The Siegert pseudostate (SPS) formulation of scattering theory, originally developed by Tolstikhin, Ostrovsky, and Nakamura [Phys. Rev. A, 58, 2077 (1998)] for $s$-wave scattering in a spherically symmetric finite-range potential, is generalized to nonzero angular momenta. The orthogonality and completeness properties of SPSs are established and SPS expansions for the outgoing-wave Green’s function, physical states, and scattering matrix are obtained. The present formulation completes the theory of SPSs in the one-channel case, making its application to three-dimensional problems possible. The results are illustrated by calculations for several model potentials.

We study the effect of parametric excitations on systems of confined ultracold Bose atoms in periodically modulated optical lattices. In the regime where Mott insulating and superfluid domains coexist, we show that the dependence of the energy absorbed by the system on the frequency of the modulation serves as an experimental probe for the existence and properties of Mott insulating-superfluid domains.

A comprehensive theory of gravitational quantum states of ultracold neutrons in a rough waveguide is presented. The theory covers recent experiments in which the ultracold neutrons were beamed between a mirror and a rough scatterer and absorber. The results are in very good agreement with experimental data. The analysis is based on a recently developed theory of quantum transport in waveguides with rough absorbing and scattering walls. The calculation is done using two methods: an exact transport equation and a simplified model of biased scattering-driven diffusion of neutrons between quantum states. Both sets of results are in excellent agreement with each other. The exit neutron count is sensitive to the amplitude and the correlation radius (lateral size) of surface inhomogeneities and to the overall time of flight (length of the waveguide). The results indicate that it is possible to choose the waveguide parameters in such a way so to observe the quantum size effect in neutron count—the quantum steps that correspond to individual quantum states—even in a weak roughness regime. Away from the obvious limiting cases, the results are not very sensitive to the ratio of the particle energy to the absorption threshold. The main unresolved issue, which is related to a complexity of required calculations for a “real” experimental cell, is the lack of accurate information on the occupation numbers of neutrons entering the waveguide. Our analysis indicates that the initial occupancies of all gravitational states are expected to be the same except for the smallest values of the waveguide width.

In order to investigate the size limit of spatial localized structures in a nonlinear system, we explore the impact of linear nonlocality on their domains of existence and stability. Our system of choice is an optical microresonator containing an additional metamaterial layer in the cavity, allowing the nonlocal response of the material to become the dominating spatial process. In that case, our bifurcation analysis shows that this nonlocality imposes another limit on the width of localized structures going beyond the traditional diffraction limit.

We calculate the effect of a Dirac point (a conical singularity in the band structure) on the transmission of monochromatic radiation through a photonic crystal. The transmission as a function of frequency has an extremum near the Dirac point, depending on the transparencies of the interfaces with free space. The extremal transmission $T_0={\Gamma }_{0}W∕L$ is inversely proportional to the longitudinal dimension $L$ of the crystal (for $L$ larger than the lattice constant and smaller than the transverse dimension $W$). The interface transparencies affect the proportionality constant ${\Gamma }_0$, and they determine whether the extremum is a minimum or a maximum, but they do not affect the “pseudodiffusive” $1∕L$ dependence of $T_0$.

We have studied Laguerre-Gaussian spatial solitary waves in strongly nonlocal nonlinear media analytically and numerically. An exact analytical solution of two-dimensional self-similar waves is obtained. Furthermore, a family of different spatial solitary waves has been found. It is interesting that the spatial soliton profile and its width remain unchanged with increasing propagation distance. The theoretical predictions may give new insights into low-energetic spatial soliton transmission with high fidelity.

Recent results, extending the Schmidt decomposition theorem to wave functions of pairs of identical particles, are reviewed. They are used to give a definition of reduced density operators in the case of two identical particles. Next, a method is discussed to calculate time averaged entanglement. It is applied to a pair of identical electrons in an otherwise empty band, and to a pair of bosons in a quadratic model with infinite range hopping. The effect of degeneracy of the spectrum of the Hamiltonian on the average entanglement is emphasized.

We consider an adiabatic quantum algorithm (Grover’s search routine) weakly coupled to a rather general environment, i.e., without using the Markov approximation. Markovian errors generally require high-energy excitations (of the reservoir) and tend to destroy the scalability of the adiabatic quantum algorithm. We find that, under appropriate conditions (such as low temperatures), the low-energy (i.e., non-Markovian) modes of the bath are most important. It turns out that the scalability of the adiabatic quantum algorithm just depends on the infrared behavior of the environment: a reasonably small coupling to the three-dimensional electromagnetic field, for example, does not destroy the scaling behavior, whereas phonons or localized degrees of freedom can be problematic.

We investigate density fluctuations in a coherent ensemble of interacting fermionic atoms. Adapting the concept of full counting statistics, well known from quantum optics and mesoscopic electron transport, we study second-order as well as higher-order correlators of density fluctuations. Using the mean-field BCS state to describe the whole interval between the BCS limit and the Bose-Einstein condensate (BEC) limit, we obtain an exact expression for the cumulant-generating function of the density fluctuations of an atomic cloud. In the two-dimensional case, we obtain a closed analytical expression. Poissonian fluctuations of a molecular condensate on the BEC side are strongly suppressed on the BCS side. The size of the fluctuations in the BCS limit is a direct measure of the pairing potential. We also discuss the BEC-BCS crossover of the third cumulant and the temperature dependence of the second cumulant.

