We present results for the corrections of order ${\alpha }^2(Z\alpha )E_F$ to the hyperfine splitting of muonium. We compute all the contributing Feynman diagrams in dimensional regularization and a general covariant gauge using a mixture of analytical and numerical methods. We improve the precision of previous results.

A diabatic correlation diagram technique is extended to assign effective quantum numbers and classify sequences for extremely high excitations in a coupled two-mode model of an isomerizing system, with multiple wells separated by a potential barrier. At low values of the stretch quantum number $n_s$, level spacings for sequences of bend excitations $n_b=0,\dots$ show a pattern of a smooth dip at the barrier, characteristic of the zero-order uncoupled system. In higher sequences $n_s=3-5$, the spectral pattern is modified with the onset of a prominent nonlinear resonance. The level spacing “tunes” to a flattened pattern similar to a harmonic oscillator, and the smooth dip at the barrier becomes almost vertical. This behavior is explained by the influence of periodic orbits of the resonance on the quantum spectrum and wave functions. In the $n_s=6$ sequence the tuning reverts to a pattern more similar to zero order.

The $2s$ photoionization and subsequent Auger transition cascade in atomic Si were studied by means of synchrotron-radiation-induced electron spectroscopy. After the $2s$ photoionization, the core hole states decay predominantly by a two-step Auger transition cascade into the triply ionized [Ne]$\mathit{nl}$ states. The ionization channels of the $2s$ core-ionized Si${}^{+}$ atoms to Si${}^{3+}$ ions were observed by measuring the conventional Auger electron spectra of the $L$${}_1$-$L$${}_{2,3}$$M$ Coster-Kronig transitions and the $L$${}_{2,3}$$M-\mathit{MMM}$ Auger transitions. The observed $L$${}_1$-$L$${}_{2,3}$$M$ and $L_{2,3}$$M-\mathit{MMM}$ Auger spectra were analyzed by means of extensive multiconfiguration Dirac-Fock computations. We found that the electron correlation plays a prominent role in the Auger cascade, especially for the final-step Auger $L$${}_{2,3}$$M$-$\mathit{MMM}$ spectrum. Additionally, it was seen that the $L_{2,3}$$M-\mathit{MMM}$ Auger spectrum of Si includes more Auger groups than the isoelectronic $L$${}_{2,3}$-$\mathit{MM}$ Auger spectrum of Al. Thus, more information on the intermediate ionic states is obtained if they are produced by Auger cascade rather than by direct photoionization.

The influence of heat annealing treatment on the $K$$\beta$-to-$K$$\alpha$ x-ray intensity ratios of $3d$ transition metal was carried out by x-ray fluorescence studies of various alloy compositions. $K$$\beta$-to-$K$$\alpha$ x-ray intensity ratios of Fe, Ni, Ti, Co, and Cu in Fe${}_x$Ni${}_{1-x}$, Ti${}_x$Ni${}_{1-x}$, and Co${}_x$Cu${}_{1-x}$ alloys unannealed and thermally annealed at different temperatures have been measured following excitation by $22.69$-keV x rays from a $10$-mCi ${}^{109}\mathrm{Cd}$ radioactive point source. The experimental data obtained after annealing treatment indicate deviations of $K$$\beta$-to-$K$$\alpha$ x-ray intensity ratios for $3d$ transition metals in different alloy compositions from the corresponding ratios for unannealed samples. The present investigation makes it possible to perform reliable interpretation of experimental $K$$\beta$-to-$K$$\alpha$ x-ray intensity ratios for various $3d$ transition metals in their alloys and can also provide quantitative information about the changes of the $K$$\beta$-to-$K$$\alpha$ x-ray intensity ratios of these metals with annealing treatment in considered systems.

Quantal calculations of electron-capture and elastic cross sections have been carried out for collisions of ${\mathrm{C}}^{4+}$ and ${\mathrm{B}}^{5+}$ with H($1s$) at collision energies $0.00025<E<0.02$ eV, where the cross sections show numerous resonances. Positions and widths of the resonances are studied by using the phase-amplitude method.

Single-electron charge exchange from simple molecular targets of biological interest to fast ion beams is investigated using the continuum-distorted-wave–eikonal-initial-state model. Thus, this model is applied for electron capture from molecules with many orbitals in the fundamental state. The role played by the representation of the initial state is analyzed and contributions from different molecular orbitals to total cross sections are calculated. The results are shown to be in very good agreement with existing experimental data for collision energies larger than a few tens of keV.

