Theory of ultracold matter

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This proposal concerns the subject of Bose-Einstein condensation (BEC) in trapped Bose gases. At ultra-low temperatures, a gas of bosonic atoms exhibits a kind of condensation in which most of the atoms fall into the lowest available quantum state. In this novel state of matter, the atoms act coherently, and exhibit quantum behaviour on scales approaching macroscopic dimensions. The implications are far-reaching and profound. Potential applications include atomic lasers, atomic lithography and quantum computing.     The proposed research can be broadly characterized as the theoretical study of the dynamics of these trapped gases at finite temperatures. Above absolute zero, the gas consists of a combination of the condensed phase, the condensate, and thermally excited atoms that constitute a thermal cloud. This system of atoms can undergo a variety of modes of oscillation that can be studied experimentally. The theoretical challenge is to provide a description of this behaviour that explains the observed mode frequencies and the rate at which the modes decay as a function of time.     Much of the interest in the subject stems from the fact that trapped gases can be manipulated in various ways. For example, the gas can be made to spin rapidly by rotating the confining potential. In this way, arrays of vortices can be generated. Part of the project will address the question of how these vortices are initially formed, and how the vortices finally arrange themselves in an ordered array.     Another way to manipulate the atoms is to simply shine light on them. If the light forms a standing wave, a periodic potential arises and the atoms effectively reside on a lattice. The theoretical tools we have at our disposal will allow us to explore the interesting dynamical behaviour of the atoms in this situation, especially at elevated temperatures when both a condensate and thermal cloud are present. The knowledge gained from such studies will extend even further our ability control atoms in these kinds of systems.