We have experimentally studied and numerically simulated the behavior of cold atomic clouds and Bose-Einstein condensates passing through a far red-detuned Gaussian beam. Several exotic phenomena such as the focusing and advancement of atomic clouds have been exhibited. The cooling effect and the effective interaction length of the dipole potential to the atoms have also been discussed.

Electronic structure in atoms and molecules modulates the amplitude and phase of high harmonic generation (HHG). We report measurements of the high harmonic spectral amplitude and phase in ${\text{N}}_2$. The phase is measured interferometrically by beating the ${\text{N}}_2$ harmonics with those of an Ar reference oscillator in a gas mixture. A rapid phase shift of $0.2\pi$ is observed in the vicinity of the HHG spectral minimum, where a shift of $\pi$ had been presumed [J. Itatani et al., Nature (London) 432, 867 (2004)]. We compare the phase measurements to a simulation of the HHG recombination step in ${\text{N}}_2$ that is based on a simple interference model. The results of the simulation suggest that modifications beyond the simple interference model are needed to explain HHG spectra in molecules.

Although the analysis of electromagnetic sources in the context of coordinate transformations and the implications for transformation optics have been discussed in the literature, a correct formulation that includes surface and line currents has not been reported. Here we derive how surface and line currents behave under coordinate transformations and validate the analysis through numerical validation of a specific example. This analysis enables transformation optics to be applied to problems that include singular source distributions, which is often the case for practical radiating systems and antennas, to make a given current distribution produce the same fields as a different current distribution by surrounding it with a material with specific electromagnetic properties.

The noise from laser phase fluctuation sets a major technical obstacle to cool the nanomechanical oscillators to the quantum region. We propose a cooling configuration based on the optomechanical coupling with two cavity modes to significantly reduce this phase noise by ${\left(2{\omega }_m/\gamma \right)}^2$ times, where ${\omega }_m$ is the frequency of the mechanical mode and $\gamma$ is the decay rate of the cavity mode. We also discuss the detection of the phonon number when the mechanical oscillator is cooled near the quantum region and specify the required conditions for this detection.

The spectral problem of the Dirac equation in an external quadratic vector potential is considered using the methods of the perturbation theory. The cases in one spatial dimension and in three spatial dimensions with spherical symmetry are explicitly studied. The problem is singular and the perturbation series is asymptotic, so that the methods for dealing with divergent series must be used. Among these, the distributional Borel sum appears to be the most well suited tool to give answers and to describe the spectral properties of the system. A detailed investigation is made in one and in three space dimensions with a central potential. We present numerical results for the Dirac equation in one space dimension: these are obtained by determining the perturbation expansion and using the Padé approximants for calculating the distributional Borel transform. A complete agreement is found with previous nonperturbative results obtained by the numerical solution of the singular boundary value problem and the determination of the density of the states from the continuous spectrum.

We generalize the standard Born-Oppenheimer approximation to the case of open quantum systems. We define the zeroth-order Born-Oppenheimer approximation for an open quantum system as the regime in which its effective Hamiltonian can be diagonalized with fixed slowly changing variables. We then establish validity and invalidity conditions for this approximation for two types of dissipations—the spin relaxation and the dissipation of center-of-mass motion. As an example, the Born-Oppenheimer approximation for a two-level open system is analyzed.

We present an approach to one-way quantum computation (1WQC) that can compensate for single-qubit errors by encoding the logical information residing on physical qubits into five-qubit error-correcting code states. A logical two-qubit cluster state that is the fundamental resource for encoded quantum teleportation is then described by a graph state containing ten vertices with constant degree seven. Universal 1WQC that incorporates error correction requires only multiple copies of this logical two-qubit state and a logical four-qubit linear cluster state, which are prepared only just in advance of their use in order to minimize the accumulation of errors. We suggest how to implement this approach in systems characterized by qubits in regular two-dimensional lattices for which entangling gates are generically global operations, such as atoms in optical lattices, quantum dots, or superconducting qubits.

