Theoretical studies of nanoscopic systems

我工作的总体目标是开发新的方法或见解，帮助理解当前感兴趣的主题中的物理现象。有了这笔赠款，我将继续发展(1)有限周期系统的新方法和途径，以及(2)半经典近似。这些应用是研究(A)半导体纳米结构中的电子，(B)光子晶体，和(C)冷原子。我们已经大大改进的方法之一是耦合波理论(CWT)，最初由Kogelnik开发用于全息图。他的版本只有一个透射波和一个反射波，但很少是可靠的。我们设计了一种半经典连续小波变换，它结合了传统连续小波变换的简单性和精确计算的准确性。它产生对光子晶体的频带宽度和其他性质的解析估计。目前，该理论需要一些扩展，以涵盖全内反射的情况，我们正在研究这一点。第二个应用领域是冷原子。在过去的十年里，物理学家已经学会了如何通过将原子冷却到极低的温度来创造一种新的物质状态。这被称为玻色凝聚态。从本质上讲，这些原子失去了身份，表现为单一的量子流体。即使它们从陷阱中释放出来，一束相干的原子也会出现，与普通光相比，它与激光有一些相似之处。我们的目标之一是为这种光束设计一种速度滤光器，以便更好地控制这种新的物质状态。在过去的六年里，我们已经学会了如何为半导体中的电子制造这样的过滤器，我们希望将其应用于原子。

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.