Probing Band Topology Using Modulational Instability

Probing the Topology in Band Insulators

Topological Insulator is a newly found state of matter. Unlike phases described by the traditional Landau theory of symmetry breaking, the topological phases do not break symmetry, and it is not obvious in which measurable quantity will the topological index manifest itself. In this thesis, our main goal is to understand how topological classification produces measurable consequences in periodi...

Modulational instability of spinor condensates

We demonstrate, analytically and numerically, that the ferromagnetic phase of the spinor Bose-Einstein condenstate may experience modulational instability of the ground state leading to a fragmentation of the spin domains. Together with other nonlinear effects in the atomic optics of ultra-cold gases (such as coherent photoassociation and four-wave mixing) this effect provides one more analogy ...

General approach to spatiotemporal modulational instability processes

Variational approach to the modulational instability.

We study the modulational stability of the nonlinear Schrödinger equation using a time-dependent variational approach. Within this framework, we derive ordinary differential equations (ODE's) for the time evolution of the amplitude and phase of modulational perturbations. Analyzing the ensuing ODE's, we rederive the classical modulational instability criterion. The case (relevant to application...

Two-dimensional modulational instability in photorefractive media

We study theoretically and experimentally the modulational instability of broad optical beams in photorefractive nonlinear media. The angular dependence of the growth rate of periodic perturbations is calculated. Our findings are confirmed by experimental measurements on a strontium barium niobate photorefractive crystal.