Issues of Continuous Quantum Measurements and Feedback Control

这项工作是关于量子力学系统中测量的理论物理。这项研究包括两个部分。首先，光散射被用作测量原子系统性质的一种方法。在真正的量子水平上，随着单个光子的计数，光到达探测器。模型系统中的光散射被精确地模拟，然后模拟结果将被用来开发统计技术来提取关于系统的信息，即使只有几个孤立的光子计数。在一个相关的问题中，为了能够在光和原子集合之间完全传输量子力学信息，原子样本理想情况下应该是致密和寒冷的。对光在冷密气体中传播的大量数值模拟表明，目前对这类系统的理解是有缺陷的。将制定新的原则来管理这一案件。这项工作是纯粹的基础研究，最终目的是帮助建立未来量子技术的科学基础。以双势阱中的玻色-爱因斯坦凝聚体为例，研究材料样品的光散射。假设使用能够单光子分辨率的探测器来监测光。利用量子轨道模拟，精确求解了光-物质-探测器联合系统的量子力学。发展了一种贝叶斯推理，作为一种从观测到的光子计数中提取关于原子的最大可能信息量的方法。目前的目标是设计重复的和相关的光子计数测量，用于监测和反馈控制量子系统。更广泛地说，光散射是一种方法，不仅可以监测双势垒凝聚体，而且可能还可以监测连续观测下的大多数原子系统。要达到单量子级别的分辨率，样品必须具有光学厚度。潜在的高密度和有利于量子相干的低温将带来原子对光的合作响应的可能性。利用经典电动力学方法模拟光在点偶极子介质中的传输，研究光与原子的相互作用。其目的是找出合作反应如何改变光散射实验的结果。

This work is on the theoretical physics of measurements in quantum mechanical systems. There are two components to this research. First, light scattering is used as a method to measure the properties of an atomic system. At the true quantum level, light arrives at a detector as individual photon counts. Light scattering in a model system is simulated exactly, and then simulation results will be used to develop statistical techniques to extract information about the system even if there are only a few isolated photon counts. In a related issue, to enable full transfer of quantum mechanical information between light and a collection of atoms, the atomic sample should ideally be dense and cold. Massive numerical simulations of light propagation in a cold dense gas have shown that the current understanding of such systems is flawed. New principles will be formulated that govern this case. This work is pure basic research, and the final aim is to help build the science basis for future quantum technologies.A Bose-Einstein condensate in a double-well potential is used as a generic example to study light scattering from a material sample. The light is assumed to be monitored using detectors capable of single-photon resolution. The quantum mechanics of the joint light-matter-detector system is solved exactly using quantum trajectory simulations. A Bayesian inference is developed as a method to extract the maximum possible amount of information about the atoms from the observed photon counts. The immediate aim is to devise repeated and correlated photon counting measurements for monitoring and feedback control of quantum systems. More generally, light scattering is the method to monitor not only double-well condensates, but also probably the majority of atomic systems under continuous observation. To reach a resolution at the level of a single quantum, the sample has to be optically thick. The potentially high densities and the low temperatures beneficial for quantum coherence will bring in the possibility of cooperative response of the atoms to light. Cooperative light-atom interaction using classical-electrodynamics simulations of light propagation in a medium of point dipoles will be studied. The objective is to find out how the cooperative response alters the results of light scattering experiments.