Dissertation Committee Chair: Mohammad Hafezi
Committee:
Maissam Barkeshli
Michael Gullans
Trey Porto
Ronald Walsworth
John Cumings
Abstract: Topological phases are intriguing phases of matter which cannot be described with traditional theories of the phase transition such as Ginzburg-Landau theory, and numerous efforts has been put to achieve these exotic phases of matter in a variety of quantum platforms. In this thesis, we discuss how topological quantum states of matter can be engineered by utilizing spatially patterned light, which has become available thanks to the recent advances in beam shaping techniques.
First, we discuss a scheme to construct an optical lattice to confine ultracold atoms on the surface of torus. We investigate the feasibility of this construction with numerical calculations as well as propose a supercurrent generation experiment to verify the non-trivial topology of the created surface. We also propose a scheme to construct fractional quantum Hall states which can demonstrate topological degeneracy. We then extend our effort for creation of topologically non-trivial surfaces for ultracold atoms to the surfaces with open boundaries, using a bilayer optical lattice with multiple pairs of twist defects. We explain how a spin-dependent optical lattice can serve as the bilayer optical lattice for this purpose as well as the scheme for preparing and optically manipulating the fractional quantum Hall states.
Then we turn our attention to driven electronic systems. In particular, we investigate a way to imprint the superlattice structure in two-dimensional electronic systems by shining circularly-polarized light. We demonstrate the wide optical tunability of this system allows to a variety of band properties. We show that these tunable band properties lead to exotic physics ranging from the topological transitions to the creation of nearly flat bands, which can allow a realization of strongly correlated phenomena in Floquet systems. We then investigate the Floqut vortex states created by shining light carrying non-zero orbital angular momentum on a 2D semiconductor. We analytically and numerically study the properties of those vortex states and show that such Floquet vortex states exhibit a wide range of tunability and illustrate the potential utility of such tunability with an example of application in quantum state engineering.