Supersolid-like square- and triangular-lattice crystallization of dipolar droplets in a box trap

Using a beyond-mean-field model including a Lee-Huang-Yang-type interaction, we demonstrate a supersolid-like spatially-periodic square- and triangular-lattice crystallization of droplets in a polarized dipolar condensate confined by an appropriate three-dimensional (3D) box trap. In this paper we consider a rectangular box (cuboid) trap, a square box (cuboid with two equal sides) trap, a cylindrical box trap and a hexagonal box (hexagonal prism) trap. The droplet lattice is always formed in the $x$-$y$ plane perpendicular to the polarization $z$ direction of dipolar atoms. In contrast to a harmonic trap, the box traps allow the formation of a large clean supersolid-like spatially-periodic crystallization in free space without any distortion. Moreover, a droplet lattice can be formed in a 3D box trap with a significantly reduced number of atoms than in a harmonic trap, which could facilitate the experimental observation of droplet lattice in a box trap. With present know-how such a supersolid-like crystallization of dipolar droplets in a 3D box trap can be realized in a laboratory thus allowing the study of a large periodic lattice of dipolar droplets in free space bounded by rigid walls.