Thermometry of simulated Bose--Einstein condensates using machine learning

Precise determination of thermodynamic parameters in ultracold Bose gases remains challenging due to the destructive nature of conventional measurement techniques and inherent experimental uncertainties. We demonstrate a machine learning approach for rapid, non-destructive estimation of the chemical potential and temperature from a single image of an in situ imaged density profiles of finite-temperature Bose gases. Our convolutional neural network is trained exclusively on quasi-2D `pancake' condensates in harmonic trap configurations. It achieves parameter extraction within fractions of a second. The model also demonstrates some zero-shot generalisation across both trap geometry and thermalisation dynamics, successfully estimating the temperature (although not the chemical potential) for toroidally trapped condensates with errors of only a few nanokelvin despite no prior exposure to such geometries during training, and maintaining predictive accuracy during dynamic thermalisation processes after a relatively brief evolution without explicit training on non-equilibrium states. These results suggest that supervised learning can overcome traditional limitations in ultracold atom thermometry, with extension to broader geometric configurations, temperature ranges, and additional parameters potentially enabling comprehensive real-time analysis of quantum gas experiments. Such capabilities could significantly streamline experimental workflows whilst improving measurement precision across a range of quantum fluid systems.