The electric-dipole $5s\text{−}5p$ resonance transitions in highly ionized promethiumlike ions have been studied applying relativistic multireference Møller-Plesset second-order perturbation theory. The transition wavelengths are determined to within 0.2 Å in the more highly charged ions, where the level degeneracies are small. For somewhat lighter ions a very large reference space was used in order to account for the many degeneracies. In order to calculate transition probabilities and lifetimes, correlation corrections have been added to the transition operator in the next order. The contributions from the higher orders of the theory—that is, frequency-dependent Breit correction, Lamb shift, and mass shifts—have been estimated. The results are used to reassess spectroscopic data from beam-foil, electron-beam ion-trap, and tokamak observations.

In this work, we investigated the influence of polarization effects on the electronic excitation of the $\tilde{a}{{}^{3}B}_{1u}$ state of ethylene. We employed the Schwinger multichannel method implemented with pseudopotentials to compute the elastic and the inelastic scattering cross sections for energies between 0 and 8 eV. Elastic calculations were performed in the static-exchange and static-exchange plus polarization approximations, and inelastic calculations were performed in a two-channel approximation with and without the inclusion of polarization effects. The scattering amplitudes are generated in the scope of the minimal orbital basis for single configuration interactions strategy. Ethylene presents a shape resonance in the ${{}^{2}B}_{2g}$ symmetry located close to the threshold of the $\tilde{a}{{}^{3}B}_{1u}$ state. We show that the inclusion of polarization effects has a great influence on the excitation cross section and also that, in this case, just the two-channel close coupling without polarization is not enough to provide reliable results. In particular, our computed inelastic differential cross sections obtained with the proper treatment of polarization are in better agreement with the experimental values. They are smaller in magnitude than those obtained in the two-channel calculation without the inclusion of polarization effects. These results confirm our expectations reported in a recent publication on electron collisions with furan [da Costa, Bettega, and Lima, Phys. Rev. A 77, 012717 (2008)].

We present an ab initio nonperturbative time-dependent approach to the problem of a helium atom driven by an intense xuv laser pulse. Based on the finite-element discrete-variable-representation, a space discretization is proposed for the radial grid in spherical coordinates. Absolute angle-integrated and triple-differential cross sections for double ionization by absorption of two photons are obtained over a range of photon energies between 39.5 eV (31.4 nm) and 54 eV (23 nm), where the process is dominated by nonsequential ionization mechanisms. We show that the agreement with several other sets of previous predictions is good, as long as the effective interaction time is defined properly. Two-photon double ionization at the photon energy of 57 eV (22 nm), for which both sequential and nonsequential channels are open, is also discussed. For double photoionization in the near-threshold regime, our results do not indicate a preferential mode of energy sharing between the two escaping electrons, while asymmetric energy sharing becomes the dominant mode with increasing excess energy. Overall, the two ionized electrons strongly prefer to escape along the polarization axis of linearly polarized laser fields.

In a previous paper [Schleif and Delos, Phys. Rev. A 76, 013404 (2007)] we described the spectrum of hydrogen atoms in near-perpendicular electric and magnetic fields. We displayed a number of previously unrecognized structures in the spectrum, most of which are connected with a classical phenomenon called “nontrivial monodromy of action and angle variables in a Hamiltonian system,” or simply “monodromy.” In that paper, we presented only the results, giving predictions of what to look for in various ranges of electric and magnetic fields. Here we present the underlying theory. Starting from Kepler action and angle variables, we give a derivation of a classical Hamiltonian to second order in perturbation theory; the derivation is different from, but the final result agrees with, previous work. We focus especially on the topological structure of the reduced phase space and on the resulting topological structure of the trajectories. We show that construction of action variables by the obvious methods leads to variables that have discontinuous derivatives. Smooth continuation of these “primitive” action variables leads to action variables that are multivalued. We show how these multivalued actions lead to lattice defects in the quantum spectrum. Finally we present a few correlation diagrams which show how quantum eigenvalues evolve from one region of near-perpendicular parameter space to another.