We study the scattering of a polarizable atom by a conducting cylindrical wire with incoming boundary conditions, that is, total absorption, near the surface of the wire. Based on the explicit expression given recently [C. Eberlein and R. Zietal, Phys. Rev. A 75, 032516 (2007)] for the nonretarded atom-wire potential, we formulate a hierarchy of approximations that enables the numerical determination of this potential to any desired accuracy as economically as possible. We calculate the complex $s$-wave scattering length for the effectively two-dimensional atom-wire scattering problem. The scattering length $\mathfrak{a}$ depends on the radius $R$ of the wire and a characteristic length $\beta$ related to the polarizability of the atom via a simple scaling relation, $\mathfrak{a}=R\hspace{0.5em}\tilde{\mathfrak{a}}(\beta /R)$. The “scaled scattering length” $\tilde{\mathfrak{a}}$ tends to unity in the thick-wire limit $\beta /R\to 0$, and it grows almost proportional to $1/R$ in the opposite thin-wire limit.

We report on the laboratory implementation of quantum-control-mechanism identification through Hamiltonian encoding and observable decoding (HE-OD). Over a sequence of experiments, HE-OD introduces a special encoded signature into the components of a previously determined control field expressed in a chosen representation. The outcome appears as a modulated signal in the controlled system observable. Decoding the modulated signal identifies the hierarchy of correlations between components of the control field in a particular representation. In cases where the initial quantum state and observable operator are fully known, then HE-OD can also identify the transition amplitudes of the various Dyson expansion orders contributing to the controlled dynamics. The basic principles of HE-OD are illustrated for second harmonic generation when the components of the field representation are simply taken as the pixels in the pulse shaper. The outcome of HE-OD agrees well with simulations, verifying the concept.

We investigate the coherent control of quantum tunneling for a single particle held in a driven double-well potential. For a moderate-frequency region, we demonstrate that the irregular quantum tunneling is associated with classically chaotic dynamics. A set of lower resonance-like frequencies is found, for which the coherent destruction of tunneling in the sense of the time average is illustrated numerically. For a high-frequency region, it is shown that the particle is located at the bottom of each well alternately for a long time and the time located in one well can be modulated by adjusting the driving field. The results could be useful for the experiments of controlling single-particle tunneling [see, e.g., E. Kierig, U. Schnorrberger, A. Schietinger, J. Tomkovic, and M. K. Oberthaler, Phys. Rev. Lett. 100, 190405 (2008).].

We consider two-photon double ionization of helium with $100$, $200$, and $400$ eV excess energy for the two ejected electrons, corresponding to photon energies of $89.5$, $139.5$, and $239.5$ eV, respectively. We focus on the case of ultrashort pulses (two oscillations of the field) and develop an approach to calculate the two-photon transition matrix elements within the lowest order of the time-dependent perturbation theory. One of the major difficulties in calculating such amplitudes is the infinite summation over a complete set of intermediate states. In the subfemtosecond regime, however, this summation can be performed accurately by means of the closure approximation. This results in a simple expression for the two-photon amplitude that contains a dipole term and a quadrupole term. The dipole term can be clearly associated to a process in which each electron absorbs a photon whereas the quadrupole term is associated to a process in which one electron absorbs two photons and ejects the second one by collision. We analyze in detail how the relative weight of both processes influences the behavior of the electron energy and angular distributions. In particular we study how the shape of these distributions changes with the amount of electron correlations taken into account in both initial and final states. For $100$ eV excess energy, our results for the electron energy distribution are compared with those obtained by solving the time-dependent Schrödinger equation. All these results unveil the crucial role of electron correlations in this transient regime of ionization which is neither sequential nor direct.

We investigate the dynamics of electron-electron recollisions in the double ionization of atoms in strong laser fields. The statistics of recollisions can be reformulated in terms of an area-preserving map from the observation that the outer electron is driven by the laser field to kick the remaining core electron periodically. The phase portraits of this map reveal the dynamics of these recollisions in terms of their probability and efficiency.

Two atoms in an ultracold gas are correlated at short interatomic distances due to threshold effects in which the potential energy of their interaction dominates the kinetic energy. The correlations manifest themselves in a distinct nodal structure of the density matrix at short interatomic distances. Pump-probe spectroscopy has recently been suggested [Phys. Rev. Lett. 103, 260401 (2009)] to probe these pair correlations: A suitably chosen, short photoassociation laser pulse depletes the ground-state pair density within the photoassociation window, creating a nonstationary wave packet in the electronic ground state. The dynamics of this nonstationary wave packet is monitored by time-delayed probe and ionization pulses. Here we discuss how the choice of the pulse parameters affects the experimental feasibility of this pump-probe spectroscopy of two-body correlations.

