Utilizing electromagnetically induced transparency (EIT) makes an otherwise opaque ensemble of alkali atoms transparent to resonant light. A collective excitation, known as a dark state polariton, is created in the process. It is a superposition of the state of light and the state of atoms. The ratio between both components governs the polariton's group velocity, which we can regulate with a coherent control light field. In this way the quantum state of the incident light is coherently transcribed into a collective state of atoms that can be reread some time later. EIT is a very promising approach to storing light. In this thesis we model the main processes of an EIT-based quantum memory on alkali atoms with an emphasis on the state analysis of individual atoms and we then numerically simulate it. We compare the simulation results to those of laboratory experiments. It proved important to consider dissipative processes for which we employ the open quantum system formalism.
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