Experimental and calculated absolute differential cross sections for the scattering of low-energy electrons from ethene are presented. Emphasis is on the excitation of the $\tilde{a}{{}^{3}B}_{1u}$ ${}^3\left(\pi ,{\pi }^{\ast }\right)$ state, but selected elastic and vibrational excitation cross sections are also given. In contrast to earlier calculations, which were nearly a factor of 2 too large, the present calculation agrees very well with the experimental triplet excitation cross section in the threshold region. The improvement is due primarily to the inclusion of target polarization, which results in proper positioning of the ${\pi }^{\ast }$ resonance, whose high-energy tail dominates the triplet state excitation near threshold. The present experimental elastic cross sections agree very well with recent calculations taking into account target polarization.

Using two different numerical methods, we study the behavior of two-component Fermi gases interacting through short-range $s$-wave interactions in a harmonic trap. A correlated Gaussian basis-set expansion technique is used to determine the energies and structural properties, i.e., the radial one-body densities and pair distribution functions, for small systems with either even or odd $N$, as functions of the $s$-wave scattering length and the mass ratio $\kappa$ of the two species. Particular emphasis is put on a discussion of the angular momentum of the system in the BEC-BCS crossover regime. At unitarity, the excitation spectrum of the four-particle system with total angular momentum $L=0$ is calculated as a function of the mass ratio $\kappa$. The results are analyzed from a hyperspherical perspective, which offers unique insight into the problem. Additionally, fixed-node diffusion Monte Carlo calculations are performed for equal-mass Fermi gases with up to $N=30$ atoms. We focus on the odd-even oscillations of the ground-state energy of the equal-mass unitary system having up to $N=30$ particles, which are related to the excitation gap of the system. Furthermore, we present a detailed analysis of the structural properties of these systems.

We describe the concept of stochastic scattering polarimetry. This method allows determination of the anisotropic polarizability of a scattering object using a statistical analysis of the polarimetrically measured intensity distributions in the wave zone (far field). We show that this anisotropic polarizability may be determined even in situations where the state of polarization of the incident field is not known. The efficiency of the recovering procedure is demonstrated by several examples of light scattering in both far- and near-field geometries.

We address the stabilization of dipole solitons in nonlocal nonlinear materials by two different approaches. First, we study the properties of such solitons in thermal nonlinear media, where the refractive index landscapes induced by laser beams strongly depend on the boundary conditions and on the sample geometry. We show how the sample geometry impacts the stability of higher-order solitons in thermal nonlinear media and reveal that dipole solitons can be made dynamically stable in rectangular geometries, in contrast to their counterparts in thermal samples with square cross section. Second, we discuss the impact of the saturation of the nonlocal nonlinear response on the properties of multipole solitons. We find that the saturable response also stabilizes dipole solitons even in symmetric geometries, provided that the input power exceeds a critical value.

The dynamics of an initially excited two-level atom in a lossy cavity is studied by using the quantum trajectory method. Unwanted losses are included, such as photon absorption and scattering by the cavity mirrors and spontaneous emission of the atom. Based on the obtained analytical solutions, it is shown that the shape of the extracted spatiotemporal radiation mode sensitively depends on the atom-field interaction. In the case of a short-term atom-field interaction we show how different pulse shapes for the field extracted from the cavity can be controlled by the interaction time.

Going beyond the currently investigated regimes in experiments on quantum transport of ultracold atoms in disordered potentials, we predict a crossover between regular and quantum-chaotic dynamics when varying the strength of disorder. Our spectral approach is based on the Bose-Hubbard model describing interacting atoms in deep random potentials. The predicted crossover from localized to diffusive dynamics depends on the simultaneous presence of interactions and disorder and can be verified in the laboratory by monitoring the evolution of typical experimental initial states.

This article provides a convenient framework for quantitative evaluation of the entanglement generated when two structureless, distinguishable particles scatter nonrelativistically in one dimension. It explores how three factors determine the amount of entanglement generated: the momentum distributions of the incoming particles, their masses, and the interaction potential. Two important scales emerge, one set by the kinematics and one set by the dynamics. This method also provides two approximate analytic formulas useful for numerical evaluation of entanglement and reveals an interesting connection between purity, linear coordinate transformations, and momentum uncertainties.