We discuss the possibility to interpret the residual entanglement for more than three qubits in terms of distributed multipartite entanglement or, in other words, possible extensions of the Coffman-Kundu-Wootters monogamy equality to higher qubit numbers. Existing knowledge on entanglement in multipartite systems puts narrow constraints on the form of such extensions. We study various examples for families of pure four-qubit states for which the characterization of three-qubit and four-qubit entanglement in terms of polynomial invariants is known. These examples indicate that, although families with such extensions do exist, a generalized monogamy equality cannot be found along those lines.

The isoelectronic series of Be, Ne, and Si are investigated using a variational determination of the second-order density matrix. A semidefinite program was developed that exploits all rotational and spin symmetries in the atomic system. We find that the method is capable of describing the strong static electron correlations due to the incipient degeneracy in the hydrogenic spectrum for increasing central charge. Apart from the ground-state energy, various other properties are extracted from the variationally determined second-order density matrix. The ionization energy is constructed using the extended Koopmans’ theorem. The natural occupations are also studied, as well as the correlated Hartree-Fock-like single-particle energies. The exploitation of symmetry allows to study the basis set dependence and results are presented for correlation-consistent polarized valence double, triple, and quadruple zeta basis sets.

For model two-electron atoms with harmonic confinement, the correlated first-order density matrix can be expressed in terms of the relative motion wave function ${\Psi }_R\left(r\right)$. Here we demonstrate that the probability density $P\left(r\right)$ associated with this wave function is directly related to the x-ray scattering factor $f\left(G\right)$. This latter quantity, in turn, is determined by the ground-state electron density $n\left(r\right)$. The Euler-Lagrange equation of the resulting density-matrix theory is thereby shown to take the form of a third-order integro-differential equation for $n\left(r\right)$ in which the probability density $P\left(r\right)={\Psi }_R^2\left(r\right)$ also appears. For two specific choices of the interaction between the two fermions under consideration, the above integro-differential equation derived here is shown to lead back to known linear homogeneous differential equations for the electron density. Finally, it is emphasized that specific equations summarized here will apply directly to theoretical study of the nonrelativistic ground-state electron density $n\left(r,Z\right)$ in the He-like ions with atomic number $Z$.

We apply the asymptotic method and a semiclassical coupled-channel approach to study the one- and two-electronic processes occurring in the course of slow collisions between multiply charged atomic ion and diatomic molecules with two active electrons. The matrix elements responsible for different processes of single and double electron transfer are calculated asymptotically correctly (for large distances $R$ between interacting particles) in the framework of the nonperturbative Landau-Herring approach. The methods are applied for study of single and double electron transfer in ${\text{H}}_2+{\text{He}}^{2+}$ collisions at impact energies 0.1–30 keV/amu. Our calculations are in fairly good agreement with available experimental data and theoretical calculations of other authors.

We devise an ab initio formalism for the quantum dynamics of Auger decay by laser-dressed atoms which are inner-shell ionized by extreme ultraviolet (xuv) light. The optical dressing laser is assumed to be sufficiently weak such that ground-state electrons are neither excited nor ionized by it. However, the laser has a strong effect on continuum electrons which we describe in strong-field approximation with Volkov waves. The xuv light pulse has a low peak intensity and its interaction with the atom is treated as a one-photon process. The quantum dynamics of the inner-shell hole creation with subsequent Auger decay is given by equations of motion (EOMs). For this paper, the EOMs are simplified in terms of an essential-states model which averages over magnetic subshells and is solved analytically. We apply our theory to the $M_{4,5}{N}_1{N}_{2,3}$ Auger decay of a $3d$ hole in a krypton atom. The orbitals are approximated by scaled hydrogenic wave functions. A single attosecond pulse produces $3d$ vacancies which Auger decay in the presence of an 800 nm laser with an intensity of ${10}^{13}\text{W}{\text{cm}}^{-2}$. We compute the Auger electron spectrum and assess the convergence of the various quantities involved.

We use a regularized harmonic-fluid approach, based on the effective low-energy Luttinger-liquid Hamiltonian, for a one-dimensional Bose gas with repulsive contact interactions to compute the complete series corresponding to the large-distance off-diagonal behavior of the one-body density matrix for any value of the Luttinger parameter $K$. We compare our results with the exact ones known in the Tonks-Girardeau limit of infinitely large interactions (corresponding to $K=1$), and different from the usual harmonic-fluid approach, we recover the full structure of the series. The structure is conserved for arbitrary values of the interaction strength with power laws fixed by the universal parameter $K$ and a sequence of subleading corrections.

