The goal of the project is to shed light on two-component Bose-Einstein Condensates (BECs) and how they differ from their single-component counterparts. The investigator and his colleagues aim to redefine the way in which modeling and analysis are developed in such systems by introducing some fundamental physical processes that were not included in presently employed models. More specifically, the team of researchers plans to: (a) develop a new model for two-component BECs, by augmenting existing models to account for processes such as inter-atomic interaction losses and higher-order magnetic (Zeeman) effects; (b) benchmark the model, by testing it in a variety of situations where the total number of atoms or ratio of atoms changes between the two components and comparing it against the newly developed partial differential equation model; (c) analyze the model mathematically by means of Galerkin projections and Lyapunov-Schmidt reductions to study finite dimensional approximations of the dynamics, whereby the existence and stability of solutions are studied and control strategies are employed to stabilize potentially unstable solution configurations; (d) produce a computational platform that enables the study of existence, stability and nonlinear dynamics of multi-component, high-dimensional variants of the nonlinear Schrodinger equations that are the key mathematical ingredient in the modeling of such atomic systems. In the process, spatially/temporally adaptive and/or parallel integrators are produced for time-stepping purposes and iterative methods are developed in order to analyze the linear stability problem around steady state solutions.
This project presents a route to systematically quantify the quantum dynamics at the lowest temperatures that arise in the Universe, namely in the recently created new form of matter represented by Bose-Einstein condensates (whose formation was awarded with the 2001 Nobel prize in Physics and whose properties, such as superfluidity, were intimately connected to the Nobel prize in Physics in 2003). The investigator and his colleagues form an interdisciplinary team to directly monitor this state of matter in the laboratory, to model the system at the physical level, to explore the resulting features at the mathematical level, and finally to fully visualize the three-dimensional dynamics of such complex systems. A continuous feedback between all the above stages is intended to ascertain not only a qualitative but also a quantitative understanding of such atomic physics systems, such as gases of rubidium, sodium and other alkali vapors. The multi-species systems under study present a wealth of opportunities for future applications, ranging from the controllable formation of ultracold microscopic patterns (in a form of "quantum lithography") to the realization of quantum gates and switches, that, in turn, aim towards the longer term goal of enabling quantum computation.
