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"Analytical Methods for Schrödinger Equation: From Two-Level System to Anderson Localization"

Dr. Hichem El Euch
Texas A&M University


In the first part of my talk, I will review our ERS (Eleuch-Rostovtsev-Scully) method. The ERS technique generates analytical solutions for general potentials beyond the adiabatic approximation for 1D, 2D and 3D Schrödinger equations. The second part of the talk will be devoted to two complimentary methods developed recently by us in order to study the dynamics of two-level system. We obtained general, analytic expressions for the atomic population of the excited state in two-level atom driven by a laser pulse of arbitrary shape out of the resonance and beyond the rotating wave approximation. Furthermore, we determine which method is adapted for the large pulse and which one is adapted for the few-cycle pulse (ultra-short pulse). Comparison between these methods and the conventional methods is implemented for several values of the laser pulse parameters. Furthermore, an interesting analogy between the dynamics of the two-level system and the scattering problems will be presented. Propagation of waves in random media will be the subject of the third part of this talk. Anderson localization has been explored extensively in the last six decades and has been observed in different systems, including electrons, photons and atoms. It has opened the door for many applications in random lasing, photonic crystals, quantum information, biological systems and cosmology. All these systems share a common wave equation, Schrödinger like equation. The analytical results in this field are limited to the low disorder, where perturbative approaches are used to disordered potentials. We have shown that the localization behavior of the standard disordered wave equation can be computed for all disorder strengths correlation lengths by using the ERS solution.

Tuesday, February 28, 2017
IQSE Seminar Room (578 MPHY), 12:00 Noon
Mitchell Physics Building

Institute for Quantum Science and Engineering
Texas A&M University

Pizza, salad and soda to be served at 11:45 a.m.)