Dissertation Committee Chair: Norbert Linke
Committee:
Trey Porto
Ian B. Spielman
Wendell T. Hill
Yanne K. Chembo
Abstract: Parametric amplification of field modes is a prevalent phenomenon in pumped nonlinear systems. This mechanism is expected to interfere with the stability of low-energy states in periodically modulated Bose-Einstein condensates, which are described by a driven nonlinear equation. Motivated by the necessity to understand and mitigate dissipative mechanisms that curtail the applicability of Floquet engineering in bosonic optical lattices, the first part of this thesis outlines a framework that models the behavior of drive-induced instabilities in condensates subject to time-modulated lattice potentials. The predictions of this model are then contrasted with the results from an experimental investigation of the condensate depletion in shaken optical lattices, from which we assess the validity and limitations of our theory.
Ring-shaped energy bands, where a continuum of degenerate minima lie along a closed loop in momentum space, are of interest in ultracold fermionic and bosonic gases as the associated singularity in the density of states is expected to stabilize unconventional phases of matter. These moatlike dispersions are also linked to enhanced properties in solid-state materials. The second part of the thesis describes the realization of a Floquet-engineered Mexican-hat band using an amplitude modulated double-well optical lattice. Since our experimental approach allowed for the coherent preparation of condensed states in this hybridized Mexican-hat band, we also examined the stability of BEC states in the presence of this dispersion using the theoretical framework described in the first part of the thesis. Our observations are in fair agreement with the theoretical prediction that a BEC at the minimum of a moat dispersion lies at the edge of an instability region and should, hence, be unstable in any realistic scenario.
Location: PSC 2136