Fast rotating condensates in an asymmetric harmonic trap

We investigate the effect of the anisotropy of a harmonic trap on the behavior of a fast rotating Bose-Einstein condensate. Fast rotation is reached when the rotational velocity is close to the smallest trapping frequency, thereby deconfining the condensate in the corresponding direction. We characterize a regime of velocity and small anisotropy where the behavior is similar to the isotropic case: a triangular Abrikosov lattice of vortices, with an inverted parabola profile. Nevertheless, at sufficiently large velocity, we find that the ground state does not display vortices in the bulk. We show that the coarse-grained atomic density behaves like an inverted parabola with large radius in the deconfined direction and keeps a fixed profile given by a Gaussian in the other direction. The description is made within the lowest-Landau-level set of states, but using distorted complex coordinates.