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It is now well established that the stability of aligned dipolar Bose gasescan be tuned by varying the aspect ratio of the external harmonic confinement.This paper extends this idea and demonstrates that a Gaussian barrier along thestrong confinement direction can be employed to tune both the structuralproperties and the dynamical stability of an oblate dipolar Bose gas alignedalong the strong confinement direction. In particular, our theoreticalmean-field analysis predicts the existence of instability islands immersed inotherwise stable regions of the phase diagram. Dynamical studies indicate thatthese instability islands, which can be probed experimentally with present-daytechnology, are associated with the going soft of a Bogoliubov--de Gennesexcitation frequency with radial breathing mode character. Furthermore, we finddynamically stable ground state densities with ripple-like oscillations alongthe radial direction. These structured ground states exist in the vicinity of adynamical radial roton-like instability.

Tuning the structural and dynamical properties of a dipolar Bose-Einstein condensate: Ripples and instability islands