The emission of x rays in the $K\beta$ region of Mg, Al, Si, Sc, Ti, Cr, Fe, Ni, and Zn induced by electron bombardment was studied by means of wavelength dispersive spectroscopy. The lines studied were: the $K{\beta }^{\mathrm{III}}$ and $K{\beta }^{\mathrm{IV}}$ spectator hole transitions, the $1s\to 3s$ quadrupole decay, the $K{\beta }_2$ and $K{\beta }_5$ diagram transitions, the structures related to radiative Auger processes, and the $K{\beta }^{\prime }$ and $K{\beta }^{″}$ lines. Relative energies and probabilities were determined through a careful spectral processing based on a parameter refinement method. The results obtained were compared with other experimental and theoretical determinations when available.

Optimal control techniques combined with femtosecond laser pulse shaping are applied to steer and enhance the strong-field induced emission of highly charged atomic ions from silver clusters embedded in helium nanodroplets. With light fields shaped in amplitude and phase we observe a substantial increase of the ${\mathrm{Ag}}^{q+}$ yield for $q>10$ when compared to bandwidth-limited and optimally stretched pulses. A remarkably simple double-pulse structure, containing a low-intensity prepulse and a stronger main pulse, turns out to produce the highest atomic charge states up to ${\mathrm{Ag}}^{20+}$. A negative chirp during the main pulse hints at dynamic frequency locking to the cluster plasmon. A numerical optimal control study on pure silver clusters with a nanoplasma model converges to a similar pulse structure and corroborates that the optimal light field adapts to the resonant excitation of cluster surface plasmons for efficient ionization.

A theoretical study of the subshell photoionization of the Xe atom endohedrally confined in ${\mathrm{C}}_{60}$ is presented. Powerful hybridization of the Xe $5s$ state with the bottom edge of ${\mathrm{C}}_{60}\hspace{0.5em}\pi$ band is found that induces strong structures in the $5s$ ionization, causing the cross section to differ significantly from earlier results that omit this hybridization. The hybridization also affects the angular distribution asymmetry parameter of Xe $5p$ ionization near the Cooper minimum. The $5p$ cross section, on the other hand, is greatly enhanced by borrowing considerable oscillator strength from the ${\mathrm{C}}_{60}$ giant plasmon resonance via the atom-fullerene dynamical interchannel coupling. Beyond the ${\mathrm{C}}_{60}$ plasmon energy range the atomic subshell cross sections display confinement-induced oscillations in which, over the large $4d$ shape resonance region, the dominant $4d$ oscillations induce their “clones” in all degenerate weaker channels known as correlation confinement resonances.

We study finite-size effects for the gap of the quasiparticle excitation spectrum in the weakly interacting regime one-dimensional Hubbard model with on-site attraction. Two types of corrections to the result of the thermodynamic limit are obtained. Aside from a power law (conformal) correction due to gapless excitations which behaves as $1/N_a$, where $N_a$ is the number of lattice sites, we obtain corrections related to the existence of gapped excitations. First of all, there is an exponential correction which in the weakly interacting regime ($\left|U\right|\ll t$) behaves as $~$$\exp (-N_a{\Delta }_{\infty }/4t)$ in the extreme limit of $N_a{\Delta }_{\infty }/t\gg 1$, where $t$ is the hopping amplitude, $U$ is the on-site energy, and ${\Delta }_{\infty }$ is the gap in the thermodynamic limit. Second, in a finite-size system a spin-flip producing unpaired fermions leads to the appearance of solitons with nonzero momenta, which provides an extra (nonexponential) contribution $\delta$. For moderate but still large values of $N_a{\Delta }_{\infty }/t$, these corrections significantly increase and may become comparable with the $1/N_a$ conformal correction. Moreover, in the case of weak interactions where ${\Delta }_{\infty }\ll t$, the exponential correction exceeds higher-order power law corrections in a wide range of parameters, namely for $N_a\lesssim (8t/{\Delta }_{\infty })\ln (4t/|U|)$, and so does $\delta$ even in a wider range of $N_a$. For a sufficiently small number of particles, which can be of the order of thousands in the weakly interacting regime, the gap is fully dominated by finite-size effects.

The zero-temperature equation of state is analyzed in low-dimensional bosonic systems. We propose to use the concept of energy-dependent $s$-wave scattering length for obtaining estimations of nonuniversal terms in the energy expansion. We test this approach by making a comparison to exactly solvable one-dimensional problems and find that the generated terms have the correct structure. The applicability to two-dimensional systems is analyzed by comparing with results of Monte Carlo simulations. The prediction for the nonuniversal behavior is qualitatively correct and the densities, at which the deviations from the universal equation of state become visible, are estimated properly. Finally, the possibility of observing the nonuniversal terms in experiments with trapped gases is also discussed.

