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.
