# Critical Opalescence across the Doping Driven Mott Transition in Optical Lattices of Ultracold Atoms

## TL;DR

This paper investigates critical opalescence in ultracold atom optical lattices, revealing fluctuation behavior near a phase transition in the fermionic Hubbard model, with implications for understanding high-temperature superconductivity.

## Contribution

It provides a detailed theoretical analysis of density fluctuations across the Mott transition, highlighting the role of nonlocal correlations and predicting observable signatures in ultracold atom experiments.

## Key findings

- Density fluctuations increase near the phase transition at low temperatures.
- Nonlocal contributions to fluctuations decrease unexpectedly as criticality approaches.
- Theoretical results align with experimental data in the high-temperature regime.

## Abstract

Phase transitions and their associated crossovers are imprinted in the behavior of fluctuations. Motivated by recent experiments on ultracold atoms in optical lattices, we compute the thermodynamic density fluctuations $\delta N^2$ of the two-dimensional fermionic Hubbard model with plaquette cellular dynamical mean-field theory. To understand the length scale of these fluctuations, we separate the local from the nonlocal contributions to $\delta N^2$. We determine the effects of particle statistics, interaction strength $U$, temperature $T$ and density $n$. At high temperature, our theoretical framework reproduces the experimental observations in the doping-driven crossover regime between metal and Mott insulator. At low temperature, there is an increase of thermodynamic density fluctuations, analog to critical opalescence, accompanied by a surprising reduction of the absolute value of their nonlocal contributions. This is a precursory sign of an underlying phase transition between a pseudogap phase and a metallic phase in doped Mott insulators, which should play an important role in the cuprate high-temperature superconductors. Predictions for ultracold atom experiments are made.