Frustrated colloidal ordering and fully packed loops in arrays of optical traps

TL;DR

This paper proposes a colloidal system in optical traps that models fully packed loops and related phases, providing a physical realization of complex loop models with potential applications in various experimental setups.

Contribution

It introduces a new colloidal system in honeycomb optical traps that realizes fully packed loop models and maps to Baxter's three-coloring problem, revealing diverse phases.

Findings

Identification of multiple phases including ordered, stripe, and disordered states.

Mapping of the system to Baxter's three-coloring problem.

Potential experimental implementations using ion traps, BEC vortices, or magnetic vortices.

Abstract

We propose that a system of colloidal particles interacting with a honeycomb array of optical traps that each contain three wells can be used to realize a fully packed loop model. One of the phases in this system can be mapped to Baxter's three-coloring problem, offering an easily accessible physical realization of this problem. As a function of temperature and interaction strength, we find a series of phases, including long range ordered loop or stripe states, stripes with sliding symmetries, random packed loop states, and disordered states in which the loops break apart. Our geometry could be constructed using ion trap arrays, BEC vortices in optical traps, or magnetic vortices in nanostructured superconductors.