Inference of the potential from absorption images: Inverting density functional theory with ultracold atoms*

We discuss an application of our new machine learning toolbox, the
Universal Neural-Network Interface for Quantum Observable Readout from
N-body wavefunctions (UNIQORN, https://arxiv.org/abs/2010.14510 ).
We follow a strategy that is inverse to density functional theory: we
infer the potential that a many-body system of indistinguishable bosonic
particles is placed in from absorption or single-shot images, i.e.,
samples of the N-body state.
We demonstrate the network’s ability to correctly learn and generalize
from such images in both real and momentum space. We thus open up new
possibilities for the analysis of experimental single-shot images.
The connection between the single-shot measurements and the inferred
potential is investigated further in a comparison to potentials obtained
via the Thomas Fermi (TF) approximation. The potentials inferred with
our model are shown to be significantly more accurate than its TF
counterparts. We plan to deploy our machine learning models for
experimental data in the future.