# Observation of universal non-Gaussian statistics of the order parameter across a continuous phase transition

## TL;DR

This study experimentally observes universal non-Gaussian fluctuations of the order parameter in a continuous phase transition of an interacting Bose gas, revealing critical scaling and challenging traditional homogeneous models.

## Contribution

It provides the first direct measurement of non-Gaussian order parameter statistics and demonstrates their universality and critical scaling across a phase transition.

## Key findings

- Non-Gaussian order parameter fluctuations are observed near the transition.
- Fluctuations exhibit universal oscillations in high-order cumulants.
- Effective potential analysis reveals a non-trivial minimum in the superfluid phase.

## Abstract

Second-order phase transitions are characterised by critical scaling and universality. The singular behaviour of thermodynamic quantities at the transition, in particular, is determined by critical exponents of the universality class of the transition. However, critical properties are also characterised by the probability distribution of order parameter across the transition, where non-Gaussian statistics are expected, but remain largely unexplored. Here, making use of single-atom-resolved detection in momentum space, we measure the full probability distribution of the amplitude of the order parameter across a continuous phase transition in an interacting lattice Bose gas. We find that fluctuations are captured by an effective potential -- reconstructed from the measured probability distribution by analogy with Landau theory -- displaying a non-trivial minimum in the superfluid (ordered) phase, which vanishes at the transition point. Additionally, we observe non-Gaussian statistics of the order parameter near the transition, distinguished by non-zero and oscillating high-order cumulants. We provide direct experimental evidence that these oscillations are universal, and show numerically that they exhibit critical scaling. Our experiments are conducted in inhomogeneous systems, challenging the conventional understanding of criticality, which is primarily based on homogeneous models. Our results underscore the crucial role of order parameter statistics in probing critical phenomena and universality.