A variational Monte Carlo calculation of the one-body density matrix and momentum distribution of a system of Fermi hard rods (HRs) is presented and compared with the same quantities for its bosonic counterpart. The calculation is exact within statistical errors since we sample the exact ground-state wave function, whose analytical expression is known. The numerical results are in good agreement with known asymptotic expansions valid for Luttinger liquids. We find that the difference between the absolute value of the bosonic and fermionic density matrices becomes marginally small as the density increases. In this same regime, the corresponding momentum distributions merge into a common profile that is independent of the statistics. Nonanalytical contributions to the one-body density matrix are also discussed and found to be less relevant with increasing density.

Different expressions for the linear polarizability of a two-level atom with radiative corrections have been derived recently. We show that an expression said to differ from that obtained by the present authors is in fact consistent with it. The same-sign and opposite-sign prescriptions for linewidths are revisited with respect to the polarizability, the scattering amplitude, and the optical theorem. Both prescriptions represent approximations to more general expressions in the two-level case, and neither is correct for transitions between excited atomic states, as we demonstrate by calculating the linear polarizability of a three-level atom.

We present a formula to evaluate the spontaneous emission spectra of an atom in contact with a radiation field with non-Markovian effects. This formula is written in terms of a two-time correlation of system observables and the environmental correlation function, and depends on the distance between the emitting atom and the detector. As an example, we use it to analyze the fluorescence spectra of a two level atom placed as an impurity in a photonic crystal. The radiation field within those materials has a gap or discontinuity where electromagnetic modes cannot propagate in the stationary limit. In that situation, the atomic emission occurs in the form of evanescent waves which are detected with less efficiency the farther we place the detector. The methodology presented in this paper may be useful to study the non-Markovian dynamics of any quantum open system in linear interaction with a harmonic oscillator reservoir and within the weak-coupling approximation.

We theoretically investigate the joint photodetection probabilities of the biexciton-exciton cascade in single semiconductor quantum dots and analytically derive the density matrix and the Bell’s inequalities of the entangled state. Our model includes different mechanisms that may spoil or even destroy entanglement such as dephasing, energy splitting of the relay excitonic states, and incoherent population exchange between these relay levels. We explicitly relate the fidelity of entanglement to the dynamics of these processes and derive a threshold for violation of Bell’s inequalities. Applied to standard InAs/GaAs self-assembled quantum dots, our model indicates that spontaneous emission enhancement of the excitonic states by cavity effects increases the fidelity of entanglement to a value allowing for violation of Bell’s inequalities.

The Coulomb excitation of highly charged few-electron ions in relativistic collisions with protons and low-$Z$ atoms is studied within the framework of first-order perturbation theory and the multiconfiguration Dirac-Fock method. Apart from the computation of the total excitation cross sections, a detailed theoretical analysis has been performed for the magnetic sublevel population of the residual ions. To describe this population, general expressions are derived for the alignment parameters of the excited states of the ions, taking into account the relativistic and many-electron effects. Calculations are performed for the $K\to L$ and $K\to M$ excitation of helium- and lithiumlike uranium ions and for a wide range of projectile energies. It is shown that the alignment of heavy few-electron ions is sensitive to relativistic and magnetic-interaction effects and, hence, to the collision energies of the projectiles. The theoretical predictions are discussed in the context of recent measurements on the Coulomb excitation of heliumlike uranium ${\text{U}}^{90+}$ ions which were recently performed at the GSI storage ring in Darmstadt.

We present accurate time-dependent ab initio calculations on fully differential and total integrated (generalized) cross sections for the nonsequential two-photon double ionization of helium at photon energies from 40 to 54 eV. Our computational method is based on the solution of the time-dependent Schrödinger equation and subsequent projection of the wave function onto Coulomb waves. We compare our results with other recent calculations and discuss the emerging similarities and differences. We investigate the role of electronic correlation in the representation of the two-electron continuum states, which are used to extract the ionization yields from the fully correlated final wave function. In addition, we study the influence of the pulse length and shape on the cross sections in time-dependent calculations and address convergence issues.

