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Supersolid edge and bulk phases of a dipolar quantum gas in a box

We investigate the novel density distributions acquired by a dipolar Bose-Einstein condensed gas confined in a box potential, with special focus on the effects of supersolidity. Differently from the case of harmonic trapping, the ground state density reveals a strong depletion in the bulk region and an accumulation of atoms near the walls, well separated from the bulk, as a consequence of the competition between the attractive and the repulsive nature of the dipolar force. In a quasi two-dimensional geometry characterized by cylindrical box trapping, we observe the emergence of a ring-like configuration near the boundary of the box, reveling peculiar supersolid and crystal effects in a useful range of parameters. In the case of square box trapping the density oscillations along the edges, caused by the enhanced accumulation of atoms near the vertices, exhibit interesting analogies with the case of box trapped one dimensional configurations. For sufficiently large values of the atom number also the bulk region can exhibit supersolidity, the resulting geometry reflecting the symmetry of the confining potential even for large systems.