El Mandouh, Mohamed2022-01-182022-01-182022-01-182021-12-10http://hdl.handle.net/10012/17912In this thesis we introduce the simplest model of a two–level system coupled to a single mode of an optical cavity, called the Jaynes-Cummings model. This model is then extended to an ensemble of identical two-level systems and is studied in more detail, also known as the Tavis-Cummings model. This model is intractable, but we show that by a clever but simple choice of basis one can reduce the dimensionality of the Tavis-Cumming system. We then demonstrate the effectiveness of this reduction by calculating interesting statistics of the system, and simulating large ensembles of two–level systems which were not practical before. Finally, we examine some dynamics of the Tavis-Cummings model in the presence of photon losses, and introduce a method for population transfer by modulating TLS-cavity interaction strength.enquantum opticsquantum informationcavity qedspin-cavityMaster Thesis