An improved homogeneous balance principle and an $F$-expansion technique are used to construct exact periodic wave solutions to the generalized two-dimensional nonlinear Schrödinger equation with distributed dispersion, nonlinearity, and gain coefficients. For limiting parameters, these periodic wave solutions acquire the form of localized spatial solitons. Such solutions exist under certain conditions, and impose constraints on the functions describing dispersion, nonlinearity, and gain (or loss). We establish a simple procedure to select different classes of solutions, using the dispersion and the gain coefficient in one case, or the chirp function and the gain coefficient in the other case, as independent parameter functions. We present a few characteristic examples of periodic wave and soliton solutions with physical relevance.

The charge transfer and excitation cross sections for protons colliding with $\mathrm{Na}\left(3s\right)$ atoms are calculated in the incident energy region from $1.7\mathrm{eV}\text{to}5\mathrm{keV}$ by a quantum-mechanical molecular-orbital close-coupling (QMOCC) method and from $1\text{to}100\mathrm{keV}$ by a two-center atomic-orbital close-coupling method. The present QMOCC charge transfer cross section for low energy $(<40\mathrm{eV})$ is in agreement with some other calculations, but disagrees with the experimental measurements [Z. Phys. A 313, 155, 1983]. For the higher energies, the cross sections calculated by the two methods are in harmony with the experimental and other theoretical data.

We study classical noise correlations between the two down-converted fields in optical parametric amplification. In particular, it is shown that the classical correlations between the conjugate quadratures of the amplified fields can violate correlation criteria which are classical analogs of those used to characterize continuous-variable entanglement.

A theoretical framework is developed that combines the systematic many-body cluster-expansion approach with the standard quantum-optical representations. A cluster-expansion transformation is derived to obtain a flexible one-to-one mapping between correlated clusters and the usual phase-space and marginal distributions discussed in quantum optics. The convergence and correlation properties of this transformation are explored through several quantum-field examples including coherent, thermal, squeezed, Fock, and Schrödinger cat states. The resulting correlation properties can be used as a basis to characterize and control many-body correlations when quantum light interacts with matter. As an application, a cluster-expansion-restoration scheme is developed that allows for the retrieval of the true quantum statistics of light from realistic measurements that are deteriorated by the reduced quantum efficiency of the detectors.

We study the quantum correlations and complexity of simulation, characterized by quantum mutual information and entanglement entropy in operator space, respectively, for thermal states in critical, noncritical, and quantum chaotic spin chains. A simple general relation between the two quantities is proposed. We show that in all cases mutual information and entanglement entropy saturate with system size, whereas as a function of the inverse temperature, we find logarithmic divergences for critical cases and uniform bounds in noncritical cases. A simple efficient quasiexact method for computation of arbitrary entropy-related quantities in thermalized $XY$ spin chains is proposed.

We present an approach using quantum walks (QWs) to redistribute ultracold atoms in an optical lattice. Different density profiles of atoms can be obtained by exploiting the controllable properties of QWs, such as the variance and the probability distribution in position space using quantum coin parameters and engineered noise. The QW evolves the density profile of atoms in a superposition of position space, resulting in a quadratic speedup of the process of quantum phase transition. We also discuss implementation in presently available setups of ultracold atoms in optical lattices.

Numerically we simulate the effect of optimized coherent control pulses with a finite duration on a qubit in a bath of spins. The pulses of finite duration are compared with ideal instantaneous pulses. In particular, we show that properly designed short pulses can approximate ideal instantaneous pulses up to a certain order in the shortness of the pulse. We provide examples of such pulses, quantify the discrepancy from the ideal case, and compare their effect for various ranges of the coupling constants.