Dynamic self-similar solutions of the nonlinear Schrödinger equation are derived describing the propagation of partially coherent solitons in media with saturable logarithmic nonlinearity. The analysis is based on both the Wigner and the coherent density formalisms and it is shown that although the approaches involve different analysis, the solutions for the evolution of the physically relevant intensity distributions are equivalent.

It has previously been shown that quantum nonlocality offers no benefit over classical correlations for performing a distributed task known as nonlocal computation. This is where separated parties must compute the value of a function without individually learning anything about the inputs. We show that giving the parties some knowledge of the inputs, however small, is sufficient to “unlock” the power of quantum mechanics to outperform classical mechanics. This role of information held locally gives insight into the general question of when quantum nonlocality gives an advantage over classical physics. Our results also reveal an interesting feature of the nonlocality embodied in the celebrated task of Clauser, Horne, Shimony, and Holt.

In this contribution we study the Landau levels arising within the relativistic quantum dynamics of a neutral particle with a permanent magnetic dipole moment interacting with an external electric field. We consider the Aharonov-Casher coupling of the magnetic dipole to the electric field and investigate an analog of Landau quantization in this system for two different field configurations. In both cases we obtain the eigenfunctions and eigenvalues of the Hamiltonian.

We propose a strategy to generate a many-body entangled state in a collection of randomly placed, dipolarly coupled electronic spins in the solid state. By using coherent control to restrict the evolution into a suitable collective subspace, this method enables the preparation of GHZ-like and spin-squeezed states even for randomly positioned spins, while in addition protecting the entangled states against decoherence. We consider the application of this squeezing method to improve the sensitivity of nanoscale magnetometer based on nitrogen-vacancy spin qubits in diamond.

We report a kinematically complete experiment of carbon $1s$ photoionization of ${\text{CO}}_2$ including Auger decay and fragmentation. By measuring in coincidence of ${\text{CO}}_2$ $\text{C}\left(1s\right)$ photoelectrons and ion fragments using synchrotron light at several energies above the $\text{C}\left(1s\right)$ threshold, we determine photoelectron angular distributions as well as Auger-electron angular distributions with full solid angle in the molecular fixed frame. We confirm recent unexpected results showing an asymmetry of the photoelectron angular distribution along the molecular axis after ionization of the $\text{C}\left(1s\right)$ orbital. Our high statistics and high resolution measurement unveils asymmetric features in the photoelectron angular distribution which change as a function of the kinetic energy release. This finding provides strong evidence that varying C–O bondlengths are the main cause for these asymmetries. The Auger-electron angular distributions do not show strong correlation with the photoelectrons.

For the family of model soft-core Coulomb potentials represented by $V\left(r\right)=-\left[Z/{\left(r^q+{\beta }^q\right)}^{1/q}\right]$, with the parameters $Z>0,\beta >0,q\ge 1$, it is shown analytically that the potentials and eigenvalues, $E_{\nu \ell }$, are monotonic in each parameter. The potential envelope method is applied to obtain approximate analytic estimates in terms of the known exact spectra for pure power potentials. For the case $q=1$, the asymptotic iteration method is used to find exact analytic results for the eigenvalues $E_{\nu \ell }$ and corresponding wave functions, expressed in terms of $Z$ and $\beta$. A proof is presented establishing the general concavity of the scaled electron density near the nucleus resulting from the truncated potentials for all $q$. Based on an analysis of extensive numerical calculations, it is conjectured that the crossing between the pair of states $\left[\left(\nu ,\ell \right),\left({\nu }^{\prime },{\ell }^{\prime }\right)\right]$ is given by the conditions ${\nu }^{\prime }\ge \left(\nu +1\right)$ and ${\ell }^{\prime }\ge \left(\ell +3\right)$. The significance of these results for the interaction of intense laser field with an atom is pointed out. Differences in the observed level-crossing effects between the soft-core potentials and the hydrogen atom confined inside an impenetrable sphere are discussed.