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Nondestructive characterization of laser-cooled atoms using machine learning

Guilherme de Sousa, M. Doris, Dario D'Amato, Brady Egleston, Justyna P. Zwolak, Ian B. Spielman

Published May 14, 2026• 0 citations
Publisher

Abstract

Laser cooling and trapping techniques are foundational to modern atomic physics, with applications including atomic clocks and sensors as well as quantum simulators and computers. These applications require stable, well-calibrated laser cooling and accurate determination of atom number and temperature. We develop machine learning techniques for estimating physical properties of laser-cooled potassium-39 atoms in a magneto-optical trap using only the scattered light—i.e., fluorescence—that is intrinsic to the cooling process. In situ snapshot images of fluorescing atomic ensembles directly reveal the spatial structure of these millimeter-scale objects but contain no obvious information regarding internal properties such as the temperature. We first assembled and labeled a balanced dataset sampling 8 × 10 3 different experimental parameters that includes examples with large and dense atomic ensembles, a complete absence of atoms, and everything in between. We describe a range of models trained to predict atom number and temperature solely from fluorescence images. These run the gamut from a poorly performing linear regression model based only on integrated fluorescence to deep neural networks that give number and temperature with fractional uncertainties of 0.1 and 0.2, respectively. These results show that fluorescence images can provide fast, nondestructive diagnostics for cold-atom experiments and may enable real-time experimental feedback.

