@Schloss2016; @Minguzzi2017], and in the Bose-Hubbard model [@Pinheiro2013; @Arwas2017; @Minguzzi2017b; @Minguzzi2018], which is naturally connected to the continuous model in the limit of tight trapping. Another recent related work has investigated the localization properties of a TG gas in a continuum version of the Aubry-Andre model (using a bi-chromatic lattice) [@Settino2017]. In this manuscript we explore the phase diagram from shallow to deep lattices for commensurate and incommensurate fillings and show how different phases can be characterized through the coherence and by direct observation of the momentum distribution. We also show that the dynamical response of the system to the driven lattice exhibits stick-slip motion and tunneling due to defect induced superfluidity.

The mansucript is organised as follows: In Section \[sec:model\] we describe the model we consider and in Section \[sec:statics\] we discuss how to characterise the different phases in the system through calculations of the coherence, the momentum distribution and the spatial auto-correlation function. In Section \[sec:driven\] we discuss both the time averaged and the instantaneous dynamics of the driven system and in Section \[sec:conclusions\] we conclude. Finally, in the Appendix we provide an in depth explanation of the dynamics in the different phases.

Basic Model {#sec:model}
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We 