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Quantum Dynamics of Condensates, Atomtronic Systems, and Photon Fluids
In the first part of this thesis, the dynamics of interacting ultracold bosonic atomic gases trapped in an optical lattice are examined from the perspective of nonlinear band theory. The mean-field Gross-Pitaevskii equation is used to model the Bloch waves for weakly and strongly interacting gases with a Kronig-Penney potential, i.e. a lattice of delta functions. The appearance of looped swallowtail structures in the energy bands is a highly nonlinear effect. These swallowtails are then related to period-doubled Bloch states by examining a two-color lattice. A stability analysis shows that the effective mass of the atoms is a main feature describing the stability properties of the system.
In the second part of this thesis, the dynamics of atomtronic systems, ultracold atom analogs of semiconductor devices, is examined. Atomtronic systems are first presented from the perspective of the fundamental building blocks needed to create a circuit. An atomtronic battery creates a chemical potential difference. An optical lattice can play the role of a wire in electronics. The combination of N-type and P-type semiconductors lead to an atomtronic diode. The physics behind this device are due to a transition between superfluid and insulating states for the atomic device, contrary to the workings of an electronic diode. An atomtronic transistor is also presented.
In the third part of this thesis, the method of evaporative cooling is applied to a photon fluid confined to a nonlinear Fabry-Perot cavity. A photon fluid is a collection of interacting photons that exhibit fluidic hydrodynamic properties. The effects of photon recombination due to atom-mediated interactions and evaporation with an energy dependent reflectivity of the cavity lead to Bose amplified stimulated emission into the lowest energy mode.