Theoretical studies of nanoscopic systems

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The general aim of my work is to develop new methods or insights that aid in understanding physical phenomena on topics of current interest. With this grant I will continue the development of (1) new methods and approaches to finite periodic systems and (2) semi-classical approximations.  The applications are to  (a) electrons in semiconductor nanostructures, (b) photonic crystals, and (c) cold atoms.One of the methods which we have greatly improved is called Coupled Wave Theory (CWT), originally developed by Kogelnik for holograms. His version had just one transmitted wave and one reflected wave, but it is seldom reliable. We devised a semiclassical CWT which combines the simplicity of conventional CWT with the accuracy of exact calculations. It produces analytic estimates of the band widths and other properties of a photonic crystal. As it stands the theory needs some extension, to cover the case of total internal reflection, and we are working on that.A second area of application is to cold atoms. During the past ten years physicists have learned how to create a new state of matter by cooling atoms to extremely low temperature. This is called a Bose-condensed state. Essentially the atoms lose their identity and behave as a single quantum fluid.  If they are released from the trap, a coherent beam of atoms emerges with some similarity to laser light as opposed to ordinary light. One of our aims is to devise a velocity filter for such a beam, to gain better control over this new state of matter. In the past six years we have learned how to make such a filter for electrons in semiconductors and we hope to apply that to atoms.