Hiperbolik metamalzemelerde kuantum kontrolu

In this thesis, we study atom-photon interactions on quantum level, inside Hyperbolic Metamaterials (HMM). First, the macroscopic Maxwell equations are examined in the light of Green's dyadics. Second, this formalism, combined with Drude-Lorentz model of materials, is used to infer the existence of \textit{Surface Plasmon Polariton} excitations and hyperbolic dispersion in layered HMM by means of \textit{Effective Medium Approximation}. Third, many-body polaritonic Hamiltonian is diagonalized, and, the medium assisted field is found to be dependent on classical Green's tensor, while no reference to microscopic model is needed. Last, as a test case, QED in complex media based on classical Green's tensor formalism is used to calculate single photon excitation probability for an atom embedded in l-HMM system (Ag/Ti$0_{2}$ layers), when it is shed by a time-inverted, conical, single photon pulse. High excitation probabilities are found, yet problem of outcoupling leaves the implementation impractical.