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Motivated by recent experiments, we theoretically study a gas of atomicbosons confined in an elliptical harmonic trap; forming a quasi-two-dimensionalatomic Bose-Einstein condensate subject to a density-dependent gauge potentialwhich realises an effective density-angular-momentum coupling. We present exactThomas-Fermi solutions which allows us to identify the stable regimes of thefull parameter space of the model. Accompanying numerical simulations revealthe effect of the interplay of the rigid body and density-angular-momentumcoupling for the elliptically confined condensate. By varying the strength ofthe gauge potential and trap anisotropy we explore how the superfluid stateemerges in different experimentally accessible geometries, while for largerotation strengths dense vortex lattices and concentric vortex ringarrangements are obtained.

Few-to-many vortex states of density-angular-momentum coupled Bose-Einstein condensates