Systems with quenched disorder play a central role in condensed matter physics, and are notoriously difficult to study theoretically and numerically, in particular in the presence of pronounced quantum effects. Recently, thanks to advances in experimental physics, in particular experimental realization of Bose-Einstein condensation, it has become possible to realize and study in a controlled way ultracold atomic gases in optical lattices. This opens entirely new paths of investigation of strongly correlated quantum systems, as well as of readdressing in the quantum context challenging open questions of classical statistical physics, such as the nature of spin glasses. It also opens possibilities of observing effects predicted earlier, but so far not realized experimentally in classical systems, such as disappearance of spontaneous magnetization in the twodimensional random field Ising model. PI's main objective is to enter this exciting new branch of physics through a collaboration with a group of M. Lewenstein at the Institut de Ciencies Fotoniques (ICFO) in Barcelona during his 2006/2007 sabbatical leave. While he has worked and continues to work extensively on mathematical physics of disordered systems, the focus of the present proposal is on physics rather than on mathematics and on fields that the PI has not worked on in the past rather than on his main area of expertise. These new fields include: 1. Theoretical physics of quantum many-body systems, especially phase transitions in quantum systems with quenched disorder in low temperatures. Most of the central problems in this field are beyond the reach of the rigorous mathematical tools currently available. Theoretical physics is very different from mathematics in its methodology and the difficult task of entering this new area will be greatly facilitated by a close working relationship with one of the leading groups in the field. 2. Design of experiments using ultracold atoms which would follow such theoretical studies and stimulate new ones. M. Lewenstein's extensive contacts with experimental groups throughout Europe and the United States, and ICFO's own experimental groups and equipment are an excellent base for starting this new line of research. 3. Applications to quantum information processing. This area is particularly important for long term research plans of the PI, who wants to continue work on it after returning to the US in 2007. The experience gained during the stay at ICFO will enable him to start working with the Optical Sciences and Physics groups at the University of Arizona and with other leading US groups. While the subject is new to him, the PI is confident that he is qualified to enter it at the current research level taking advantage of the chance to collaborate with a world-class research team. Quenched disorder may be realized using pseudo-random incommensurate superlattices, random lattices generated by speckle radiation, or quenched random scatterers. We will study feasibility of realizing a large class of such systems and to investigate their properties; among others, quantum random field systems with various symmetries and motion in a random potential. Disordered atomic gases promise to have a big impact on quantum information processing and we will specifically focus will be on systems relevant for this application. The subject of this project is multidisciplinary, spanning atomic physics, quantum optics, quantum statistical physics, quantum field theory, condensed matter physics, quantum information, and mathematical physics. The long-term objectives of the project are: To design new ways of realizing disorder in ultracold atomic gases in optical lattices, to identify interesting disordered systems particularly sensitive to the disorder, and their quantum versions (among systems of interest are ferromagnetic and antiferromagnetic Ising models in a random magnetic field of various orientations, Heisenberg model in random fields with various symmetries, Potts models, spin glasses and electron propagation in random potential), to study usefulness of such systems for quantum information theory, to investigate methods of preparing, manipulating and detecting such systems; in particular we will study possibilities of cooling such systems to temperatures near zero and of experimental measurements of their sensitivity to boundary conditions, to work on random field systems and come up with proposals of relevant experiments, at the organizational level, to establish lasting research relationship with a prominent European physics group, to continue and broaden this collaboration, with the participation of the research groups at the University of Arizona and at other US centers.
In collaboration with one of the leading quantum optics groups, we propose a project, whose results will significantly broaden understanding of disordered systems which are of crucial importance for condensed matter physics, including high temperature superconductivity. The systems we will to study also play a central role in quantum information processing. Most of the research plan belongs to fields which are new to the PI, in particular all of the proposed work is in physics as opposed to mathematics. The PI is convinced that his keen interest in the subject, the detailed research plan, broad contacts and the resources of ICFO will make it possible to enter the new area and conduct a fruitful collaboration.
We expect to establish at the University of Arizona a group collaborating on a broad scale with ICFO as well as with leading U.S. groups working in related areas. This will include education at advanced undergraduate and Ph.D. levels and organization of schools and conferences, encouraging participation of students and underrepresented groups. The interdisciplinary character of the project will bring together researchers from various fields, facilitating dissemination of ideas. The quantum information aspect of the project has ample potential for technological applications, crucial for the information age society. This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).