Relating to magnified image formation systems, we consider two processes in this work: quantum and classical incoherent imaging. There are similarities and differences between them. A similarity is that the optical transfer functions (OTFs) of both systems are obtained by calculating a correlation function. Concerning the differences, only two were found. The first difference is that, unlike classical incoherent imaging, quantum imaging with photon pairs generated by spontaneous parametric down-conversion is sensitive to the phase in the function which describes the object. The second difference is that the OTF of the quantum imaging system is a cross-correlation function of the OTFs of the signal and idler arms, while the OTF of the classical incoherent imaging system is an autocorrelation of the only pupil function existing in this case. We explore experimentally the second difference. We report the observation of a highly resolved image produced by a quantum light source in a setup where an incoherent light source is unable to spatially resolve the image of the object. The spatial resolution of the image is studied in a situation where the size of the object is magnified at the image.

We study emission of a single photon from a spherically symmetric cloud of $N$ atoms (one atom is excited; $N-1$ are in the ground state) and present an exact analytical expression for eigenvalues and eigenstates of this many-body problem. We found that some states decay much faster than the single-atom decay rate, while other states are trapped and undergo very slow decay. When the size of the atomic cloud is small compared with the radiation wavelength, we found that the radiation frequency undergoes a large shift.

We provide an estimate of the absolute values of the emission rate of photon pairs produced by spontaneous parametric down-conversion in a bulk crystal when all interacting fields are in single transverse Gaussian modes. Both collinear and noncollinear configurations are covered, and we arrive at a fully analytical expression for the collinear case. Our results agree reasonably well with values found in typical experiments, which allows this model to be used for understanding the dependency on the relevant experimental parameters.

A characterization of multipartite quantum states having $N$ subsystems, based on negativities of matrices obtained by selective partial transposition of the state operator, is proposed. The $K$-way partial transpose with respect to a subsystem is constructed by imposing constraints involving the states of $K$ subsystems of the multipartite composite system. The $K$-way negativity, defined as the negativity of $K$-way partial transpose, quantifies the $K$-way coherences of the composite system. For an $N$-partite system the fraction of $K$-way negativity $\left(2\le K\le N\right)$, contributing to global negativity, is obtained. The entanglement measures for a given state $\widehat{\rho }$ are identified as the partial $K$-way negativities of the corresponding canonical state.

We develop a grid method for multichannel scattering of atoms in a waveguide with harmonic confinement. This approach is employed to extensively analyze the transverse excitations and deexcitations as well as resonant scattering processes. Collisions of identical bosonic and fermionic as well as distinguishable atoms in harmonic traps with a single frequency $\omega$ permitting the center-of-mass (c.m.) separation are explored in depth. In the zero-energy limit and single mode regime we reproduce the well-known confinement-induced resonances (CIRs) for bosonic, fermionic, and heteronuclear collisions. In the case of the multimode regime up to four open transverse channels are considered. Previously obtained analytical results are extended significantly here. Series of Feshbach resonances in the transmission behavior are identified and analyzed. The behavior of the transmission with varying energy and scattering lengths is discussed in detail. The dual CIR leading to a complete quantum suppression of atomic scattering is revealed in multichannel scattering processes. Possible applications include, e.g., cold and ultracold atom-atom collisions in atomic waveguides and electron-impurity scattering in quantum wires.

