In partial fulfillment of the requirements for the degree of 

Doctor of Philosophy in Physics 

School of Physics Thesis Dissertation Defense

Bar Alluf 

Dr. Carlos Sá de Melo, School of Physics, Georgia Institute of Technology (Advisor)

Breaking Duality: Mobility Regions and Topological Phases in Spin-Orbit Coupled Atomic Wires

Date: Friday, April 10, 2026

Time: 10:00 a.m.

Location: Pettit Microelectronics, 102A&B 

Committee members:

Dr. Michael Chapman, School of Physics, Georgia Institute of Technology

Dr. Zhigang Jiang, School of Physics, Georgia Institute of Technology

Dr. Xueda Wen, School of Physics, Georgia Institute of Technology

Dr. Luiz Santos, Department of Physics, Emory University

Abstract:

Ultracold atoms serve as a highly useful platform for studying a wide variety of quantum systems due to the high degree of control and tunability which is experimentally achievable. A particularly interesting phenomenon is the emergence of mobility edges, which separate localized and extended states within the same energy spectrum. In strictly one-dimensional quasiperiodic systems described by the standard Aubry-André model, these mobility edges are conventionally absent due to an inherent global self-duality. This thesis investigates the localization properties in Aubry-André atomic wires, demonstrating that the simultaneous addition of spin-orbit coupling and transverse Rabi fields explicitly breaks this self-duality. The effects of the fermionic filling factor and the varying degrees of duality breaking are studied to build a comprehensive picture of how these fields generate robust mobility regions. Additionally, this thesis explores the topological properties of the system by treating the relative optical laser phase as a synthetic dimension, enabling an exact mapping to two-dimensional quantum Hall systems to classify three distinct topological phases.