Quantum toolbox for cavity quantum electrodynamics

This Thesis describes a custom-made cavity quantum electrodynamics (QED) toolbox for a quantum dot (QD) emitter in an optical micropillar. The toolbox has been developed using MATLAB and it allows using either a full cavity-QED model or an effective adiabatic Hamiltonian to work only with the QD subspace. The toolbox simulates output intensities, first- and second-order correlations, and flux spectral densities both in continuous and pulsed wave regime. The results show that the adiabatic model reduces the computational cost in comparison to the full model, and allows performing accurate quantum optics simulations in the weak coupling regime between the QD and the cavity. For the approximation to yield satisfactory results, the cavity must decay at a faster timescale than the other subsystems, including the QD dynamics and the incoming field: the Rabi frequency of the QD must be much slower than the cavity damping rate, whereas, for the incoming field, its evolution must be slow compared to the photon lifetime in the cavity. This work also finds applications in the more general context of excited dipoles in 1-D photonic crystal waveguides and nanocavities, and it can be generalized to more complex and realistic systems. This includes the description of anisotropic neutral quantum dots, described by 3-level systems, or charged quantum dots with a spin degree of freedom, modeled by 4-level systems, taking into account the polarization degree of freedom for the cavity and input/output fields.