DOI
10.1016/j.newton.2026.100518

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Laser cooling and trapping techniques are foundational to modern atomic physics, with applications including atomic clocks and sensors as well as quantum simulators and computers. These applications require stable, well-calibrated laser cooling and accurate determination of atom number and temperature. We develop machine learning techniques for estimating physical properties of laser-cooled potassium-39 atoms in a magneto-optical trap using only the scattered light—i.e., fluorescence—that is intrinsic to the cooling process. In situ snapshot images of fluorescing atomic ensembles directly reveal the spatial structure of these millimeter-scale objects but contain no obvious information regarding internal properties such as the temperature. We first assembled and labeled a balanced dataset sampling 8 × 10 3 different experimental parameters that includes examples with large and dense atomic ensembles, a complete absence of atoms, and everything in between. We describe a range of models trained to predict atom number and temperature solely from fluorescence images. These run the gamut from a poorly performing linear regression model based only on integrated fluorescence to deep neural networks that give number and temperature with fractional uncertainties of 0.1 and 0.2, respectively. These results show that fluorescence images can provide fast, nondestructive diagnostics for cold-atom experiments and may enable real-time experimental feedback.
We develop a form of nondestructive optical thermometry to deterministically measure the temperature of the selected segment of a cold-atom ensemble. The essence is to monitor the thermal expansion of the targeted cold atoms after their labeling through manipulation of the internal states, and the nondestructive property relies on nearly lossless detection via the driving of a cycling transition. The temperature information is extracted from the change of densities via a bucket detector without the necessity of a complicated imaging setup. We also focus on the application of this method to isotropic laser cooling, and it has the capability of addressing only the atoms on the optical detection axis within the enclosure, which is readily compatible with typical configurations of atomic clocks or quantum sensing. Our results confirm the sub-Doppler-cooling features of isotropic laser cooling, and we further investigate the relevant cooling properties. Furthermore, we demonstrate the recently developed optical configuration with injection of cooling-laser light in the form of hollow beams, which helps to enhance the cooling performance and accumulate more cold atoms in the central regions.
Coulomb crystals---ordered structures of cold ions confined in ion traps---have applications in a variety of research fields. The number and temperature of the ions forming the Coulomb crystals are two key attributes of interest in many trapped-ion experiments. Here, we present a fast and accurate approach to determining these attributes from fluorescence images of the ions based on convolutional neural networks (CNNs). In this approach, we first generate a large number of images of Coulomb crystals with different numbers of ions at different temperatures using molecular-dynamics simulations and then train CNN models on these images to classify the desired attributes. The classification performance of several common pretrained CNN models is compared in example tasks. We find that for crystals with numbers of ions in the range 100--299 and secular temperatures of 5--15 mK, the best-performing model can discern variations of a single ion with an accuracy of 93% and temperature changes of 1 mK with an accuracy of 92%. Since the trained models can be directly integrated into experiments, in situ determination of these attributes can be realized in a noninvasive fashion. This has the potential to greatly enhance the analysis and control of trapped ions in real time.
Abstract 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, minimally 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-two-dimensional ‘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.
Neutral atoms trapped in optical lattices are promising candidates for quantum information processing and quantum simulation. Over the last decades, elegant tools for the manipulation of the internal and external states of optically trapped atoms have been developed. The crucial capability of scalable internal state readout in these systems, however, still relies on destructive methods. In spite of the important role of near-resonant illumination for the manipulation and detection of atoms in the lattice, there also exists a significant lack of studies on the heating and cooling dynamics of optically trapped atoms interacting with near-resonant light. An in-depth understanding of the heating and cooling processes is essential to finding the conditions of illumination that enable the non-destructive internal state readout of multiple atoms. This work presents an experimental system to cool, trap, manipulate, and detect the internal and external states of a small ensemble of 87Rb neutral atoms trapped in a one-dimensional optical lattice. A high photon detection efficiency in our experimental system allows for fast fluorescence imaging with acquisition times of 20 ms and fast position determination of atoms in the optical lattice with an accuracy of ∼ 40 nm. Using this experimental system, we investigate the heating dynamics of a neutral atom trapped in a standing wave dipole trap illuminated by a single near-resonant laser beam. A theoretical description to describe our measurements is provided in two experimentally relevant regimes. First, we consider the case of a weak near-resonant beam and later the case of off-resonant illumination. From this analysis, we find settings for the illumination light which allows an atom to scatter many photons before it is expelled from the trap. Building on these results we demonstrate simultaneous, non-destructive determination of the internal state of spatially resolved atoms trapped in a one-dimensional optical lattice with a fidelity of 98.6 ± 0.2% and a survival probability of 99.0 ± 0.2%. During the readout process, less than 2% of the atoms change their initial ground state. In order to determine the state of atoms that are not spatially resolved, a novel image analysis technique is presented. The technique uses Bayesian methods, which include the statistics of the detected photons as well as the response from the EMCCD camera. The Bayesian method is implemented on experimental data for atoms trapped in a one-dimensional optical lattice and its accuracy is tested by numerical simulations. In addition, an extension of this algorithm for atoms trapped in two-dimensional lattices is provided. Finally, the non-destructive state detection method is utilized as a tool for the state determination following the coherent control of the internal and external states of atoms in the optical trap. Here Raman sideband cooling is implemented and utilized in an atomic compression sequence for the creation of a small and dense atomic ensemble. These techniques will play an important role in experiments studying the collective light interaction of the atomic ensemble in a recently added optical fiber cavity.
Cooling and trapping neural atoms with laser beams became a standard method of studying atom properties in temperatures close to absolute zero. Precise knowledge of physical parameters of the atomic sample is of prime importance in such studies, particularly the knowledge of the number of trapped atoms, their density and temperature. Diagnostics aiming at determination of these parameters has to be performed optically, mainly with the spectroscopic methods. In this paper, we present basic principles of obtaining ultra-cold atoms and methods used for their diagnostics. Some examples of quantum effects specific for low-temperatures, revealed by these methods, are also demonstrated.
Machine learning based on artificial neural networks has emerged as an efficient means to develop empirical models of complex systems. Cold atomic ensembles have become commonplace in laboratories around the world, however, many-body interactions give rise to complex dynamics that preclude precise analytic optimisation of the cooling and trapping process. Here, we implement a deep artificial neural network to optimise the magneto-optic cooling and trapping of neutral atomic ensembles. The solution identified by machine learning is radically different to the smoothly varying adiabatic solutions currently used. Despite this, the solutions outperform best known solutions producing higher optical densities.