This award will support theoretical research on the properties of atoms cooled to ultralow temperatures. The research will be done in an undergraduate environment at Wellesley College. The research topic is one of great current excitement and is highly interdisciplinary, residing at the interface between condensed matter physics and atomic physics. There will be opportunities for undergraduate students to participate.
The proposed work explores novel properties of ultracold bosonic atoms in a periodic optical lattice potential, an ideal system for the study of superfluid and Mott-insulating phases of bosons. Using a combination of analytical and numerical techniques, salient features of systems where superfluid and Mott-insulating regions coexist side by side will be deduced. Investigations include (1) the spectroscopic signal from the superfluid regions of a coexisting system, (2) the collective modes of a three dimensional shell of superfluid, (3) the evolution of the system after its release from the trap, (4) the Josephson physics of concentric superfluid shells with an intervening Mott-insulating layer, and (5) critical properties of the quantum phase transition between superfluid and Mott insulator probed by new geometries of confinement. The proposed work exploits the unprecedented laboratory control over the strength of the interatomic interactions, strength of the optical lattice potential, and shape of the confining trap unique to the ultracold atomic system. Because of this reliance, close collaboration with an experimental group actively developing new probes of this system is an integral element of the research. The proposed work features involvement of undergraduates at Wellesley College in independent research on these topics throughout the project. Intellectual Merit: The control over microscopic parameters as well as macroscopic geometry present in trapped dilute gases allows the creation of nearly perfect superfluid and Mott-insulating systems, thereby improving our fundamental understanding of quantum behavior. The proposed work on superfluid shells will yield qualitative understanding of the expected behavior of superfluids in new geometries and quantitative predictions relevant to experiments on inhomogeneous systems. The possibility of using atomic systems to probe models of many-body condensed matter shows great promise and is a very active area of research. The extent to which the quantum phase transitions present in such models (e.g. the Bose-Hubbard model) can be realized in atomic systems is an open and important question. The proposed research will develop and model promising directions for future experiments in this area. Broader Impact: Theories of superfluid and Mott-insulating phases of bosons, as well as the quantum phase transition between them, have direct bearing on superconducting systems. Increased understanding of the Bose-Hubbard model can lead to insights into strongly-interacting superconducting systems and may consequently aid the development of new electronic devices. Further progress of quantum computing schemes based on ultracold bosons in optical lattices depends on a better understanding of the interplay of superfluid and Mott-insulating behavior in finite, trapped systems. The proposed work will be carried out at Wellesley College, a non-Ph.D.-granting women's college. The project will engage undergraduates in independent research projects, including senior theses and summer research, throughout its duration. The proposed undergraduate projects include analytical and numerical work on the interaction of a superfluid region with a time-varying magnetic field, hydrodynamic modes of the superfluid regions, and the expansion of superfluid systems after release from their traps. The undergraduate research component of the project will give underrepresented physics students (all women) at a small liberal arts college the opportunity to gain theoretical modeling skills and working knowledge of the emerging field of Bose-Einstein condensation in dilute gases.
