Quantum Spin Dynamics in Fock Space Following Quenches: Caustics and Vortices.

Caustics occur widely in dynamics and take on shapes classified by catastrophe theory. At finite wavelengths they produce interference patterns containing networks of vortices (phase singularities). Here we investigate caustics in quantized fields, focusing on the collective dynamics of quantum spins. We show that, following a quench, caustics are generated in the Fock space amplitudes specifying the many-body configuration and which are accessible in experiments with cold atoms, ions, or photons. The granularity of quantum fields removes all singularities, including phase singularities, converting point vortices into nonlocal vortices that annihilate in pairs as the quantization scale is increased. Furthermore, the continuous scaling laws of wave catastrophes are replaced by discrete versions. Such "quantum catastrophes" are expected to be universal dynamical features of quantized fields.

Floquet-Bloch solutions in a sawtooth photonic crystal.

Band structure of a sawtooth photonic crystal for optical wave propagation along the axis of periodicity is investigated. Floquet-Bloch solutions are found and illustrated for the bandgaps, allowed bands, and bandedges of the crystal. Special attention is given to the cases where Floquet-Bloch solutions become periodic functions.

Resonant carrier dynamics in strongly biased superlattices.

We study coherent electron dynamics in a biased undriven ideal semiconductor superlattice coupled to the continuum, near energy level anticrossings. In particular, we examine the dependence of wavepacket dynamical characteristics on electric field detuning, and investigate mixed regimes involving a superposition of energy level anticrossings showing both Rabi oscillations and resonant tunnelling. In earlier work (Abumov and Sprung 2007 Phys. Rev. B 75 165421), Rabi and Zener resonances were shown to have a common origin, and a criterion for the occurrence of either was proposed. The present results allow a better understanding of the nature of an interminiband resonance, which can be useful in the areas of microwave radiation generation and matter manipulation on the particle level, as well as demonstrating an alternative approach to examining electron level structure of a finite superlattice.

Semiclassical coupled wave theory for TM waves in one-dimensional photonic crystals.

Semiclassical coupled wave theory is extended to waves with the electric field polarized parallel to the plane of incidence (TM waves) in one-dimensional periodic dielectric structures. Using this theory, the bandwidths and reflection/transmission characteristics of such structures, as functions of the incident wave frequency, are in good agreement with exact numerical simulations even for very high refractive index contrast.

Semiclassical coupled-wave theory and its application to TE waves in one-dimensional photonic crystals.

A semiclassical coupled-wave theory is developed for TE waves in one-dimensional periodic structures. The theory is used to calculate the bandwidths and reflection/transmission characteristics of such structures, as functions of the incident wave frequency. The results are in good agreement with exact numerical simulations for an arbitrary angle of incidence and for any achievable refractive index contrast on a period of the structure.