Achieving the control of matter at the quantum level requires the detailed understanding of many-body systems at the quantum level. This project is expected to enhance the understanding of quantum mechanical processes of fundamental importance, in particular the thermodynamical properties of ultracold few-body systems of fermionic atoms. Ultimately, understanding quantum mechanical phenomena from a bottom-up perspective will have important technological implications for a wide range of every-day tasks ranging from improved cell phone technology to improved surgical tools. Today's world is technology driven and requires a highly skilled workforce. This project will train the next generation of young scientists. Undergraduate and graduate students will be involved in all aspects of the project, and the analytical and computational skills that the students gain will prepare them well for future pursuits in industry and academia.
This project will advance science by developing numerical and analytical tools that allow for the study of the temperature dependence and dynamics of quantum mechanical few-body systems. Few-body physics has played an important role in the development of quantum mechanics from the very beginning. For example, the helium atom, one of the simplest atoms of the periodic table and an effective three-body system, has been instrumental in developing a concise understanding of electron-electron correlations as well as fragmentation and (auto-) ionization. The experimental realization of ultracold fermionic gases consisting of a small number of particles (two, three, four, etc.) provides a new theoretically accessible model system with which to study quantum mechanical few-body phenomena at zero and finite temperature. Moreover, time-dependent measurements can be compared directly with theoretical predictions. This project aims to conduct theoretical studies of cold few-atom systems. Finite-temperature calculations for trapped few-atom systems will be performed using an efficient and flexible path-integral Monte Carlo code developed by the investigator, which has been shown to yield reliable results for small bosonic and fermionic systems over a wide range of temperatures. The path-integral Monte Carlo code will be made available to the broader scientific community as part of the Venture Fund for Software Reuse program. Time-dependent studies will be performed using an efficient and highly accurate grid-based time propagation scheme that expands the time evolution operator in terms of Chebychev polynomials.