Precise numerical calculation of transition intervals between metastable states in the antiprotonic helium atom is performed. Theoretical consideration includes a complete account of the relativistic and radiative corrections of order $R_{\infty }{\alpha }^4$ in the nonrecoil limit. The final uncertainty is estimated to be about 1–2 MHz.

Collision dynamics of ${\mathrm{He}}^{2+}+\mathrm{H}\left(1s\right)$ ionization in a hot, dense (Debye) plasma is studied by the two-center atomic orbital close-coupling (AOCC) method in the energy range $5–300\mathrm{keV}∕\mathrm{u}$. The target AO basis contained all $n\le 6$ bound states and 117 quasicontinuum states, while that on the projectile contained all $n\le 4$ bound states. The eigenenergies and wave functions of all these states were obtained variationally as a function of the screening parameter in a Debye-Hückel potential and used in AOCC dynamics calculations. With increasing the screening, more and more discrete states enter the target and projectile continuum and increase the ionization cross section, particularly at low collision energies. The ionization to target continuum is the main ionization channel, while the ionization to the projectile continuum becomes important only for large screenings and collision energies below $\sim 50\mathrm{keV}∕\mathrm{u}$.

We demonstrate a spectroscopy method that can be applied in an atomic beam, light-pressure-induced spectroscopy (LiPS). A simple pump and probe experiment yields a dispersivelike spectroscopy signal that can be utilized for laser frequency stabilization. The underlying principles are discussed and compared to Monte Carlo simulations. The shape of the dispersive signal is well described by the simulations. The zero crossing point of the signal is redshifted with respect to the atomic resonance by $\sim 3\text{MHz}$ (one-tenth of the natural linewidth) and depends slightly on the laser intensity. The shift of the zero crossing is determined by laser-induced fluorescence and compared with results of Doppler-free saturation spectroscopy. To check the potential of LiPS for frequency stabilization purposes, it was used to frequency-stabilize the laser for 400 min. Frequency fluctuations of only 0.12 MHz were measured.

Motivated by the possibility of creating non-Abelian fields using cold atoms in optical lattices, we explore the richness and complexity of noninteracting two-dimensional electron gases (2DEGs) in a lattice, subjected to such fields. In the continuum limit, a non-Abelian system characterized by a two-component “magnetic flux” describes a harmonic oscillator existing in two different charge states (mimicking a particle-hole pair) where the coupling between the states is determined by the non-Abelian parameter, namely, the difference between the two components of the “magnetic flux.” A key feature of the non-Abelian system is a splitting of the Landau energy levels, which broaden into bands, as the spectrum depends explicitly on the transverse momentum. These Landau bands result in a coarse-grained “moth,” a continuum version of the generalized Hofstadter butterfly. Furthermore, the bands overlap, leading to effective relativistic effects. Importantly, similar features also characterize the corresponding two-dimensional lattice problem when at least one of the components of the magnetic flux is an irrational number. The lattice system with two competing “magnetic fluxes” penetrating the unit cell provides a rich environment in which to study localization phenomena. Some unique aspects of the transport properties of the non-Abelian system are the possibility of inducing localization by varying the quasimomentum, and the absence of localization of certain zero-energy states exhibiting a linear energy-momentum relation. Furthermore, non-Abelian systems provide an interesting localization scenario where the localization transition is accompanied by a transition from relativistic to nonrelativistic theory.

We analyze the phase diagram of ultracold bosons in a one-dimensional superlattice potential with disorder, using the time-evolving block decimation algorithm for infinite-sized systems. For degenerate potential energies within the unit cell of the superlattice, loophole-shaped insulating phases with noninteger filling emerge with a particle-hole gap proportional to the boson hopping. Addition of a small amount of disorder destroys this gap. For not too large disorder, the loophole Mott regions detach from the axis of vanishing hopping, giving rise to insulating islands. Thus the system shows a transition from a compressible Bose glass to a Mott-insulating phase with increasing hopping amplitude. We present a straightforward effective model for the dynamics within a unit cell which provides a simple explanation for the emergence of Mott-insulating islands. In particular, it gives rather accurate predictions for the inner critical point of the Bose glass to Mott insulator transition.

