The quantum jump method: photon statistics and macroscopic quantum jumps of two interacting atoms

We first use the quantum method to replicate the well-known results of a single atom relaxing, whilst demonstrating the intuitive picture it provides for dissipative dynamics. By use of individual "quantum trajectories", the method allows for simulation of systems inaccessible to ensemble treatments. This is shown by replicating resonance fluorescence, allowing us to concurrently demonstrate the method's facilitation of calculating photon statistics by the creation of discrete photon streams. To analyse these, we solidify the theoretical basis for, and implement, a computational method of calculating second-order coherence functions. A process by which to model interacting two-atom systems to allow for computation with the quantum jump method is then developed. Using this, we demonstrate cooperative effects leading to greatly modified emission spectra, before investigating the decoupling of states from dissipative and coherent interactions. Here, we find the novel insight provided by the quantum jump method both births and provides the tools with which to begin an investigation into the occurrence of macroscopic jumps and the formation of macroscopic dark periods in a system of two two-level dipole-dipole coupled atoms.