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

TL;DR

This paper demonstrates the formation of supersolid-like droplet lattices with square, honeycomb, and triangular geometries in a dipolar condensate, revealing universal energy scaling and potential for experimental observation.

Contribution

It introduces the possibility of multiple droplet lattice geometries in dipolar condensates using a beyond-mean-field model, highlighting their energetic probabilities and degeneracies.

Findings

Square-lattice, honeycomb, and triangular droplet crystallizations are energetically probable.

Energy scales as E ~ N^{0.4} for all three lattice types.

Square-lattice with central site occupied is a promising candidate for experiments.

Abstract

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 interactions and the same trap frequencies. The energy $E$ of all three crystallization as a function of number $N$ of atoms satisfy the universal scaling relation $E\sim N^{0.4}$ 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 quasi-degenerate 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.