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This is confusing to me as I thought the simple act of measuring the wave collapsed the wavefunction.
Indeed, the article is extremely confusing. The wave in wave-particle duality is not the wave (function), one that collapses. For instance, electromagnetic wave is not the same thing as the wave function of the photon.
The arxiv has more details. They sparsely populated a dense lattice with particles. Then they turned off the lattice, which allowed all the particles’ wave functions to evolve according to the Schrödinger equation. Then they turned the lattice back on, which constitutes a measurement and collapses the wave functions. Then they took statistics on how far and in which direction each particle traveled and compared those statistics to the ones implied by Schrödinger’s equation.
So is this really just a different version of the double-slit experiment, building up a statistical measurement of the waveform by performing many discrete measurements?
In a way, although the double slit demonstrated self interference. In this experiment, I think the lattice is so sparsely populated that interference effects are negligible and particles move as free wave packets while the lattice is disabled.
Here's the abstract from the paper[1]:

> [W]e use quantum gas microscopy to image the in-situ spatial distribution of deterministically prepared single-atom wave packets as they expand in a plane. We achieve this by controllably projecting the expanding wavefunction onto the sites of a deep optical lattice and subsequently performing single-atom imaging. The protocol established here for imaging extended wave packets via quantum gas microscopy is readily applicable to the wavefunction of interacting many-body systems in continuous space, promising a direct access to their microscopic properties, including spatial correlation functions up to high order and large distances.

Still goes mostly over my head but it's a lot clearer than TFA imho. Also, I tried looking up Quantum Gas Microscopy on Wikipedia and was disappointed in the results. Google Scholar yields more articles for those interested [2].

1. https://arxiv.org/abs/2404.05699

2. https://scholar.google.com/scholar?q=quantum+gas+microscope