# Verifying thermodynamic equilibrium of molecular manifolds: Kennard-Stepanov spectroscopy of a molecular gas

## TL;DR

This study confirms that molecular manifolds in a high-pressure gas environment reach thermodynamic equilibrium, validated through Kennard-Stepanov spectroscopy, enabling precise temperature measurement from spectral data.

## Contribution

It demonstrates that the electronic state manifolds of molecular gases can be verified to be in thermal equilibrium using spectral ratios, even with nonlinear excitation techniques.

## Key findings

- Spectral ratios follow Kennard-Stepanov scaling across different molecules.
- The electronic state manifold is in thermodynamic equilibrium.
- Gas temperature can be accurately determined from spectra without calibration.

## Abstract

The degree of thermalization of electronically excited state manifolds of an absorber can be tested via optical spectroscopy. In the thermalized-manifold case, the ratio of absorption and emission is expected to follow a universal Boltzmann-type frequency scaling, known as the Kennard-Stepanov relation. Here, we investigate absorption and emission spectral profiles of rubidium, cesium, and potassium molecular dimers in a high-pressure argon buffer-gas environment and study the effect of collisionally induced redistribution. We find that, despite the use of nonlinear excitation techniques, the ratio of absorption and emission well follows the Kennard-Stepanov scaling for a variety of molecular transitions. We conclude that the upper electronic state rovibrational manifold of the molecular gas is well in thermodynamic equilibrium. Further, we demonstrate an accurate, calibration-free determination of the gas temperature from the measured spectroscopic data.