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

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