This page contains some of the numerical calculations that I have done.

Bloch Oscillations:

The below two figures are the Bloch oscillations performed by a particle in 1D lattice. The left one is a moving mode and the right one is a breathing mode. The initial wavefunction is gaussian located at the center of the lattice. The magnitude of the wavefunction as a function of position and time are plotted.

A Bloch Zener Oscillations in Brick Wall lattice:

Taruell et al. came up with the idea of using Bloch Zener oscillations to detect Dirac points in the optical lattice experiment. The model used is the Brick wall lattice. We have tried to reproduce their results for two different parameters in the below two videos.

Bloch Zener Oscillations in Kitaev-Hubbard Model

The Bloch-Zener oscillations in a model with spin-dependent hopping on the honeycomb lattice called the Kitaev-Hubbard model

Dirac points merging and emerging

The tight binding model of Kitaev-Hubbard has interesting Dirac Point merging and emerging as a function of the spin dependent parameter t'.

Rotating Cloud Experiment for detecting Pancharatnam Berry Curvature:

Nematic Liquid Crystals

Vortex Dynamics in Nematic Liquid crystals