According to the theory of Veselago, when a particle immersed within a metamaterial with negative refractive index is illuminated by plane wave, it experiences a reversed radiation force due to the antiparallel directions of the phase velocity and energy flow. By employing an ab initio method, we show that, in the limit of zero losses, the effect of reversed radiation pressure is generally true only for the specular beam. Waves generated by diffraction of the incident light at the surface of the slab of the metamaterial can produce a total force which is parallel to the radiation flow. However, when the actual losses of the materials are taken into account, the phenomenon of reversed radiation force is evident within the whole range of a negative refractive index band.

Absolute cross sections for the production of the two astronomy-relevant negative ions $\mathrm{H}\mathrm{C}{\mathrm{C}}^{-}$ and $\mathrm{H}\mathrm{C}\mathrm{C}\mathrm{C}{\mathrm{C}}^{-}$ by dissociative electron attachment to acetylene ${\mathrm{C}}_2{\mathrm{H}}_2$ and diacetylene ${\mathrm{C}}_4{\mathrm{H}}_2$ were measured (with a $\pm 25\%$ error bar). Acetylene yielded the ${\mathrm{C}}_2{\mathrm{H}}^{-}$ ion at an electron energy of $2.95\mathrm{eV}$ with a cross section of $3.6\pm 0.9{\mathrm{pm}}^2$ and also the ${\mathrm{C}}_2^{-}$ ion at $8.1\mathrm{eV}$ with a cross section of $4.1\pm 1{\mathrm{pm}}^2$. Diacetylene yielded the ${\mathrm{C}}_4{\mathrm{H}}^{-}$ ion at $2.5\mathrm{eV}$ with a cross section of $3.0\pm 0.8{\mathrm{pm}}^2$ and at $5.25\mathrm{eV}$with a cross section of $73\pm 17{\mathrm{pm}}^2$. Weaker ${\mathrm{C}}_4^{-}$, ${\mathrm{C}}_2{\mathrm{H}}^{-}$, and ${\mathrm{C}}_2^{-}$ signals were also observed from diacetylene. The identity of the negative ion resonances mediating the dissociation and the consequences for the production of these ions in discharges are discussed. An alternate path for ${\mathrm{C}}_4{\mathrm{H}}^{-}$ formation, from the ${\mathrm{O}}^{-}\text{−}{\mathrm{C}}_4{\mathrm{H}}_2$ ion-molecule reaction, was also observed.

The role of spin-orbit interaction in the ground state and thermal entanglement of a Heisenberg $XYZ$ two-qubit system in the presence of an inhomogeneous magnetic field is investigated. We show that the ground state entanglement tends to vanish suddenly for a certain value of the spin-orbit parameter $D$ and, when $D$ crosses its critical value $D_c$, the entanglement undergoes a revival. Indeed, when $D$ crosses its critical value $\left(D_c\right)$, the ground state entanglement tends to its maximum value $\left(C=1\right)$. Also, at finite temperatures there are revival regions in the $D\text{−}T$ plane. In these regions, entanglement first increases with increasing temperature and then decreases and ultimately vanishes for temperatures above a critical value. We find that this critical temperature is an increasing function of $D$ and that the amount of entanglement in the revival region depends on the spin-orbit parameter. Therefore when spin-orbit interaction is included larger thermal entanglement can exist at higher temperatures. We also show that the rate of enhancement of thermal entanglement by $D$ is not the same for ferromagnetic $\left(J_z<0\right)$ and antiferromagnatic $\left(J_z>0\right)$ chains. The entanglement teleportation via the quantum channel constructed by the above system is also investigated, and the influence of the spin-orbit interaction on the fidelity of teleportation and entanglement of replica states is studied. We show that, by introducing spin-orbit interaction, the entanglement of the replica state and fidelity of teleportation can be increased for the case of $J_z<0$. We also argue that a minimal entanglement of the channel is required to realize efficient entanglement teleportation and, in the case of $J_z<0$, this minimal entanglement can be achieved by introducing spin-orbit interaction.

