Rydberg crystallization detection by statistical means

TL;DR

This paper demonstrates how to detect a phase transition to Rydberg crystallization in an atomic ensemble using statistical analysis of the number distribution of Rydberg atoms, bypassing the need for correlation measurements.

Contribution

It introduces a method to identify the Rydberg crystal phase transition solely through the probability distribution of Rydberg atom counts, simplifying experimental detection.

Findings

Critical interaction strength identified for phase transition

Phase transition detectable via probability distribution $P(M)$

Numerical simulation confirms the method's effectiveness

Abstract

We investigate an ensemble of atoms which can be excited into a Rydberg state. Using a disordered quantum Ising model, we perform a numerical simulation of the experimental procedure and calculate the probability distribution function $P(M)$ to create a certain number of Rydberg atoms $M$, as well as their pair correlation function. Using the latter, we identify the critical interaction strength above which the system undergoes a phase transition to a Rydberg crystal. We then show that this phase transition can be detected using $P(M)$ alone.