Single-shot images are the standard readout of experiments with ultracold atoms, the imperfect reflection of their many-body physics. The efficient extraction of observables from single-shot images is thus crucial. Here we demonstrate how artificial neural networks can optimize this extraction. In contrast to standard averaging approaches, machine learning allows both one- and two-particle densities to be accurately obtained from a drastically reduced number of single-shot images. Quantum fluctuations and correlations are directly harnessed to obtain physical observables for bosons in a tilted double-well potential at an extreme accuracy. Strikingly, machine learning also enables a reliable extraction of momentum-space observables from real-space single-shot images and vice versa. With this technique, the reconfiguration of the experimental setup between in situ and time-of-flight imaging is required only once to obtain training data, thus potentially granting an outstanding reduction in resources.
Single-shot images are the standard readout of experiments with ultracold atoms, the imperfect reflection of their many-body physics. The efficient extraction of observables from single-shot images is thus crucial. Here we demonstrate how artificial neural networks can optimize this extraction. In contrast to standard averaging approaches, machine learning allows both one- and two-particle densities to be accurately obtained from a drastically reduced number of single-shot images. Quantum fluctuations and correlations are directly harnessed to obtain physical observables for bosons in a tilted double-well potential at an extreme accuracy. Strikingly, machine learning also enables a reliable extraction of momentum-space observables from real-space single-shot images and vice versa. With this technique, the reconfiguration of the experimental setup between in situ and time-of-flight imaging is required only once to obtain training data, thus potentially granting an outstanding reduction in resources.
Absorption imaging is the most common probing technique in experiments with ultracold atoms. The standard procedure involves the division of two frames acquired at successive exposures, one with the atomic absorption signal and one without. A well-known problem is the presence of residual structured noise in the final image, due to small differences between the imaging light in the two exposures. Here, we solve this problem by performing absorption imaging with only a single exposure, where instead of a second exposure the reference frame is generated by an image-completion autoencoder neural network. The network is trained on images without an absorption signal, such that it can infer the noise overlaying the atomic signal based only on the information in the region encircling the signal. We demonstrate our approach on data captured with a quantum degenerate Fermi gas. The average residual noise in the resulting images is below that of the standard double-shot technique. Our method simplifies the experimental sequence, reduces the hardware requirements, and can improve the accuracy of extracted physical observables. The trained network and its generating scripts are available as an open-source repository (absDL.github.io).
The ability to detect atoms in high spatiotemporal resolution provides a powerful tool for us to investigate the quantum properties of ultracold quantum gases. Plenty of useful imaging methods, including absorption imaging, phase contrast imaging and fluorescence imaging, have been implemented in detecting atoms. Among them, absorption imaging is the most widely used method in cold atoms laboratory. However, the traditional absorption imaging method is affected by perturbations such as interference between optical elements, fluctuation of laser power, frequency, and spatial position, resulting in residual spatially structured noise and degradation of imaging quality. Especially for regions with lower density or for longer time-of-flight, a large number of repetitions are often required to obtain better signal-to-noise ratio, which would increase the time cost and induce other noise. One must reduce the time between two imaging pulses to suppress the spatial noise. A better charge coupled device (CCD) with higher frame transfer rate or other method like fast-kinetic mode will be used to improve the imaging quality. In this paper, a single-shot cold atom imaging method based on machine learning is proposed, in which only one absorption imaging of cold atoms is required, and the corresponding background image can be generated through the neural network of an autoencoder. This effectively reduces the spatial striped noise in imaging, significantly improves the imaging quality, and makes it possible for cold atoms to be imaged multiple times in a single cycle.
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.
In this thesis, the behavior of ultracold bosonic systems in external potentials is investigated. Such systems are typically realized as Bose-Einstein condensates, where dilute atomic gases cooled to extremely low temperatures exhibit collective quantum behavior. Because of the large degree of control they allow over the external potential and over the interaction parameters of the many-body system, Bose-Einstein condensates constitute a testing ground for the dedicated study of coherence, correlations, and quantum phase transitions in interacting bosonic systems. This thesis presents an investigation of the many-body physics of ultracold bosons, focusing specifically on how the many-body properties of these ultracold bosonic systems change with changing external potential, how they manifest themselves in experimentally accessible observables, and how these properties can be analyzed using both numerical many-body methods and data-driven approaches. The first part of this thesis focuses on the theoretical description of ultracold bosonic systems in external trapping potentials. Using the multiconfigurational time-dependent Hartree method for bosons (MCTDH-X), numerically exact simulations were performed that allow the calculation of reduced density matrices, natural orbitals, and correlation functions. These quantities were used to analyze the coherence properties and fragmentation of trapped bosonic systems. In particular, double-well systems were investigated as model scenarios in which the gradual formation of a central barrier leads to a redistribution of natural occupations and a transition from a condensed to a fragmented many-body state. In this context, we demonstrate the usefulness of single-shot images, which represent projective measurements of the many-body wave function, for the experimental investigation of the many-body physics of fragmenting system. Single-shot images can be simulated numerically using MCTDH-X, but they are more commonly obtained through experimental measurements. The possibility of extracting many-body information in an experimental context, where said many-body information is not otherwise accessible, is discussed. Supervised machine learning models were trained on simulated single-shot data sets to investigate whether information about the underlying many-body state can be inferred directly from measurement outcomes. The results show that machine learning models are capable of learning patterns in the single-shot images that correlate with properties of the underlying many-body state and can therefore predict density-related quantities with good accuracy. The second part of this thesis focuses on a joint theoretical and experimental investigation of a system of ultracold bosons coupled to an optical cavity. In this system, the atoms interact with a dynamically generated optical potential produced by the cavity field. We use a new theoretical framework that combines a mean-field treatment of the cavity field with a many-body description of the atomic degrees of freedom to be able to capture the emergence of a superradiant self-organized phase and the subsequent transition to a self-organized Mott-insulating state. Our simulations show good agreement with the experimental results, and we discuss where the use of a beyond mean-field treatment in the simulations becomes essential in describing the physics of the different involved phases and quantum states. In summary, the results presented in this thesis demonstrate how numerical many-body simulations and machine learning methods can be used to analyze experimentally accessible observables and to gain insight into the many-body physics of ultracold bosonic systems.
The quantum state of ultracold atoms is often determined through measurement of the spatial distribution of the atom cloud. Absorption imaging of the cloud is regularly used to extract this spatial information. Accurate determination of the parameters which describe the spatial distribution of the cloud is crucial to the success of many ultracold atom applications. In this work, we present modified deep learning image classification models for image regression. To overcome challenges in data collection, we train the model on simulated absorption images. We compare the performance of the deep learning models to least-squares techniques and show that the deep learning models achieve accuracy similar to least-squares, while consuming significantly less computation time. We compare the performance of models which take a single atom image against models which use an atom image plus other images that contain background information, and find that both models achieved similar accuracy. The use of single image models will enable single-exposure absorption imaging, which simplifies experiment design and eases imaging hardware requirements.