Defense of thesis Zoubair Daouma

Defense of thesis Zoubair Daouma - laboratory PhLAM

Abstract : 

This thesis investigates the effects of symmetries and universality classes on quantum localization in disordered systems through the study of a quantum kicked rotor (QKR) model with spin–orbit coupling. The QKR provides an ideal quantum simulator for exploring coherent interference phenomena and disorder–induced metal–insulator transitions in a highly controllable framework.
After reviewing the theoretical foundations of Anderson localization and the one–parameter scaling theory, we introduce several variants of the kicked rotor — standard, double–period, and spin–orbit coupled — and analyze their symmetry properties (orthogonal, unitary, symplectic). We show how spin–orbit coupling breaks time–reversal symmetry and alters the interference between reciprocal paths, leading to a crossover between weak localization and weak anti–localization regimes.
A detailed study of the Spin–Double–Period Quantum Kicked Rotor (SDQKR) model is presented, highlighting coherent interference effects such as Coherent Backscattering (CBS) and anti–CBS, and their dependence on temporal periodicity and symmetry class. The spectral statistics of the Floquet operator reveal the expected transitions between Wigner–Dyson ensembles (GOE, GUE, GSE).
Finally, we investigate the Anderson transition in the two-dimensional symplectic case. Using advanced numerical methods. The obtained scaling function validates the one–parameter scaling hypothesis and displays the characteristic corrections for the symplectic class.
This work deepens our understanding of the role of symmetry in disordered quantum transport and paves the way toward the first experimental observation of weak anti–localization using a spin–orbit coupled atomic kicked rotor.

Keywords : disorder, cold atoms, Quantum simulation