Supersolid-like square- and honeycomb-lattice crystallization of droplets in a dipolar condensate

We demonstrate a supersolid-like spatially periodic square- and honeycomb-lattice crystallization of droplets in addition to the commonly studied triangular-lattice crystallization in a cylindrically symmetric quasi-two-dimensional trapped dipolar condensate, using a beyond-mean-field model including a quantum-fluctuation Lee-Huang-Yang-type interaction. These three types of crystallization of droplets may appear for the same atomic interaction and the same trap frequencies. The energies E of all three crystallizations as a function of the number N of atoms satisfy the universal scaling relation E similar to N-0.4, indicating that all three arrangements of the droplets should be energetically probable processes of phenomenological interest. The state of square-lattice crystallization may have the central site occupied or unoccupied, corresponding to a parity-symmetric or parity-antisymmetric state, respectively. The state of square-lattice crystallization with the occupied central site and the state of triangular-lattice crystallization, for a fixed N, constitute two quasidegenerate ground states, while the other states are low-lying excited states. This makes the square-lattice crystallization with the occupied central site an ideal candidate for future experimental observation.