We consider the correlations and superfluid properties of a Bose gas in an external potential. Using a Bogoliubov scheme, we obtain expressions for the correlation function and the superfluid density in an arbitrary external potential. These expressions are applied to a one-dimensional system at zero temperature subject to a quasiperiodic modulation. The critical parameters for the Bose glass transition are obtained using two different criteria and the results are compared. The Lifshitz glass is seen to be the limiting case for vanishing interactions.

We conduct a rigorous investigation into the thermodynamic instability of an ideal Bose gas confined in a cubic box, without assuming a thermodynamic limit or a continuous approximation. Based on the exact expression of the canonical partition function, we perform numerical computations up to ${10}^6$ particles. We report that if the number of particles is equal to or greater than a certain critical value, which turns out to be $7616$, the ideal Bose gas subject to the Dirichlet boundary condition reveals a thermodynamic instability. Accordingly, we demonstrate that a system consisting of a finite number of particles can exhibit a discontinuous phase transition that features a genuine mathematical singularity, provided we keep not volume but pressure constant. The specific number, $7616,$ can be regarded as a characteristic number of a “cube,” which is the geometric shape of the box.

We study how stable excited many-body states of the Bose-Hubbard model, including both the gaslike state for strongly attractive bosons and bound cluster state for repulsive bosons, can be produced with cold bosonic atoms in an one-dimensional optical lattice. Starting from the initial ground states of strongly interacting bosonic systems, we can achieve stable excited states of the systems with opposite interaction strength by suddenly switching the interaction to the opposite limit. By exactly solving dynamics of the Bose-Hubbard model, we demonstrate that the produced excited state can be a very stable dynamic state. This allows the experimental study of excited state properties of ultracold atoms system in optical lattices.

We investigate macroscopic tunneling from an elongated quasi-one-dimensional trap, forming a “cigar-shaped” Bose-Einstein condensate (BEC). Using a recently developed formalism we get the leading analytical approximation for the right-hand side of the potential wall, i.e., outside the trap, and a formalism based on Wigner functions, for the left side of the potential wall, i.e., inside the BEC. We then present accomplished results of numerical calculations, which show a “blip” in the particle density traveling with an asymptotic shock velocity, as resulted from previous works on a dotlike trap but with significant differences from the latter. Inside the BEC a pattern of a traveling dispersive shock wave is revealed. In the attractive case, we find trains of bright solitons frozen near the boundary.

We theoretically demonstrate features of Anderson localization in a Tonks-Girardeau gas confined in one-dimensional potentials with controlled disorder. That is, we investigate the evolution of the single-particle density and correlations of a Tonks-Girardeau wave packet in such disordered potentials. The wave packet is initially trapped, the trap is suddenly turned off, and after some time the system evolves into a localized steady state due to Anderson localization. The density tails of the steady state decay exponentially, while the coherence in these tails increases. The latter phenomenon corresponds to the same effect found in incoherent optical solitons.

A physical construct for the cloaking of relativistic spin-$\frac{1}{2}$ matter waves is proposed. It is shown that when the effective energy and mass of relativistic spin-$\frac{1}{2}$ particles moving in an effective vector field in a spherical shell are controlled, their matter waves can be perfectly guided through the shell without any distortion or loss; that is, the construct provides a three-dimensional cloaking shell for relativistic spin-$\frac{1}{2}$ matter waves. The proposal serves as the basis for some interesting applications such as providing a method to guide the matter waves of spin particles and an ideal setup to exhibit spin-spin interactions as well as perfect quantum interferences of some global effects in spin-$\frac{1}{2}$ matter waves.

We numerically investigate the pulse compression mechanism in the infrared spectral range based on the successive action of nonlinear pulse propagation in a hollow-core fiber followed by linear propagation through bulk material. We found an excellent agreement of simulated pulse properties with experimental results at 1.8 $\mu$m in the two-optical-cycle regime close to the Fourier limit. In particular, the spectral phase asymmetry attributable to self-steepening combined with self-phase modulation is a necessary prerequisite for subsequent compensation by the phase introduced by glass material in the anomalous dispersion regime. The excellent agreement of the model enabled simulating pressure and wavelength tunability of sub-two cycles in the range from 1.5 to 4 $\mu$m with this cost-efficient and robust approach.

Rains of solitons constitute a class of nonlinear dynamics of dissipative soliton ensembles that we briefly reported in Opt. Express 17, 11776 (2009) from a fiber laser experiment. The existence of a relatively intense noisy background together with several tens of soliton pulses aggregated in a condensed soliton phase constitutes a necessary condition for their appearance. New soliton pulses form spontaneously from the background fluctuations and drift until they reach the condensed soliton phase. We here relate in detail the experimental conditions under which soliton rains manifest and their key features, describe related dynamics observed in their vicinity, and propose an explanation for soliton rain dynamics.