Coupling a two-level medium, described by the Maxwell-Bloch (MB) equations, to an external cavity mode results in a prescribed boundary value for the electric field that can be tuned to the forbidden band gap of the medium. It is shown that there exists a threshold of energy density flux above which a solitonlike light pulse is generated and propagates in the medium at a fraction of the light velocity. When the driving frequency becomes close to the band gap edge, where the group velocity vanishes, the MB equations tend to the nonlinear Schrödinger equation which furnishes the theoretical ground to understand soliton generation by evanescent fields as a manifestation of nonlinear supratransmission, produced by an instability of the evanescent wave. Moreover, the propagation at a fraction of light velocity is shown to result from a continuous periodic exchange between polarization (electromagnetic energy) and population (density of atoms in the excited level). The process is demonstrated to occur at twice the internal frequency of the generated gap soliton. Last, when the medium spatial extension is of the order of the soliton dimension, an optical bistability is shown to occur at the supratransmission threshold allowing for different output intensities corresponding to a given input value.

We demonstrate that rotating quasi-one-dimensional potentials, periodic or parabolic, support solitons in settings where they are otherwise impossible. Ground-state and vortex solitons are found in defocusing media, if the rotation frequency $\alpha$ exceeds a critical value. The revolving periodic potentials exhibit the strongest stabilization capacity at a finite optimum value of their strength, while the rotating parabolic trap features a very sharp transition to stability with the increase of $\alpha$.

We study the dynamical process of disentanglement of two qubits and two qutrits coupled to an Ising spin chain in a transverse field, which exhibits a quantum phase transition. We use the concurrence and negativity to quantify entanglement of two qubits and two qutrits, respectively. Explicit connections between the concurrence (negativity) and the decoherence factors are given for two initial states, the pure maximally entangled state and the mixed Werner state. We find that the concurrence and negativity decay exponentially with fourth power of time in the vicinity of the critical point of the environmental system.

Time-resolved extreme ultraviolet photoabsorption spectra of a manganese plasma have been recorded using the dual laser plasma technique. The $43–73\mathrm{eV}$ photon energy range is dominated by the $3p\text{−}3d$ giant resonance and to a lesser extent the $3p\text{−}4s$ resonances in both ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Mn}}^{3+}$, recorded at interplasma time delays of 80 and $30\mathrm{ns}$, respectively. These experimentally observed resonances are well reproduced by synthetic spectra calculated using the Hartree-Fock method. The synthetic spectra allow for absorption from excited states of the ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Mn}}^{3+}$ ions.

The leading-order relativistic corrections to the ground-state energy of the positronium molecule $\left({\mathrm{Ps}}_2\right)$ have been computed within the framework of perturbation theory. As the zero-order wave function we used a highly accurate nonrelativistic variational expansion in terms of 6000 explicitly correlated Gaussians that yielded the lowest variational upper bound for this system to date. We also report some expectation values representing the properties of ${\mathrm{Ps}}_2$.

The structure of the unnatural parity states of PsH, LiPs, NaPs, and KPs are investigated with the configuration interaction and stochastic variational methods. The binding energies (in hartree) are found to be $8.17\times {10}^{-4}$, $4.42\times {10}^{-4}$, $15.14\times {10}^{-4}$, and $21.80\times {10}^{-4}$, respectively. These states are constructed by first coupling the two electrons into a configuration which is predominantly ${}^{3}P^e$, and then adding a $p$-wave positron. All the active particles are in states in which the relative angular momentum between any pair of particles is at least $L=1$. The LiPs state is Borromean since there are no three-body bound subsystems (of the correct symmetry) of the (${\mathrm{Li}}^{+}$, $e^{-}$, $e^{-}$, $e^{+}$) particles that make up the system. The dominant decay mode of these states will be radiative decay into a configuration that autoionizes or undergoes positron annihilation.

In this paper we derive an analytic approximation to the density of states for atoms in a combined optical lattice and harmonic trap potential as used in current experiments with quantum degenerate gases. We compare this analytic density of states to numerical solutions and demonstrate its validity regime. Our work explicitly considers the role of higher bands and when they are important in quantitative analysis of this system. Applying our density of states to a degenerate Fermi gas, we consider how adiabatic loading from a harmonic trap into the combined harmonic-lattice potential affects the degeneracy temperature. Our results suggest that occupation of excited bands during loading should lead to more favorable conditions for realizing degenerate Fermi gases in optical lattices.

We derive general approximate formulas that provide with remarkable accuracy the ground-state properties of any mean-field scalar Bose-Einstein condensate with short-range repulsive interatomic interactions, confined in arbitrary cylindrically symmetric harmonic traps. Our formulation is even applicable for condensates containing a multiply quantized axisymmetric vortex. We have checked the validity of our formulas by numerically solving the three-dimensional Gross-Pitaevskii equation.