Photoionization of heliumlike targets accompanied by transition of the residual ions into the arbitrary $nl$ state is studied. The method of nonrelativistic perturbation theory with respect to the interelectron interaction is employed. Cross sections are deduced in the form of universal scalings, which hold for nonrelativistic energies including the near-threshold range. Numerical calculations are compared both with available experimental and with theoretical results.

Based on quantum theory, we investigate the distribution of the electrons scattered in the nonlinear Compton effect by an electromagnetic plane wave. The monochromatic case, examined in detail, reveals features of the electron distribution that are useful in the understanding of the pulsed plane-wave case for particular intensity and electron energy regimes. The graphs displayed focus on the case of a head-on or nearly head-on collision of an energetic electron with an electromagnetic circularly polarized pulsed plane wave and show that the deviation in direction is extremely small, while the distribution in energy can be visibly different from that of the initial electron. Two pulse shapes, several laser intensities, and high incident electron energies are considered.

Critical dynamics of an ultracold Bose gas far from equilibrium is studied in two spatial dimensions. Superfluid turbulence is created by quenching the equilibrium state close to zero temperature. Instead of immediately rethermalizing, the system approaches a meta-stable transient state, characterized as a nonthermal fixed point. A focus is set on the vortex density and vortex-antivortex correlations which characterize the evolution towards the nonthermal fixed point and the departure to final (quasi-)condensation. Two distinct power-law regimes in the vortex-density decay are found and discussed in terms of a vortex unbinding process and a kinetic description of vortex scattering. A possible relation to decaying turbulence in classical fluids is pointed out. By comparing the results to equilibrium studies of a two-dimensional Bose gas, an intuitive understanding of the location of the nonthermal fixed point in a reduced phase space is developed.

We analyze the quantum states of two identical bosons in a combined harmonic oscillator and periodic lattice trap in one spatial dimension. In the case of tight-binding and only nearest-neighbor tunneling, the equations of motion are conveniently represented in the momentum representation. We show that in the case of strong attraction between the particles, the different time scales of relative and center-of-mass motions validate a separation of the problem similar to the Born-Oppenheimer approximation applied in the description of electronic and nuclear motions in molecules.

We demonstrate steady-state, mirrorless superradiance in a cold vapor pumped by weak optical fields. Beyond a critical pump intensity of 1 mW/cm${}^2$, the vapor spontaneously transforms into a spatially self-organized state: a density grating forms. Scattering of the pump beams off this grating generates a pair of new, intense optical fields that act back on the vapor to enhance the atomic organization. We map out experimentally the superradiant phase transition boundary and show that it is well described by our theoretical model. The resulting superradiant emission is nearly coherent, persists for several seconds, displays strong temporal correlations between the various modes, and has a coherence time of several hundred $\mu$s. This system therefore has applications in fundamental studies of many-body physics with long-range interactions as well as all-optical and quantum information processing.

We investigate the nonlinear propagation of coherent light beams in planar samples of low-birefringence nematic liquid crystals, changing the input polarization and the incidence angle in order to enhance reorientational self-focusing and generate optical spatial solitons under a variety of previously unexplored launch conditions. We find that reorientational spatial solitons require larger excitation powers in low-birefringence than in high-birefringence nematic liquid crystals but remain stable. We compare the experimental results with full-vectorial numerical simulations.

We study the effect of interactions on the propagation of quantum correlations in the bosonic two-body quantum walk. The combined effect of interactions and Hanbury Brown–Twiss interference results in unique spatial correlations which depend on the strength of the interaction, but not on its sign. We experimentally measure the weak interaction limit of these effects using light propagating in a highly nonlinear photonic lattices. Finally, we propose an experimental approach to observe the strong interaction limit using few atoms in optical lattices.

Despite the fact that quantum tunneling has been studied since the advent of quantum mechanics, the literature appears to contain no simple (textbook) formula for tunneling in generic asymmetric double-well potentials. In the regime of strong localization, I derive a succinct analytical formula based on the Wentzel-Kramers-Brillouin semiclassical approach. Two different examples of asymmetric potentials are discussed: the cases when the two localized levels are degenerate and when they are not degenerate. For the first case, I also discuss a time-dependent problem showing the quantum Zeno effect.