Unconditionally secure nonrelativistic bit commitment is known to be impossible in both the classical and the quantum worlds. But when committing to a string of $n$ bits at once, how far can we stretch the quantum limits? In this paper, we introduce a framework for quantum schemes where Alice commits a string of $n$ bits to Bob in such a way that she can only cheat on $a$ bits and Bob can learn at most $b$ bits of information before the reveal phase. Our results are twofold: we show by an explicit construction that in the traditional approach, where the reveal and guess probabilities form the security criteria, no good schemes can exist: $a+b$ is at least $n$. If, however, we use a more liberal criterion of security, the accessible information, we construct schemes where $a=4{\text{log}}_{2}n+O\left(1\right)$ and $b=4$, which is impossible classically. We furthermore present a cheat-sensitive quantum bit string commitment protocol for which we give an explicit tradeoff between Bob’s ability to gain information about the committed string, and the probability of him being detected cheating.

We report here experimental evidence of the reflection of a large fraction of a beam of low energy antiprotons by an aluminum wall. This derives from the analysis of a set of annihilations of antiprotons that come to rest in rarefied helium gas after hitting the end wall of the apparatus. A Monte Carlo simulation of the antiproton path in aluminum indicates that the observed reflection occurs primarily via a multiple Rutherford-style scattering on Al nuclei, at least in the energy range $1–10\mathrm{keV}$ where the phenomenon is most visible in the analyzed data. These results contradict the common belief according to which the interactions between matter and antimatter are dominated by the reciprocally destructive phenomenon of annihilation.

We consider a many-body system of pseudo-spin-$1∕2$ bosons with spin-orbit interactions, which couple the momentum and the internal pseudo-spin degree of freedom created by spatially varying laser fields. The corresponding single-particle spectrum is generally anisotropic and contains two degenerate minima at finite momenta. At low temperatures, the many-body system condenses into these minima generating a type of entangled Bose-Einstein condensate. We show that in the presence of weak density-density interactions the many-body ground state is characterized by a twofold degeneracy. The corresponding many-body wave function describes a condensate of “left-” and “right-moving” bosons. By fine-tuning the parameters of the laser field, one can obtain a bosonic version of the spin-orbit coupled Rashba model. In this symmetric case, the degeneracy of the ground state is very large, which may lead to phases with nontrivial topological properties. We argue that the predicted type of Bose-Einstein condensates can be observed experimentally via time-of-flight imaging, which will show characteristic multipeak structures in momentum distribution.

We analyze the scattering and bound state physics of a pair of atoms in a one-dimensional optical lattice interacting via a narrow Feshbach resonance. The lattice provides a structured continuum allowing for the existence of bound dimer states both below and above the continuum bands, with pairs above the continuum stabilized by either repulsive interactions or their center-of-mass motion. Inside the band the Feshbach coupling to a closed channel bound state leads to a Fano resonance profile for the transmission, which may be mapped out by rf or photodissociative spectroscopy. We generalize the scattering length concept to the one-dimensional lattice, where a scattering length may be defined at both the lower and the upper continuum thresholds. As a function of the applied magnetic field the scattering length at either band edge exhibits the usual Feshbach divergence when a bound state enters or exits the continuum. Near the scattering length divergences the binding energy and wave function of the weakly bound dimer state acquires a universal form reminiscent of those of free-space Feshbach molecules. We give numerical examples of our analytic results for a specific Feshbach resonance, which has been studied experimentally.

We propose an experimental method that allows for scaling of all the diagonal correlation functions (such as the density and pair correlation function) during the expansion of harmonically trapped cold atomic gases with arbitrary interactions even if the trapping is anisotropic. To do this we require that the interaction be tunable by the use of a Feshbach resonance and that the trapping potential can be manipulated independently along the axial and radial directions. This permits a much greater accuracy and resolution in measurements of correlation functions. We explain the explicit control procedure, outline the scaling ansatz that we use, and briefly discuss the systems where it could be applied as well as possible experimental obstacles to its implementation.

Based on high-order harmonic generation (HHG) spectra obtained from solving the time-dependent Schrödinger equation for atoms, we established quantitatively that the HHG yield can be expressed as the product of a returning electron wave packet and photorecombination cross sections, and the shape of the returning wave packet is shown to be largely independent of the species. By comparing the HHG spectra generated from different targets under identical laser pulses, accurate structural information, including the phase of the recombination amplitude, can be retrieved. This result opens up the possibility of studying the target structure of complex systems, including their time evolution, from the HHG spectra generated by short laser pulses.

