Maintaining supersolidity in one and two dimensions

TL;DR

This paper explores how trap geometry influences the formation of supersolid states in three-dimensional dipolar Bose-Einstein condensates, demonstrating the potential for stable two-dimensional supersolids and developing a variational model for their analysis.

Contribution

It introduces a variational model to study droplet arrays in dipolar BECs, showing conditions for stable 2D supersolids and outlining experimental creation of exotic states.

Findings

Supersolidity is stable in one-dimensional arrays.

Two-dimensional supersolids are feasible with proper atom number scaling.

The variational model agrees well with numerical simulations.

Abstract

We theoretically investigate supersolidity in three-dimensional dipolar Bose-Einstein condensates. We focus on the role of trap geometry in determining the dimensionality of the resulting droplet arrays, which range from one-dimensional to zigzag, through to two-dimensional supersolids in circular traps. Supersolidity is well established in one-dimensional arrays, and may be just as favorable in two-dimensional arrays provided that one appropriately scales the atom number to the trap volume. We develop a tractable variational model--which we benchmark against full numerical simulations--and use it to study droplet crystals and their excitations. We also outline how exotic ring and stripe states may be created with experimentally-feasible parameters. Our work paves the way for future studies of two-dimensional dipolar supersolids in realistic settings.