We investigate a Landau-Zener (LZ) transition process modeled by a quantum two-level system (TLS) coupled to a photon mode when the bias energy is varied linearly in time. The initial state of the photon field is assumed to be a superposition of coherent states, leading to a more intricate LZ transition. Applying the rotating-wave approximation (RWA), analytical results are obtained revealing the enhancement of the LZ probability by increasing the average photon number. We also consider the creation of entanglement and the change of photon statistics during the LZ process. Without the RWA, we find some qualitative differences of the LZ dynamics from the RWA results; e.g., the average photon number no longer monotonically enhances the LZ probability. The ramifications and implications of these results are explored.

We study the nonlocal properties of two-qubit maximally entangled and $N$-qubit Greenberger-Horne-Zeilinger states under local decoherence. We show that the (non)resilience of entanglement under local depolarization or dephasing is not necessarily equivalent to the (non)resilience of Bell-inequality violations. Apart from entanglement and Bell-inequality violations, we consider also nonlocality as quantified by the nonlocal content of correlations and provide several examples of anomalous behaviors, both in the bipartite and multipartite cases. In addition, we study the practical implications of these anomalies on the usefulness of noisy Greenberger-Horne-Zeilinger states as resources for nonlocality-based physical protocols given by communication complexity problems.

We investigate the strong-coupling regime of a linear $x$-$x$ coupled harmonic-oscillator system by performing a direct diagonalization of the Hamiltonian. It is shown that the $x$-$x$ coupled Hamiltonian can be equivalently described by a Mach-Zehnder-type interferometer with a quadratic unitary operation in each of its arms. We show a sharp transition of the unitary operation from an elliptical phase rotator to an elliptical squeezer as the coupling gets stronger, leading to the continuous generation of entanglement, even for a significantly thermal state in the ultrastrong-coupled regime. It is also shown that this critical regime cannot be achieved by a classical Hookian coupling. Finally, the effect of a finite-temperature environment is analyzed, showing that entanglement can still be generated from a thermal state in the ultrastrong-coupled regime but is destroyed rapidly.

We address the experimentally relevant problem of robust mitigation of dephasing noise acting on a qubit. We first present an extension of the method of Kuopanportti et al. [Phys. Rev. A 77, 032334 (2008)] for representing $1/{\omega }^{\alpha }$ noise to the efficient representation of arbitrary Markovian noise. We then add qubit control pulses to enable the design of numerically optimized, two-dimensional, bounded amplitude control functions capable of decoupling the qubit from the dephasing effects of a broad variety of Markovian noise spectral densities during one- and two-qubit quantum operations. We illustrate the method with development of numerically optimized control pulse sequences that minimize decoherence due to a combination of $1/\omega$ and constant-offset noise sources. Comparison with the performance of standard dynamical decoupling protocols shows that the numerically optimized pulse sequences are considerably more robust with respect to zero-frequency noise. Application to the mitigation of dephasing noise on spin qubits in silicon indicates that high-fidelity quantum gates may, in principle, be implemented for such qubits with the assistance of current pulse-generation technology.

We have carried out calculations for one-dimensional model systems using the self-consistency algorithm of the recently published partition density-functional theory. The issues of uniqueness of occupation numbers and a relation to the self-consistent atomic deformation model are addressed. Possibilities for obtaining more accurate representations of the kinetic-energy functional and its potential are discussed.

High-precision multipole polarizabilities, ${\alpha }_{\ell }$ for $\ell \le 4$ of the $1s$ ground state of the hydrogen isoelectronic series, are obtained from the Dirac equation using the $B$-spline method with Notre Dame boundary conditions. Compact analytic expressions for the polarizabilities as a function of $Z$ with a relative accuracy of 10${}^{-6}$ up to $Z=100$ are determined by fitting to the calculated polarizabilities. The oscillator strengths satisfy the sum rules ${\sum }_i{f}_{gi}^{\left(\ell \right)}=0$ for all multipoles from $\ell =1$ to $\ell =4$. The dispersion coefficients for the long-range H-H and H-He${}^{+}$ interactions are given.

The cluster effect in the average charge and the energy loss of swift carbon-cluster ions with kinetic energy of MeV per atom in a linear-chain structure with equal separation of 0.127 nm, passing through carbon foil, was theoretically investigated on the basis of the dielectric function formalism together with the wave-packet model. We assume that inside a foil the dissipated and the conservative forces due to electron polarization are acting on constituent partially stripped ions as well as the repulsive Coulomb forces. In addition, the reductive effect of the cluster average charge is incorporated in a self-consistent manner. On the other hand, outside a foil, only a repulsive Coulomb interaction is assumed to be working. The equation of motion for constituent ions is numerically solved using the molecular dynamics method under the action of the above forces. The calculated results are presented as a function of the incident orientation angle $\theta$. By taking the average over $\theta$, the energy loss per ion of the carbon cluster displays a sublinear dependence on the number of atoms at lower energies, while at higher energies it shows a superlinear dependence in spite of including the average charge reduction. These two trends in the energy loss are in good agreement with existing experimental results, in which not only the spatial correlation but also the reduction of cluster average charge is found to play a significant role.

