Fluctuation Phenomena and Measurement Theory in Mesoscopic Electronic and Optical Systems

这项理论研究有两个不同的重点领域：用于超灵敏检测和放大的纳米电子器件，以及通常尺寸为10-100微米的微腔谐振器和激光器。该项目的电子学方面将分析介观探测器实现量子限制检测的条件，这是指在不确定原则允许的情况下，对被测量子系统进行反向作用最小程度的测量。这样的问题在量子信息物理学中是相关的，在量子信息物理学中，被测量的量子系统将是一个量子比特，探测器是读出设备。由于零点起伏的存在，同样的条件决定了与充当放大器的任何量子系统相关的最小噪声。早期对没有电子-电子相互作用的介观散射探测器的分析工作发现了一个达到量子极限的简单条件，该条件可以用信息来表示-理论上：不应该有关于被测系统的信息印在探测器的输入变量中，而不是通过测量输出变量来提取。在当前的项目中，将分析相互作用的探测器，特别是存在退相的介观散射探测器(共振隧穿结构)和电荷简并点附近的半导体量子点的量子极限条件。人们希望，一般信息论原理也将被开发出来，以定性地理解更广泛类别的量子放大器中检测量子极限的方法，如金属和超导单电子晶体管以及超导量子干涉设备。该项目的光学方面涉及介质微腔谐振器和激光，由于它们的形状不对称，会产生复杂的、至少部分是混沌的光线动力学。尽管存在光线混沌，但这种谐振器具有定向发射的高Q共振性，与标准的圆形对称回音廊谐振器相比，它们在集成光学器件中具有潜在的应用价值。该项目将分析由于光线混沌的影响，这种高Q共振所产生的瞬逝泄漏速率(光子隧穿)的预测增强。它还将分析锁模行为，这种行为预计会发生在这种谐振器的非线性区域，特别是稳定轨道多重态的情况，可以通过解析计算。为了了解模式竞争和这种激光器与微柱激光器相比在输出功率方面的巨大增长，将发展一种更普遍的关于这种复杂谐振腔中的激光的理论。这种谐振器和激光器的光子统计数据预计将与传统激光器截然不同，并将在这个项目中进行详细研究，目的是提出新的和有趣的实验。这两个重点研究领域都对当前的科学和技术产生了更广泛的影响。量子放大器的性质在量子信息物理和量子计算领域具有重要意义。众所周知，量子信息处理器预计将具有革命性的特性，例如用于解码的因式分解算法的指数加速。固体超导量子比特是现实的，操纵它们并读出它们的测量设备正在全世界范围内开发；这将量子测量理论的抽象主题带入了纳米结构物理的现实世界。这项研究解决了这一领域的几个重要问题。光学领域涉及到当前技术感兴趣的几个问题。首先，它涉及用于通信应用的集成光学技术的发展；其次，它涉及新型蓝光和紫外光半导体光源的发展，这将对光刻、传感、显示和数据存储应用具有重要意义。这项理论研究有两个不同的重点领域：用于超灵敏检测和放大的纳米电子器件，以及通常尺寸为10-100微米的微腔谐振器和激光器。对于这两个主题，这项研究将基础研究与可能的技术应用结合在一起。除了研究的基本性质外，技术应用还涉及量子信息系统和用于先进计算机的新型光源。研究生和博士后助理都将参与该项目。

This theoretical research has two different focus areas: nanoelectronic devices for ultrasensitive detection and amplification, and microcavity resonators and lasers, typically on the size scale of 10-100 microns.The electronic aspect of the project will analyze the conditions under which a mesoscopic detector achieves quantum-limited detection, which refers to a measurement with the minimum degree of backaction on the measured quantum system allowed by the uncertainty principle. Such questions are of relevance in quantum information physics where the measured quantum system would be a quantum bit and the detector is the read-out device. The same condition determines the minimum noise associated with any quantum system that acts as an amplifier due to the presence of zero point fluctuations. Earlier work analyzing mesoscopic scattering detectors without electron-electron interactions found a simple condition for reaching the quantum limit which can be expressed information-theoretically: There should be no information about the measured system imprinted in the input variable to the detector which is not extracted by measuring the output variable. In the current project the quantum limit condition will be analyzed for interacting detectors, specifically mesoscopic scattering detectors (resonant tunneling structures) in the presence of dephasing, and semiconducting quantum dots near the charge degeneracy points. It is hoped that general information-theoretic principles will also be developed to understand qualitatively the approach to the quantum limit of detection in wider classes of quantum amplifiers such as metallic and superconducting single-electron transistors and superconducting quantum interference devices.The optics aspect of the project treats dielectric microcavity resonators and lasers, which, due to their asymmetric shape, generate complex, and at least partially chaotic, ray dynamics. Despite the presence of ray chaos, such resonators have high-Q resonances with directional emission, making them potentially useful for integrated optical devices when compared to standard whispering gallery resonators with circular symmetry. The project will analyze the predicted enhancement of the rate of evanescent leakage (tunneling of photons) out of such high-Q resonances due to the effect of ray chaos. It will also analyze the mode-locking behavior, which is expected to occur in the non-linear regime of such resonators, specifically focusing on the case of stable orbit multiplets which can be calculated analytically. A more general theory of lasing in such complex resonators will be developed with the aim of understanding mode competition and the enormous increase in output power such lasers display in comparison to microcylinder lasers. The photon statistics of such resonators and lasers is predicted to be very different from conventional lasers and will be studied in detail during this project with the goal of proposing novel and interesting experiments.Both of these focus areas of research have a broader impact on current science and technology. The properties of quantum amplifiers have become of great importance in the field of quantum information physics and quantum computation. As is now well known, quantum information processors are predicted to have revolutionary properties such as an exponential speed-up of factoring algorithms for decoding. Solid-state superconducting qubits are a reality and the measuring devices to manipulate them and read them out are being developed worldwide; this has brought the abstract topic of quantum measurement theory into the real world of the physics of nanostructures. This research addresses several important questions in this field.The optics area relates to several problems of current technological interest. First, it relates to the development of integrated optical technology for communication applications; and second it relates to the development of novel blue and ultraviolet semiconductor light sources which will be important for lithographic, sensing, display and data storage applications. Three inventions relating to these areas have been patented based on earlier stages of this research.%%% This theoretical research has two different focus areas: nanoelectronic devices for ultrasensitive detection and amplification, and microcavity resonators and lasers, typically on the size scale of 10-100 microns. With both topics, the research blends fundamental research with possible technological applications. Besides the fundamental nature of the research, the technological applications touch on quantum information systems and novel light sources for application in advanced computers. Both graduate students and postdoctoral associates will participate in the project.***