Strong correlation physics in ultra cold atomic gases

I plan to study theoretically some fundamental questions in physics, which involves new forms of matter. Very recent experiments have created a new material at record low temperatures, never seen before in the Universe. Unlike materials made by labs all over the world, most aspects of this material is under the direct control of the experimentalists, and can even be changed into something completely different after the material was created. In everyday materials and materials created in labs, the atoms, electrons and ions interact amongst themselves: this leads to the atoms having a preferred distance between each other, and this dictates what the structure and properties the material has. In this new material however, the atoms are trapped at extremely low temperatures into a regular pattern: this pattern is created by a set of lasers that experimentalists can control. For example, it is easy to make the atom stay at rest, rather than hop around on this regular pattern, just by changing the intensity of the laser. Or we can change the types and number of atoms trapped in this pattern; even the interactions between the atoms can be changed. Furthermore, there are no dirt nor defects in this artificial material, unlike in real solids. All this has to happen at extremely low temperatures, so that the atoms cannot move around too much. Then, atoms obey the laws of quantum mechanics: the basic laws of physics at small distances and low temperatures, which say that particles like atoms also behave like waves (as in light waves). Thus, much richer and stranger phenomena can occur in this new artificial material.With this ease and level of control, it becomes possible to study a whole range of fundamental quantum phenomena that are difficult--or impossible--to study in normal materials. Working in parallel with experimentalists, I plan to study what happens to the trapped cold atoms, when there are strong interactions between the atoms. For example, when atoms are forced to stay in a line, they cannot avoid each other (just as in a traffic jam!). When one atom moves a bit, this affects its neighbours, which in turn affects their neighbours, and so on. The end result is that all of the atoms participate together to form a global pattern of motion: the individuality of the atoms are lost altogether. Physicists have developed sophisticated mathematical methods to treat such behaviour in real solids. I plan to use such techniques (and perhaps invent some new ones) to see how new exotic forms of matter can develop, when we change various aspects of this new material . For example, if we put in more than one type of atoms, and there is attraction between the different types, but repulsion between the same type, then one atom of each type may clump together to form a new particle, and these new particles may in turn form a new global pattern. Furthermore, experimentalists can follow in time how changes occur, which is rather hard to do in normal materials. Thus, I plan to study how the new forms of matter may change from one form to another, when we slowly or suddenly change some aspects of the material . In my proposed work, I will calculate properties of these new forms of matter, to compare with experiments. This in turn may suggest new experiments to help us understand the basic principles underlying these new forms of matter. Furthermore, these new principles may benefit the study of strong interactions in more normal materials. Finally, it has been proposed that this sort of artificial material can be used for quantum computing. This takes advantage of the quantum wave-like nature of atoms to process information in parallel, to hugely increase computing power. My work will provide the basic understanding needed for this potentially revolutionary application.