We study superfluorescence (SF) from spherical and cigar-shaped clouds of laser-cooled Rubidium atoms from the $5D_{5/2}$ level through the $6P_{3/2}$ level to the $5S_{1/2}$ ground level. The atomic system is initially excited to the $5D_{5/2}$ level from the ground state via two-photon excitation through the intermediate $5P_{3/2}$ level. The fluorescence on the $6P\text{−}5S$ transition at 420 nm is recorded using time-resolved measurements. The time delays of the observed SF emission peaks typically scale as $\sim N^{-1}$, where $N$ is the atom number, and are much smaller than the time delay expected for uncorrelated cascade fluorescence. Since $N$ is significantly smaller than the threshold number for SF on the 420 nm transition, and larger than the threshold number for the $5D\text{−}6P$ transition at $5.2\mu \text{m}$, our observations suggest that the 420 nm SF emission is triggered by rapid deexcitation of the $5D$ to the $6P$ level via SF at $5.2\mu \text{m}$. The observed SF time delays for 420 nm emission agree with SF time-delay estimates for the $5.2\mu \text{m}$ transition. For spherical clouds, the SF is isotropic. For cigar-shaped clouds, the SF is highly anisotropic. Along the long axis of cigar-shaped atom clouds, SF and incoherent cascade fluorescence produce temporally well-resolved peaks in the detected signal. In this case, the SF component of the signal is highly concentrated along a direction in between the directions of the two almost parallel excitation beams. The observed SF intensities scale as $N$, suggesting that the $5D$ level is regeneratively pumped during the SF decay.

In this paper, we study the phase diagram of a homogeneous Bose gas with a repulsive interaction near a wide Feshbach resonance at zero temperature. The Bose-Einstein-condensation (BEC) state of atoms is a metastable state. When the scattering length $a$ exceeds a critical value depending on the atom density $n$, $n{a}^3>0.035$, the molecular excitation energy is imaginary and the atomic BEC state is dynamically unstable against molecule formation. The BEC state of diatomic molecules has lower energy, where the atomic excitation is gapped and the molecular excitation is gapless. However, when the scattering length is above another critical value, $n{a}^3>0.0164$, the molecular BEC state becomes an unstable coherent mixture of atoms and molecules. In both BEC states, the binding energy of diatomic molecules is reduced due to the many-body effect.

The dynamics of $M$-site, $N$-particle Bose-Hubbard systems is described in quantum phase space constructed in terms of generalized $\text{SU}\left(M\right)$ coherent states. These states have a special significance for these systems as they describe fully condensed states. Based on the differential algebra developed by Gilmore, we derive an explicit evolution equation for the (generalized) Husimi $\left(Q\right)$ and Glauber-Sudarshan $\left(P\right)$ distributions. Most remarkably, these evolution equations turn out to be second-order differential equations where the second-order terms scale as $1/N$ with the particle number. For large $N$ the evolution reduces to a (classical) Liouvillian dynamics. The phase-space approach thus provides a distinguished instrument to explore the mean-field many-particle crossover. In addition, the thermodynamic Bloch equation is analyzed using similar techniques.

We find that the overlap of a topological quantum color-code state, representing a quantum memory, with a factorized state of qubits can be written as the partition function of a three-body classical Ising model on triangular or Union Jack lattices. This mapping allows us to test that different computational capabilities of color codes correspond to qualitatively different universality classes of their associated classical spin models. By generalizing these statistical mechanical models for arbitrary inhomogeneous and complex couplings, it is possible to study a measurement-based quantum computation with a color-code state and we find that their classical simulability remains an open problem. We complement the measurement-based computation with the construction of a cluster state that yields the topological color code and this also gives the possibility to represent statistical models with external magnetic fields.

The model of exact trajectories involved in a semiclassical computation of (vib)rotational linewidths and shifts is extended to the case of asymmetric top colliders. General expressions for the second-order contributions to the scattering matrix are given which define the pressure broadening and shift of the line. This theoretical approach is tested on the particular case of the infrared ${\nu }_7$ band linewidths of ${\text{C}}_2{\text{H}}_4$ broadened by ${\text{N}}_2$ which is frequently required for atmospheric applications. The computed linewidths compare favorably with available experimental data.