We study systems of fully polarized ultracold atomic gases obeying Fermi statistics. The atomic transition interacts dispersively with a mode of a standing-wave cavity, which is coherently pumped by a laser. In this setup, the intensity of the intracavity field is determined by the refractive index of the atomic medium, and thus by the atomic density distribution. Vice versa, the density distribution of the atom is determined by the cavity field potential, whose depth is proportional to the intracavity field amplitude. In this work, we show that this nonlinearity leads to an instability in the intracavity intensity that differs substantially from dispersive optical bistability, as this effect is already present in the regime, where the atomic dipole is proportional to the cavity field. Such instability is driven by the matter-wave fluctuations and exhibits a peculiar dependence on the fluctuations in the atomic density distribution.

The nonlinear TE-polarized surface waves localized at the interface between a nonlinear uniform material and a semi-infinite one-dimensional photonic crystal are investigated. We assume that the nonlinear material is right handed and the photonic crystal is made of alternate left-handed metamaterial and right-handed material. We study the intensity-dependent properties of the nonlinear surface waves for both self-focusing and defocusing Kerr-like nonlinearity. Unlike the linear regime, it is shown that in the case of self-focusing nonlinearity the dispersion curve has two branches corresponding to two types of surface mode structures (one structure with a hump at the interface and the other one with two humps). While, in the case of defocusing nonlinearity the dispersion curve has a single branch. We also show that the existence region of the surface waves is intensity dependent (independent) in the case of self-focusing (defocusing) nonlinear regime and the presence of left-handed materials and nonlinear medium provides a possibility for forward or backward waves selection in the given structure by adjusting the intensity parameter at the interface.

A different x-ray phase contrast imaging technique based on the combination of structured illumination and an optimized hybrid input-output algorithm for phase and amplitude retrieval is presented and discussed. Based on a modified and flexible experimental setup, compared to standard propagation-based x-ray imaging setups, the method we propose here represents a real advance in the phase-contrast imaging technique relating to the determination of the phase and amplitude distribution. Moreover, in coherent diffractive imaging applications, the proposed technique may yield high spatial resolution with currently available imaging detectors.

The effect of the collisions on the control of coherent population transfer in a closed inverse $Y$-type four-level system driven by three laser fields is investigated with the stimulated Raman adiabatic passage technique. An arbitrary coherent superposition between the initial state and target state can be created either by varying the Rabi frequency of the control laser field or by tuning the one-photon detunings of the pump and Stokes laser fields. When the three laser fields with nearly equal peak Rabi frequencies are each tuned to resonance with the respective transitions, the low transfer efficiency due to the nonadiabatic coupling between two degenerate adiabatic states could be enhanced dramatically with the increase of the collision-induced coherence decay rates to the value nearly comparable to the Rabi frequency of the control field. The enhanced transfer efficiency results from the collision-controlled electromagnetically induced transparency in the $\Lambda$-type three-level subsystem and electromagnetically induced absorption in the ladder-type three-level subsystem of the four-level system.

The triple differential cross section of $\mathrm{Ca}\left(4s^2\right)$ is calculated by using the distorted wave Born approximation with exchange and with exchange and post-collision interaction. The calculations have been carried out at different impact energies ($4–58.5\mathrm{eV}$ above the first ionization potential of Ca). The present calculations are in close agreement with the recent $(e,2e)$ experimental studies [A. J. Murray, Phys. Rev. A. 72, 062711 (2005)]. The calculations show an improvement in agreement with the experiment as compared with the earlier theoretical works.

We demonstrate that chemical reactions in collisions of molecular beams can generally produce low-velocity molecules in the laboratory-fixed frame. Our analysis shows that collisions of beams may simultaneously yield slow reactant molecules and slow products. The reaction products are formed in selected rovibrational states and scattered in a specific direction, which can be controlled by tuning the kinetic energies of the incident beams and the angle between the beams. Our calculations indicate that chemical reactions of polar alkali-metal dimers are barrierless and we suggest that chemical reactions involving alkali-metal dimers may be particularly suitable for producing slow molecules in crossed beams.