Rare and Exotic Nonlinear Effects in Cold Atomic Gases

University Of Massachusetts Boston, Dorchester MA

Investigators

Abstract

Symmetries provide both means for unification of otherwise disparate branches of science and a language for communication between scientists and non-scientists. Two symmetries are prominent in this project: multidimensional kaleidoscopes and the quantum-mechanical supersymmetry that relates the motion with obstacles to the motion in free space. Through these symmetries some real physical effects---prohibition of chemical processes and slowdown of relaxation in waveguide-confined gases, transparency of solitary waves for other waves, etc---are tightly intertwined with tiling with polygons, Platonic solids, and cat-eye reflectors. The PI's presentation at the "Meet the Scientists!" at the Science Discovery Museum, entitled "Kaleidoscopes, tilings, Newton's cradles, and atoms at a billionth degree above absolute zero", scheduled for the beginning of May 2014, has effectively the same content as one of the three parts of this project. This project constitutes an indispensable pedagogical tool for training undergraduate and masters-level students. Each of the three sub-projects, while touching upon a range of advanced methods of modern theoretical physics, from Lie groups to quantum mechanical supersymmetry, does so gently, dealing with objects as graspable as ordinary differential equations. The sub-projects are also modular, divisible into several year-long smaller projects, and so ideal for an honors or MS thesis. Many qualitative ideas developed in the course of preparation for the project greatly contributed to the development of an undergraduate-oriented book. Nonlinear physics is famous for its archipelagoes of small under- or unexplored islands. The ultracold atomic gases are the ideal vehicle for visiting such islands. The nonlinear phenomena considered in this project are as follows: a protocol for an experimental generation of a Gross-Pitaevskii breather, in a waveguide for cold attractive bosons. (A further study will address the integrability-induced robustness of the chemical composition of one-dimensional Bose gases.); an analysis of the transparency of the Andreev-Bogoliubov-de Gennes BCS soliton to quasi-particles, using information previously acquired in a study of transparency of the Bogoliubov-de Gennes equations for known integrable partial differential equations. At the moment, it is not clear what physical phenomenon the BCS soliton transparency is supposed to enable, with the primary candidate being the Andreev reflection. A systematic study of quantum and classical cases of the three body scattering without diffraction associated with non-crystallographic and exceptional crystallographic root systems (kaleidoscopic mirror arangements) will also be performed. A particular sequence of mass triplets-with ( sqrt(5) + 2) : 1 : (sqrt(5) + 2) being the first nontrivial member that behave similarly to the Newton cradle will be identified. Here, the momentum distribution remains invariant under three-body collisions. The plan includes a systematic molecular-dynamics study of many-body mass mixtures, with masses controlled by optical lattices, with an expectation that the relaxation time will show peaks at the "extended Newton cradle" mass ratios.