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。这项研究有两个组成部分。首先，光散射被用作测量原子系统性质的方法。在真正的量子水平上，光到达探测器时是作为单个光子计数的。对模型系统中的光散射进行精确模拟，然后利用模拟结果开发统计技术来提取系统的信息，即使只有很少的孤立光子计数。在一个相关的问题中，为了使量子力学信息在光和原子集合之间完全传递，理想的原子样品应该是致密和冷的。光在冷致密气体中传播的大量数值模拟表明，目前对这种系统的理解是有缺陷的。将制定新的原则来管理这一情况。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。用双阱势中的玻色-爱因斯坦凝聚体作为研究材料样品光散射的一般例子。光被假定是用能够单光子分辨率的探测器来监测的。利用量子轨迹模拟精确地解决了光-物质-探测器联合系统的量子力学问题。贝叶斯推理是一种从观察到的光子计数中提取有关原子信息的最大可能量的方法。当前的目标是为量子系统的监测和反馈控制设计重复和相关的光子计数测量。更一般地说，光散射不仅是监测双井凝聚体的方法，而且可能是监测大多数连续观测的原子系统的方法。为了达到单量子水平的分辨率，样品必须具有光学厚度。有利于量子相干的潜在高密度和低温将使原子对光的协同响应成为可能。利用经典电动力学模拟光在点偶极介质中的传播将研究协同光原子相互作用。目的是找出协同响应如何改变光散射实验结果。

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.