An effective Mexican-hat band for ultracold atoms in a time-modulated optical lattice

Abstract

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 since 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. This thesis describes the realization and characterization of a Mexican-hat band generated with an amplitude modulated double-well optical lattice, where the effective static Hamiltonian giving rise to the moat band can be understood using a Floquet analysis. Since our experimental approach allowed for the coherent preparation of Bose condensed (BEC) clouds in this hybridized ring-shaped band, we also examined the stability of BEC dressed states in the presence of the moatlike dispersion, which we modeled using a linear stability analysis of the mean-field solutions to the driven Gross-Pitaevskii equation. Our observations are in fair agreement with the theoretical prediction that a single-momentum BEC at the minimum of a moatlike band (which is a competing bosonic ground state in several interesting phase diagrams associated with ring-shaped dispersions) lies at the edge of an instability region and should, hence, be unstable in any realistic scenario. Motivated by the necessity to understand and mitigate dissipative mechanisms that curtail the applicability of Floquet engineering in bosonic optical lattices, this thesis also discusses a framework to model drive-induced instabilities in condensates subject to time-modulated lattice potentials. A linear stability analysis, similar to the one employed to model the BEC stability in the presence of the effective moat band, leads to parametric instabilities. Unlike the moat-induced instability, which is inherent to the Floquet generated effective static band, these instabilities are coupled via the modulation, and depend on the details of the modulation parameters. The predictions of this model are contrasted with the results from an experimental investigation of the condensate depletion in shaken optical lattices, as a function of the modulation parameters, from which we assess the validity and limitations of the theory.