ we obtain a result that is about 40% smaller than that found previously by Bouchiat and Piketty [Phys. Lett. B 269, 195 (1991)]. Applying this result to ${}^{133}\mathrm{Cs}$ leads to an increase in the experimental value of nuclear anapole moment and exacerbates differences between constraints on PNC meson coupling constants obtained from the Cs anapole moment and those obtained from other nuclear parity violating experiments. Nuclear spin-dependent PNC dipole matrix elements, including contributions from the combined weak-hyperfine interaction, are also given for the ${7s}_{1/2}-{8s}_{1/2}$ transition in ${}^{211}\mathrm{Fr}$ and for transitions between ground-state hyperfine levels in K, Rb, Cs, ${\mathrm{Ba}}^{+},$ Au, Tl, Fr, and ${\mathrm{Ra}}^{+}.$

A sequence of five laser pulses is presented, implementing a controlled-NOT gate in a linear arrangement of trapped ions. This gate works if the quantum number of the collective vibration (phonon bus) is zero or one. We interpret this property as tolerance against errors caused by imperfect ground-state preparation. The periodicity of two Rabi frequencies is used in order to obtain this property. The gate implementation is designed in a way which does not correspond to the well-known phase-gate construction.

We investigate on how to generate maximally entangled states in systems characterized by the Hamiltonian of the $\mathrm{XXZ}$ model with defects. Some proposed quantum computers are described by such a model. Defects embedded in this otherwise homogeneous spin chain are used to obtain Einstein-Podolsky-Rosen and W states. It is well known that a large defect localizes an excitation on the defect site. We can then consider a few identical and large defects to create a subsystem whose eigenstates are entangled. Here, we examine the cases of one and two excitations.

We present the full experimental quantum tomographic characterization of a single-qubit device achieved with a single entangled input state. The entangled input state plays the role of all possible input states in quantum parallel on the tested device. The method can be trivially extended to any n-qubit device by just replicating the whole experimental setup n times.

The relativistic distorted-wave Born approximation is used to calculate differential and total cross sections for inner shell ionization of neutral atoms by electron and positron impact. The target atom is described within the independent-electron approximation using the self-consistent Dirac-Fock-Slater potential. The distorting potential for the projectile is also set equal to the Dirac-Fock-Slater potential. For electrons, this guarantees orthogonality of all the orbitals involved and simplifies the calculation of exchange T-matrix elements. The interaction between the projectile and the target electrons is assumed to reduce to the instantaneous Coulomb interaction. The adopted numerical algorithm allows the calculation of differential and total cross sections for projectiles with kinetic energies ranging from the ionization threshold up to about ten times this value. Algorithm accuracy and stability are demonstrated by comparing differential cross sections calculated by our code with the distorting potential set to zero with equivalent results generated by a more robust code that uses the conventional plane-wave Born approximation. Sample calculation results are presented for ionization of K- and L-shells of various elements and compared with the available experimental data.

We present total single- and double-ionization cross sections for the collision systems $\overline{p}+\mathrm{He}$ and $\overline{p}+{\mathrm{Li}}^{+}$ in the 1–1000 keV impact energy range with emphasis on microscopic response effects during the collision. The calculations rely on the basis generator method. In both collision systems, the response of the effective electronic interaction to the time-dependent density reduces the ionization cross section at low impact energies significantly. It is shown, in comparison with other theories, that this reduction is a consequence of time-dependent screening rather than due to dynamical correlation effects.

Double K-shell photoionization of Ne at 5000 eV was observed by recording the KK-KLL Auger-electron hypersatellite spectrum. The measured Auger spectrum is compared with the results of multiconfiguration Dirac-Fock calculations. Shake calculations are used to identify likely multivacancy states produced by photoexcitation or ionization in addition to double-$K$ vacancies, and their calculated Auger spectra are compared with the measured spectrum. The measured relative intensities of hypersatellite and diagram Auger lines are combined with experimental and theoretical determinations of branching ratios from single- and double-$K$ vacancies into final states to determine the ratio of double-to-single K-shell photoionization cross sections to be 0.32(4)%. This ratio is much larger than the calculated high-energy-limit ratio and indicates a large contribution of dynamic electron correlation.

The optimized structure and electronic properties of neutral and singly charged magnesium clusters have been investigated using ab initio theoretical methods based on density-functional theory and systematic post–Hartree-Fock many-body perturbation theory accounting for all electrons in the system. We have systematically calculated the optimized geometries of neutral and singly charged magnesium clusters consisting of up to 21 atoms, electronic shell closures, binding energies per atom, ionization potentials, and the gap between the highest occupied and the lowest unoccupied molecular orbitals. We have investigated the appearance of the elements of the hcp structure and metallic evolution of the magnesium clusters, as well as the stability of linear chains and rings of magnesium atoms. The results obtained are compared with the available experimental data and the results of other theoretical works.

We study nonlinear electron-positron pair creation in the process where huge amounts of energy and momentum are imparted into the physical vacuum due to the collision of an ultrarelativistic nucleus with a high-intensity laser beam. We use an approach which fully accounts for the interaction of the leptons with the laser field, while the treatment of their interaction with the nucleus is restricted to the first order of perturbation theory. We calculate energy and angular spectra for one of the produced leptons, and the total production rate as a function of the energy of the nucleus. Our results suggest that by the aid of the upcoming accelerator generation, pair production in such collisions might be experimentally observable. Moreover, according to our calculations, the pair creation occurs as a highly nonlinear process far above the energy threshold, which leads to distinct features of the differential production rates.

By using the Green-function concept of quantization of the electromagnetic field in dispersing and absorbing media, the quantized field in the presence of a dispersing and absorbing dielectric multilayer plate is studied. Three-dimensional input-output relations are derived for both amplitude operators in the $\mathbf{k}$ space and the field operators in the coordinate space. The conditions are discussed, under which the input-output relations can be expressed in terms of bosonic operators. The theory applies to both (effectively) free fields and fields, created by active atomic sources inside and/or outside the plate, including also evanescent-field components.

We investigate the dynamics of a composite quantum system, comprised of coupled subsystems, of which only one is significantly interacting with the environment. The validity of the conventional ad hoc approach—assuming that relaxation terms can be extracted directly from the master equation of the subsystem interacting with the reservoir—was examined. We derived the equation of motion for the composite system’s reduced density matrix—applying only the factorization approximation, but not the conventional sequence of Markoff, coarse grain, and secular approximations. From our analysis, we concluded that the conventional ad hoc approach is applicable to zero-temperature reservoir, but fails for finite temperatures. It is further shown that at finite temperatures, the standard procedure does not even yield a master equation for the composite system, and its dynamics has to be studied by the equations of motion which are developed here. For demonstration we considered a system of a three-level atom, the two excited states are coupled to each other, and only one of them communicates with the ground state via a radiation reservoir.

We show that the eight-port interferometer used by Noh, Fougères, and Mandel [Phys. Rev. Lett. 71, 2579 (1993)] to measure their operational phase distribution of light can also be used to measure the canonical phase distribution of weak optical fields, where canonical phase is defined as the complement of photon number. A binomial reference state is required for this purpose, which we show can be obtained to an excellent degree of approximation from a suitably squeezed state. The proposed method requires only photodetectors that can distinguish among zero photons, one photon, and more than one photon and is not particularly sensitive to photodetector imperfections.