The Siegert states of atoms and molecules in a static electric field are the solutions of the stationary Schrödinger equation satisfying the regularity and outgoing-wave boundary conditions. Recently, an efficient method for calculating Siegert states in the single-active-electron approximation based on the adiabatic expansion in parabolic coordinates was proposed [P. A Batishchev et al., Phys. Rev. A 82, 023416 (2010); O. I. Tolstikhin et al., Phys. Rev. A 84, 053423 (2011)]. So far, this method has been implemented only for axially symmetric potentials, which corresponds to atoms and linear molecules aligned along the field. In the present work, we extend its implementation to a general class of soft-core molecular potentials. This makes it possible to calculate the Siegert eigenvalue $E=\mathcal{E}-i\Gamma /2$ defining the energy $\mathcal{E}$ and ionization rate $\Gamma$ of the corresponding state as functions of the electric field for arbitrarily oriented polyatomic molecules. The method is illustrated by calculations for the $1s\sigma$ and $2p\pi$ states of H${}_2^{+}$. Comparison of the results with the predictions of perturbation theory for $\mathcal{E}$ and weak-field asymptotic theory for $\Gamma$ is discussed.

We investigate the dynamics of two bosons trapped in an infinite one-dimensional optical lattice potential within the framework of the Bose-Hubbard model and derive an exact expression for the wave function at finite time. As initial condition we chose localized atoms that are separated by a distance of $d$ lattice sites and carry a center-of-mass quasimomentum. An initially localized pair ($d=0$) is found to be more stable as quantified by the pair probability (probability to find two atoms at the same lattice site) when the interaction and/or the center-of-mass quasimomentum is increased. For initially separated atoms ($d\ne 0$) there exists an optimal interaction strength for pair formation. Simple expressions for the wave function, the pair probability, and the optimal interaction strength for pair formation are computed in the limit of infinite time. Whereas the time-dependent wave function differs for values of the interaction strength that differ only by the sign, important observables such as the density and the pair probability do not. With a symmetry analysis this behavior is shown to extend to the $N$-particle level and to fermionic systems. Our results provide a complementary understanding of the recently observed [Winkler et al., Nature (London) 441, 853 (2006)] dynamical stability of atom pairs in a repulsively interacting lattice gas.

Based on a mean-field approach, spontaneously crystalline ground states, called quantum crystals, of a trapped Rydberg-dressed Bose-Einstein condensate are numerically investigated. In a quasi-two-dimensional geometry, a hexagonal lattice of condensate droplets manifests when dressed coupling is above a critical value. The onset of the crystallized state is characterized by a drastic drop of the nonclassical rotational inertia fraction (NCRIF). Nevertheless, the NCRIF remains a large value for a large span of dressed coupling, which indicates that the long-range phase coherence of a superfluid is preserved in the crystallized state. By relaxing the confinement against the two-dimensional geometry and by introducing an anisotropic interaction, an $AB$ stacking bilayer lattice and a nearly square lattice, respectively, are also available in the system. A quasi-one-dimensional lattice is also shown.

We present two simple designs of matter-wave beam splitters in a trapped Bose-Einstein condensate (BEC). In our scheme, identical pairs of atomic solitons are produced by an adequate control—in time and/or space—of the scattering length. Our analysis is performed by numerical integration of the Gross-Pitaevskii equation and supported by several analytical estimates. Our results show that these devices can be implemented in the frame of current BEC experiments. The system has potential applications for the construction of a soliton interferometer.

We present a detailed study of scattering by an amplitude-modulated potential barrier using three distinct physical frameworks: quantum, classical, and semiclassical. Classical physics gives bounds on the energy and momentum of the scattered particle, while also providing the foundation for semiclassical theory. We use the semiclassical approach to selectively add quantum-mechanical effects such as interference and diffraction. We find good agreement between the quantum and semiclassical momentum distributions. Our methods and results can be used to understand quantum and classical aspects of transport mechanisms involving time-varying potentials, such as quantum pumping.