# Detecting One-Dimensional Dipolar Bosonic Crystal Orders via Full Distribution Functions

## TL;DR

This paper investigates various crystal order states of dipolar bosons in optical lattices, analyzing their transitions and how to observe these states through full distribution functions derived from simulated imaging.

## Contribution

It introduces a method to identify crystal orders in dipolar bosonic systems using full distribution functions from simulated single-shot images.

## Key findings

- Multiple crystal states emerge depending on interaction strength and lattice depth.
- Transitions between different crystal orders are characterized and mapped.
- Full distribution functions effectively reveal the underlying crystal structures.

## Abstract

We explore the groundstates of a few dipolar bosons in optical lattices with incommensurate filling. The competition of kinetic, potential, and interaction energies leads to the emergence of a variety of crystal state orders with characteristic one- and two-body densities. We probe the transitions between these orders and construct the emergent state diagram as a function of the dipolar interaction strength and the lattice depth. We show that the crystal state orders can be observed using the full distribution functions of the particle number extracted from simulated single-shot images.