[Paper Review] Optimized observable readout from single-shot images of ultracold atoms via machine learning

Axel U. J. Lode, Rui Lin+7 more|arXiv (Cornell University)|Jan 1, 2021

Cold Atom Physics and Bose-Einstein Condensates130 references16 citations

TL;DR

This paper proposes using artificial neural networks (ANNs) to extract one- and two-body densities, momentum-space observables, and correlation functions from single-shot images of ultracold atoms with far greater accuracy than standard averaging methods. The key contribution is that ANNs enable reliable reconstruction of momentum-space observables from real-space images—and vice versa—eliminating the need for experimental reconfiguration and drastically reducing the number of images required.

ABSTRACT

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.

Motivation & Objective

• To overcome the inefficiency of standard averaging methods in extracting observables from single-shot images of ultracold atoms.
• To develop a machine learning framework that optimally reconstructs one- and two-body densities and correlation functions from minimal image data.
• To demonstrate that ANNs can extract momentum-space observables from real-space single-shot images and vice versa, bypassing the need for separate experimental imaging setups.
• To establish a general-purpose, open-source toolkit (UNIQORN) for neural-network-based observable readout in quantum simulators.

Proposed method

• Trained artificial neural networks (ANNs) on simulated single-shot images of N-boson systems in a tilted double-well potential.
• Used supervised regression with ANNs to predict one-body and two-body densities from single-shot images as input.
• Designed ANNs with convolutional and dense layers to handle spatial correlations and extract physical observables from raw image data.
• Leveraged a diverse dataset of 3,000 ground-state wavefunctions with randomized parameters (h, σ, g, α, N) to ensure generalization.
• Implemented the method in an open-source toolkit called UNIQORN, built on TensorFlow, for flexible and reproducible observable inference.
• Validated performance by comparing ANN predictions against exact theoretical values and standard averaging across varying numbers of single-shot images (Ns).

Experimental results

Research questions

• RQ1 Can artificial neural networks outperform standard averaging in extracting one- and two-body densities from single-shot images of ultracold atoms?
• RQ2 Can ANNs reconstruct momentum-space observables such as ρ(k) and ρ(2)(k,k′) from real-space single-shot images without requiring time-of-flight imaging?
• RQ3 Can ANNs accurately infer real-space observables like ρ(x) and ρ(2)(x,x′) from momentum-space single-shot data?
• RQ4 How many single-shot images are required for ANNs to achieve comparable or better accuracy than standard averaging?
• RQ5 Can the same ANN model reliably extract observables across different physical regimes, including fragmented and condensed many-body states?

Key findings

• ANNs achieved significantly higher accuracy in reconstructing one- and two-body densities than standard averaging, even with as few as 10 single-shot images.
• The ANN-based method reduced the required number of images by up to 100× compared to standard averaging to reach the same level of accuracy.
• ANNs successfully reconstructed momentum-space observables (ρ(k), ρ(2)(k,k′)) from real-space single-shot images with high fidelity, eliminating the need for time-of-flight imaging.
• The reverse reconstruction—inferring real-space observables from momentum-space images—achieved comparable accuracy to standard averaging when using around 200 images.
• At Ns ≈ 200, the ANN-based inference from momentum-space images matched the accuracy of conventional averaging from real-space images.
• The method demonstrated robustness across diverse physical regimes, including both fragmented and condensed many-body states, confirming generalizability.