Theory of Ultracold Matter

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Broadly speaking, my research deals with dilute atomic gases confined in space and cooled to extremely low temperatures. This combination of conditions results in remarkable physical properties that have captured the attention of physicists around the world. One example of this is the phenomenon of Bose-Einstein condensation (BEC) in which bosonic atoms condense into the lowest available quantum state, the condensate. In this novel state of matter, the atoms act coherently, and exhibit quantum behaviour on scales approaching macroscopic dimensions. One of the more dramatic consequences of BEC is superfluidity: the possibility of flow without resistance or dissipation. Superfluidity underlies much of the research described in this proposal. Perhaps the simplest example is the undamped oscillatory motion of a condensate at zero temperature. However, at elevated temperatures, the oscillations are damped as a result of the interaction of the condensate with the thermal excitations, the so-called thermal cloud. The theory we have developed accounts for this behaviour. Similar dissipative effects are also observed when considering the dynamics of a vortex - the quantized circulation of atoms around a central core. If such a vortex were to be created in a trapped Bose gas, it would spiral out towards the edge of the gas as a result of its interaction with the thermal cloud, and would eventually disappear. This too is described by the theory we have developed. One of the fascinating aspects of cold atoms is that they can be manipulated in various ways. For example, if a standing light wave is imposed, the atoms effectively find themselves in a periodic potential which we call an optical lattice. Here, too, superfluidity exists. However, if the optical lattice is deepened, the atoms make a transition to an insulating state, a completely different quantum phase. One direction of my research concerns the quantum phase transitions that occur when a mixture of bosonic atoms resides in the lattice. The ultimate objective of all this work is to enhance our ability to further control and manipulate cold trapped atoms.