# Characterizing critical exponents via Purcell effect

## TL;DR

This paper explores how phase transitions influence the spontaneous emission rate of quantum emitters, revealing that critical exponents significantly affect emission and can be used to identify universality classes through optical methods.

## Contribution

It introduces a novel link between critical phenomena and spontaneous emission, showing the Purcell effect as a tool to probe phase transition universality classes.

## Key findings

- Emission rate is suppressed in the broken symmetry phase due to photon mass.
- Spontaneous emission depends on critical exponents, enabling optical determination of universality class.
- Purcell effect can serve as an optical probe for critical phenomena.

## Abstract

We investigate the role of phase transitions into the spontaneous emission rate of quantum emitters embedded in a critical medium. Using a Landau-Ginzburg approach, we find that, in the broken symmetry phase, the emission rate is reduced or even suppressed due to the photon mass generated by the Higgs mechanism. Moreover, we show that the spontaneous emission presents a remarkable dependence upon the critical exponents associated to a given phase transition, allowing for an optical determination of the universality class. Our findings not only demonstrate that the Purcell effect constitutes an efficient optical probe of distinct critical phenomena, but they also unveil that a more general connection between phase transitions and spontaneous emission exist, as previous experimental and numerical evidences suggest.