Dewan, AftaabDriven systems have been of particular interest in the field of ultracold atomic gases. Theprecise control and relative purity allows for construction of many novel Hamiltonians. One such system is the ‘breathing’ lattice, where both the frequency and amplitude is modulated in time, much like an accordion. We present the results of a phenomenological investigation of a proposed experiment, one where we apply a two-frequency breathing lattice to an atomic system. The results are surprising, as they indicate the possibility of a phase-dependent transition between nearest-neighbour and beyond nearest-neighbour interactions.enDissertationAtomic physicsMolecular physicsOpticsBECDriven SystemFloquetTheoreticalTime-DependentTunneling