To achieve large changes in adiabatic invariants using small control input, a conservative dynamical system must possess an internal resonance. Capture into resonance is an inherently probabilistic process. We propose a control method to make it more structured. We study the motion of charged particles in an electromagnetic field as an example of such a system. When the nominal dynamics brings particles close to a resonance surface, a short control pulse forces the capture of a particle into the resonance with the wave. A captured particle is transported by the wave across the energy levels. The second pulse releases a particle from the resonance when the desired energy level is achieved. We discuss the distribution of energy achieved by the method.

We carried out experimental studies of the self-assembly of metallic micron-size particles in poorly conducting liquid subject to a constant electric field. Depending on the experimental conditions, the particles self-assemble into long chains directed along the electric field lines and form vortices and other structures. The vortices perform Brownian-type random motion due to self-induced chaotic hydrodynamic flows. We measured the diffusivity constant of the vortices and the conductivity and mechanical stiffness of the chains.

We have successfully observed two-photon above-threshold ionization in rare gas atoms (Ar, Xe, and He) by the fifth harmonic (25 eV photon energy) of a KrF laser. Use of the energy-resolved photoelectron counting system together with our laser, providing strong 25 eV radiation at 40–100 Hz, enabled us to detect the very weak single-color two-photon above-threshold ionization signals. Experimental data are in good agreement with our theoretical calculations newly developed along the line of multichannel quantum defect theory.

Kerr-nonlinearity induced optical parametric oscillation in a microcavity is reported for the first time. Geometrical control of toroid microcavities enables a transition from stimulated Raman to optical parametric-oscillation regimes. Optical parametric oscillation is observed at record low threshold levels (174 micro-Watts of launched power) more than 2 orders of magnitude lower than for optical-fiber-based optical parametric oscillation. In addition to their microscopic size (typically tens of microns), these oscillators are wafer based, exhibit high conversion efficiency (36%), and are operating in a highly ideal “two photon” emission regime, with near-unity ($0.97\pm 0.03$) idler-to-signal ratio.

We demonstrate the first fully controlled generation of immobile and slow spatial gap solitons in nonlinear periodic systems with band-gap spectra, and observe the key features of gap solitons that distinguish them from discrete solitons, including a dynamical transformation of gap solitons due to nonlinear interband coupling. We also describe theoretically and confirm experimentally the effect of the anomalous steering of gap solitons in optically induced photonic lattices.

We study how a decrease of the coupling strength causes a desynchronization in the Kuramoto model of $N$ globally coupled phase oscillators. We show that, if the natural frequencies are distributed uniformly or close to that, the synchronized state can robustly split into any number of phase clusters with different average frequencies, even culminating in complete desynchronization. In the simplest case of $N=3$ phase oscillators, the course of the splitting is controlled by a Cherry flow. The general $N$-dimensional desynchronization mechanism is numerically illustrated for $N=5$.

We derive the semiclassical equation of motion for the wave packet of light taking into account the Berry curvature in momentum-space. This equation naturally describes the interplay between orbital and spin angular momenta, i.e., the conservation of the total angular momentum of light. This leads to the shift of wave-packet motion perpendicular to the gradient of the dielectric constant, i.e., the polarization-dependent Hall effect of light. An enhancement of this effect in photonic crystals is also proposed.

Broadband analysis of a prototype model associated with electromagnetic waves absorption in a lossy dielectric slab renders a closed-form theoretical prediction of an infinite number of optimal absorption paths in the complex refractive index domain. While for thin slabs (in terms of incident wavelength range) each path corresponds to a lossy Fabry-Perot-type resonance modes of order $m=0,1,2,\dots$ and provides at least 50% absorption of the incident wave power even for ultrathin slabs, for optimal thick slabs, the fraction of absorbed power, asymptotically estimated via Lambert $W$ function, increases up to 100% for consecutive continuation of the $m=1$ normal mode only.

A rationale for the empirically observed Strouhal-Reynolds number relation for vortex shedding in the wake of a cylinder is provided. This rationale derives from a mechanism of vortex formation observed in numerical simulations of two-dimensional vortex shedding coupled with an order of magnitude estimate of the terms in the vorticity transport equation based on this mechanism.

We demonstrate generalized synchronization in a spatiotemporal chaotic system, a liquid crystal spatial light modulator with optoelectronic feedback.

