Few-Body Physics with Ultra Cold Atoms

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Most every-day life processes are governed by classical mechanics. Newton's second law of motion is a well-known example of this. In certain situations, quantum mechanical laws come into play and the classical laws no longer provide an accurate description of the system dynamics. The quantum mechanical laws are well established. However, applying these laws and making quantitative predictions is a highly challenging task of fundamental and technical importance. The periodic table and nuclear chart, for example, are the result of quantum mechanical considerations, as are the working principles of solar cells. The activities supported by the grant will greatly advance our understanding of quantum mechanical few-body systems. These systems serve as prototypes for more complex systems. Where possible, the planned theoretical studies will be benchmarked against experimental results. As part of this program, multiple graduate and undergraduate students will be trained. These students will have access to state-of-the-art computing resources and will develop strong numerical and analytical skills; thus, they will be well prepared for a variety of future pursuits in academia, at national labs or in industry.Near zero temperature, few-body correlations are often times governed by just a few parameters such as the two-body s-wave scattering length and the two-body effective range. This suggests that effective low-energy few-atom Hamiltonians can be utilized to describe the key aspects of cold few-body collisions and of weakly-bound few-body states. The idea of replacing the true interactions by effective interactions is similar to what Fermi did in his groundbreaking 1934 paper on the scattering between slow neutrons and bound hydrogen atoms. The present grant capitalizes on experimental and theoretical advances in cold atom physics and provides support for theoretical studies of cold few-atom systems. Techniques will be developed and applied to solve the time-independent Schrodinger equation for different classes of non-trivial few-body systems, with the goal of developing a deeper understanding of few-particle correlations and universal low-energy features. The analytical approaches include perturbative treatments around the strongly-coupled regime and the use of a hyperspherical coordinate approach that can be viewed as a trap analog of the Bethe ansatz. Numerical techniques include a Lippmann-Schwinger equation based treatment and a basis set expansion technique that utilizes explicitly correlated Gaussians.