Realization of Discrete Quantum Billiard in 2D Optical Lattices

We propose the method for optical visualization of Bose-Hubbard model with two interacting bosons in the form of two-dimensional (2D) optical lattices consisting of optical waveguides, where the waveguides at the diagonal are characterized by different refractive index than others elsewhere, modeling the boson-boson interaction. We study the light intensity distribution function averaged over direction of propagation for both ordered and disordered cases, exploring sensitivity of the averaged picture with respect to the beam injection position. For our finite systems the resulting patterns reminiscent the ones set in billiards and therefore we introduce a definition of discrete quantum billiard discussing the possible relevance to its well established continuous counterpart

Optically induced orientational transitions in nematics with planar alignment

Theoretical study of dynamical phenomena induced by a linearly polarized plane wave incident perpendicularly on a planar aligned nematic layer with the light intensity as the control parameter is reported. We find the threshold of the Optically Induced Freedericksz Transition for the planar state as a function of the problem parameters. It occurs that the threshold is substantially lower than that expected before. Above the primary instability the director settles either to a stationary or to an oscillatory states depending on a thickness of the layer. These states become unstable at a secondary threshold through a heteroclinic bifurcation and the director settles to a new stationary distorted state

Interaction induced fractional Bloch and tunneling oscillations

We study the dynamics of few interacting bosons in a one-dimensional lattice with dc bias. In the absence of interactions the system displays single particle Bloch oscillations. For strong interaction the Bloch oscillation regime reemerges with fractional Bloch periods which are inversely proportional to the number of bosons clustered into a bound state. The interaction strength is affecting the oscillation amplitude. Excellent agreement is found between numerical data and a composite particle dynamics approach. For specific values of the interaction strength a particle will tunnel from the interacting cloud to a well defined distant lattice location.Comment: 4 pages, 4 figure