The double to single ionization ratios $R_{21}$ of helium bombarded by slow $\left(v_{\text{Bohr}}<v<4v_{\text{Bohr}}\right)$ ${\text{C}}^{2+}$ and ${\text{C}}^{3+}$ ions are measured by the time-of-flight and coincidence technique. When the velocity is about $3v_{\text{Bohr}}$, the values of $R_{21}$ by ${\text{C}}^{q+}$ reach a maximum and are found to be 2 times the values for bare ions such as ${\text{He}}^{2+}$ and ${\text{Li}}^{3+}$. A simple model is presented to estimate the single and double ionization cross sections of helium by various ions, and to present the scenario of multi-ionization in the low to intermediate energy range. The calculation results by the model are in excellent agreement with the experimental data.

By means of an adapted mean-field expansion for large fillings $n⪢1$, we study the evolution of quantum fluctuations in the time-dependent Bose-Hubbard model, starting in the superfluid state and approaching the Mott phase by decreasing the tunneling rate or increasing the interaction strength in time. For experimentally relevant cases, we derive analytical results for the temporal behavior of the number and phase fluctuations, respectively. This allows us to calculate the growth of the quantum depletion and the decay of off-diagonal long-range order. We estimate the conditions for the observability of the time dependence in the correlation functions in the experimental setups with external trapping present. Finally, we discuss the analogy to quantum effects in the early universe during the inflationary epoch.

We study the steady state of a zero-temperature Bose gas near a Feshbach or photoassociation resonance using a two-channel mean-field model that incorporates atomic and molecular condensates, as well as correlated atom pairs originating from dissociation of molecules into pairs of atoms. We start from a many-body Hamiltonian for atom-molecule conversion, and derive the time-dependent version of the mean-field theory. The stationary solution of the time-dependent model is rendered unique with an approximation that entails that all noncondensate atoms are correlated, as if emerging from dissociation of molecules. The steady state is solved numerically, but limiting cases are also found analytically. The system has a phase transition in which the atomic condensate emerges in a nonanalytic fashion. We quantify the scaling of the observable quantities, such as fractions of atomic and molecular condensates, with the detuning and the atom-molecule conversion strength. Qualitatively, the dependence on detuning rounds out with increasing coupling strength. A study of the thermodynamics shows that the pressure of the atom-molecule system is negative, even on the molecule side of the resonance. This indicates the possibility of mechanical instability.

We develop a perturbation theory for bright solitons of the $F=1$ integrable spinor Bose-Einstein condensates (BEC) model. The formalism is based on using the Riemann-Hilbert problem and provides the means to analytically calculate evolution of the soliton parameters. Both rank-one and rank-two soliton solutions of the model are obtained. We prove equivalence of the rank-one soliton and the ferromagnetic rank-two soliton. Taking into account a splitting of a perturbed polar rank-two soliton into two ferromagnetic solitons, it is sufficient to elaborate a perturbation theory for the rank-one solitons only. Treating a small deviation from the integrability condition as a perturbation, we describe the spinor BEC soliton dynamics in the adiabatic approximation. It is shown that the soliton is quite robust against such a perturbation and preserves its velocity, amplitude, and population of different spin components, only the soliton frequency acquires a small shift. Results of numerical simulations agree well with the analytical predictions, demonstrating only slight soliton profile deformation.

The theory of surface-second-harmonic generation in a dielectric microsphere using whispering-gallery modes (WGMs) is developed. The second-order nonlinearity is restricted to the surface of the sphere. The coupling coefficients for a coupled-mode theory are derived and conditions for double resonance and phase matching are discussed for TE and TM polarizations. We demonstrate that phase matching of WGMs amounts to conservation of the angular momentum of the electromagnetic mode while at the same time we obtain an analytical expression for the coherence length.