The optical and structural properties of dense colloidal suspensions in the presence of long-range electrostatic repulsion are determined from both light and small-angle neutron scattering experiments. Short-range structural order induces an enhancement of the scattering strength while at the same time the total transmission shows strong wavelength dependence, reminiscent of a photonic crystal. Interestingly, the interplay between diffusive scattering and local order leads to negative values of the scattering anisotropy parameter. The tunable optical properties of these liquids furthermore suggest potential applications such as transparency switches or filters.

We have realized a Brownian motor by using cold atoms in a dissipative optical lattice as a model system. In our experiment the optical potential is spatially symmetric and the time symmetry of the system is broken by applying appropriate zero-mean ac forces. We identify a regime of rectification of forces and a regime of rectification of fluctuations, the latter corresponding to the realization of a Brownian motor.

The weakly nonlinear dynamics of long waves embedded in marginally stable shear flows that vary in the streamwise direction are shown to be governed by a variable-coefficient Boussinesq equation. Depending on the local stability characteristics of the flow, new nonmodal or modal instabilities may emerge that serve as natural mechanisms for achieving amplitude thresholds necessary for weakly nonlinear instability and the transition to fully finite-amplitude states.

We report on the first experimental evidence of negative refraction at telecommunication wavelengths by a two-dimensional photonic crystal field. Samples were fabricated by chemically assisted ion beam etching in the InP-based low-index constrast system. Experiments of beam imaging and light collection show light focusing by the photonic crystal field. Finite-difference time-domain simulations confirm that the observed focusing is due to negative refraction in the photonic crystal area.

We obtain a general result for the Lamb shift of excited states of multilevel atoms in inhomogeneous electromagnetic structures and apply it to study atomic hydrogen in inverse-opal photonic crystals. We find that the photonic-crystal environment can lead to very large values of the Lamb shift, as compared to the case of vacuum. We also suggest that the position-dependent Lamb shift should extend from a single level to a miniband for an assembly of atoms with random distribution in space, similar to the velocity-dependent Doppler effect in atomic/molecular gases.

We study the free decay of capillary turbulence on the charged surface of liquid hydrogen. We find that decay begins from the high frequency end of the spectral range, while most of the energy remains localized at low frequencies. The apparent discrepancy with the self-similar theory of nonstationary wave turbulent processes is accounted for in terms of a quasiadiabatic decay wherein fast nonlinear wave interactions redistribute energy between frequency scales in the presence of finite damping at all frequencies. Numerical calculations based on this idea agree well with experimental data.

We investigate the possibility of quantum (or wave) chaos for the Bogoliubov excitations of a Bose-Einstein condensate in billiards. Because of the mean field interaction in the condensate, the Bogoliubov excitations are very different from the single particle excitations in a noninteracting system. Nevertheless, we predict that the statistical distribution of level spacings is unchanged by mapping the non-Hermitian Bogoliubov operator to a real symmetric matrix. We numerically test our prediction by using a phase shift method for calculating the excitation energies.

We demonstrate targeting and control over spatiotemporal chaos in an optical feedback loop experiment. Different stationary target patterns are stabilized in real time by means of a two dimensional space extended perturbation field driven by an interfaced computer and applied in real space to a liquid crystal display device inserted within a control optical loop. The flexibility of the system in switching between different target patterns is also demonstrated.

The statistical properties of velocity and acceleration fields along the trajectories of fluid particles transported by a fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. We present results for Lagrangian velocity structure functions, the acceleration probability density function, and the acceleration variance conditioned on the instantaneous velocity. These are compared with predictions of the multifractal formalism, and its merits and limitations are discussed.

The coarsening and wave number selection of striped states growing from random initial conditions are studied in a nonrelaxational, spatially extended, and far-from-equilibrium system by performing large-scale numerical simulations of Rayleigh-Bénard convection in a large-aspect-ratio cylindrical domain with experimentally realistic boundaries. We find evidence that various measures of the coarsening dynamics scale in time with different power-law exponents, indicating that multiple length scales are required in describing the time dependent pattern evolution. The translational correlation length scales with time as $t^{0.12}$, the orientational correlation length scales as $t^{0.54}$, and the density of defects scale as $t^{-0.45}$. The final pattern evolves toward the wave number where isolated dislocations become motionless, suggesting a possible wave number selection mechanism for large-aspect-ratio convection.