We present a wide array of quantum measures on numerical solutions of one-dimensional Bose- and Fermi-Hubbard Hamiltonians for finite-size systems with open boundary conditions. Finite-size effects are highly relevant to ultracold quantum gases in optical lattices, where an external trap creates smaller effective regions in the form of the celebrated “wedding cake” structure and the local density approximation is often not applicable. Specifically, for the Bose-Hubbard Hamiltonian we calculate number, quantum depletion, local von Neumann entropy, generalized entanglement or Q measure, fidelity, and fidelity susceptibility; for the Fermi-Hubbard Hamiltonian we also calculate the pairing correlations, magnetization, charge-density correlations, and antiferromagnetic structure factor. Our numerical method is imaginary time propagation via time-evolving block decimation. As part of our study we provide a careful comparison of canonical versus grand canonical ensembles and Gutzwiller versus entangled simulations. The most striking effect of finite size occurs for bosons: we observe a strong blurring of the tips of the Mott lobes accompanied by higher depletion, and show how the location of the first Mott lobe tip approaches the thermodynamic value as a function of system size.

The one-dimensional propagation of waves in a bichromatic potential may be modeled by the Aubry-André Hamiltonian. This, in turn, presents a localization transition that has been observed in recent experiments using ultracold atoms or light. It is shown here that, in contrast to the Anderson model, the localization mechanism has a classical origin, namely it is not due to a quantum suppression of a classically allowed transport process, but rather is produced by a trapping by the potential. Explicit comparisons with the Anderson model as well as with experiments are presented.

Superradiance scattering from a Bose-Einstein condensate is studied with a two-frequency pumping beam. We demonstrate the possibility of fully tuning the backward mode population as a function of the locked initial relative phase between the two frequency components of the pumping beam. This result comes from an imprinting of this initial relative phase on two matter wave gratings, formed by the forward mode or backward mode condensate plus the condensate at rest so cooperative scattering is affected. A numerical simulation using a semiclassical model agrees with our observations.

We explore the quantum entanglement between two collective fields via atomic coherence effects. For three-level atoms in $\mathsf{V}$ configuration driven by two applied fields on two-photon resonance, one coherent superposition of the excited states is not excited, which is the counterpart of coherent population trapping. The coherence-induced depopulation makes two cavity fields in each collection combine into a quantum-beat, i.e., equivalently, the difference mode of the two components decouples from the driven atoms. The two sum modes, when they are arranged in the four-wave mixinglike interactions, can be prepared in Einstein-Podolsky-Rosen entangled state. Correspondingly, any two individual fields from different collective modes are entangled with each other. Furthermore, the effects of thermal reservoir and laser linewidths are discussed, and a generalization is given to the case in which each quantum beat involves more than two modes.

We show that a two-dimensional wormhole geometry is equivalent to a catenoid, a minimal surface. We then obtain the curvature-induced geometric potential and show that the ground state with zero energy corresponds to a reflectionless potential. By introducing an appropriate coordinate system we also obtain bound states for different angular momentum channels. Our findings can be realized in suitably bent bilayer graphene sheets with a neck, in a honeycomb lattice with an array of dislocations, or in nanoscale waveguides in the shape of a catenoid.

We present a strategy to generate long-range entanglement in noisy quantum networks. We consider a cubic lattice whose bonds are partially entangled mixed states of two qubits, and where quantum operations can be applied perfectly at the nodes. In contrast to protocols designed for one- or two-dimensional regular lattices, we find that entanglement can be created between arbitrarily distant qubits if the fidelity of the bonds is higher than a critical value, independent of the system size. Therefore, we show that a constant overhead of local resources, together with connections of finite fidelity, is sufficient to achieve long-distance quantum communication in noisy networks.

Multiphoton ionization of hydrogen molecular ions in a 480-nm intense laser field is investigated by solving the time-dependent Schrödinger equation numerically in prolate spheroidal coordinates. We discretize space on a generalized pseudospectral grid and propagate the electronic wave function using a second-order split-operator method. By including and excluding the $2p{\sigma }_u$ state in the basis expansion, we confirm that the observed 10-eV peak in a recent experiment [Litvinyuk et al., New J. Phys. 10, 083011 (2008)] comes from the enhanced ionization via three-photon resonant excitation of the molecular ions. By folding the calculated ionization rates with the vibrational density distribution, the kinetic energy release spectra are obtained, which are in reasonable agreement with the experimental measurement. Furthermore, using this enhanced ionization, a pump-probe experiment is suggested to trace the vibrational wave packet.

