School of Physics - Theses
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ItemThe Jaynes-Cummings-Hubbard model( 2011)This thesis comprises an intensive investigation of the Jaynes-Cummings-Hubbard (JCH)system. This Hamiltonian describes a system of coupled photonic cavities, each cavitycontains a single two-level system. This system is rich in the physics it contains. Thepresence of the two-level system provides a mechanism by which the photons may interactwith each other, providing an interesting array of non-linear phenomena. Using the meanfieldapproximation, the phase diagram of this system has been shown to display what areeffectively two different phases - a superfluid phase, and a Mott-insulator phase. In thisthesis we show that by using exact diagonalisation for a finite number of cavities, thereis a rich structure to the phases that goes beyond this dual division of phases. We alsogenerate phase diagrams that could be experimentally realised using an ion trap system.Investigating the time dependent properties of the one-dimensional JCH system, we obtainboth localised and delocalised behaviour, despite having only one excitation in the system.In certain limits the 1D JCH system approximates two Heisenberg spin chains. We findit is also possible in the one excitation, one-dimension time dependent case to activelycontrol the location of the excitation, by means of a potential, thus creating all standardcomponents of linear optics: we specifically investigate waveguides and beamsplitters. Finally,we investigate the use of matrix product states (MPS) to study the one-dimensionalJCH system in the time domain. MPS is used to show how two colliding excitations canshow the signature of photon blockade.