We perform finite-temperature dynamical simulations of the arrest of a rotating Bose-Einstein condensate by a fixed trap anisotropy, using a Hamiltonian classical-field method. We consider a quasi-two-dimensional condensate containing a single vortex in equilibrium with a rotating thermal cloud. Introducing an elliptical deformation of the trapping potential leads to the loss of angular momentum from the system. We identify the condensate and the complementary thermal component of the nonequilibrium field and compare the evolution of their angular momenta and angular velocities. By varying the trap anisotropy we alter the relative efficiencies of the vortex-cloud and cloud-trap coupling. For strong trap anisotropies the angular momentum of the thermal cloud may be entirely depleted before the vortex begins to decay. For weak trap anisotropies, the thermal cloud exhibits a long-lived steady state in which it rotates at an intermediate angular velocity.

The spectral polarization shaping of ultrashort pulses is shown to allow retrieval of two-dimensional individual tensorial components of the second-harmonic-generation response of molecular samples in nonlinear microscopy imaging. This configuration, which cannot be performed by traditional polarization-controlled excitation, provides a structural contrast that can be directly related to information on the local symmetry and order of the sample, with submicrometric spatial resolution. Phase shaping, in addition to polarization spectral manipulation, is proposed as a possible scheme for imaging individual tensorial components without the need for a spectral information extraction.

We theoretically study the spectral phase shift of a midinfrared (MIR) femtosecond pulse generated through parametric frequency down-conversion in dispersive media, with an emphasis on the effect of group-velocity dispersion (GVD), with the aim of obtaining guidelines for dispersion compensation and pulse compression in such systems. It is found that the spectral phase of the generated MIR pulse differs significantly from that of due to its linear propagation. We consider two common ways of MIR femtosecond pulse generation: difference frequency generation (DFG) and optical parametric amplification (OPA). The resultant spectral phase is determined by the initial injection condition, and the transfer of the spectral phase accumulated by the higher-frequency fields. Our results show that in DFG, pump depletion has little effect on the spectral phase, while in OPA, the combined effect of linear GVD and high parametric gain leads to a notable dependence of spectral phase on gain—the higher the gain, the less the spectral phase. Quantitatively, under conditions where the MIR pulse is generated through injection of two higher-frequency fields, its spectral phase is close to only half of that accumulated through linear propagation in DFG, while it is even smaller in OPA. To obtain the shortest MIR femtosecond pulse, these results determine the amount of dispersion that needs compensation.

Tensor rank refers to the number of product states needed to express a given multipartite quantum state. Its nonadditivity as an entanglement measure has recently been observed. In this Brief Report, we estimate the tensor rank of multiple copies of the tripartite state $|W\rangle =\frac{1}{\sqrt{3}}(|100\rangle +|010\rangle +|001\rangle )$. Both an upper bound and a lower bound of this rank are derived. In particular, it is proven that the rank of $|W{\rangle }^{\otimes 2}$ is $7$, thus resolving a previously open problem. Some implications of this result are discussed in terms of transformation rates between $|W{\rangle }^{\otimes n}$ and multiple copies of the state $|\mathrm{GHZ}\rangle =\frac{1}{\sqrt{2}}(|000\rangle +|111\rangle )$.

We analyze the suppression of decoherence by means of dynamical decoupling in the pure-dephasing spin-boson model for baths with power law spectra. The sequence of ideal $\pi$ pulses is optimized according to the power of the bath. We expand the decoherence function and separate the canceling divergences from the relevant terms. The proposed sequence is chosen to be the one minimizing the decoherence function. By construction, it provides the best performance. We analytically derive the conditions that must be satisfied. The resulting equations are solved numerically. The solutions are very close to the Carr-Purcell-Meiboom-Gill sequence for a soft cutoff of the bath while they approach the Uhrig dynamical-decoupling sequence as the cutoff becomes harder.

We present a formalism for rigorous multichannel scattering calculations of cross sections for inelastic collisions of atoms and molecules confined in one-dimensional optical lattices. We obtain analytical expressions for the mean frequency of inelastic collisions in a confined gas in the temperature regime $T~\hslash \omega$ and at temperatures $T\gg \hslash \omega$, where $\omega$ is the oscillation frequency of trapped particles in the confining potential. Our numerical calculations for the gaseous mixture of Li and Rb atoms show that inelastic collisions in the temperature regime $T~\hslash \omega$ exhibit a deviation from three-dimensional scattering. This deviation is more significant for systems with stronger confinement and larger scattering lengths. We find that the ratios of rate constants for inelastic scattering and elastic collisions are suppressed in confined gases at $T~\hslash \omega$, and this suppression is significant for Li-Rb collisions at $T<40$ $\mu$K.