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The precise imaging of many-body systems, which are comprised of many interacting particles, can help to validate theoretical models and better understand how individual particles in these systems influence each other. Ultracold quantum gases, collections of atoms cooled to temperatures close to absolute zero, are among the most promising experimental platforms for studying many-body interactions.

To study these gases, most physicists use a technique known as single atom–resolved imaging, which allows them to detect individual atoms and probe correlations in their behavior. Despite its advantages, this imaging method has a relatively low resolution, thus it fails to pick up a system's subtler features.

Researchers at Heidelberg University recently devised a new strategy to magnify atomic wave functions, offering a mathematical description of the system's quantum state, which could help to overcome the limitations of conventional single-atom imaging techniques.

Their approach, presented in a paper in Â鶹ÒùÔºical Review Letters, was successfully used to directly image strongly interacting ultracold atoms at a microscopic scale, shedding new light on their organization and correlations between them.

"The motivation for our study was to add the ability to directly resolve the position of individual atoms in our system," Sandra Brandstetter, first author of the paper, told Â鶹ÒùÔº. "In earlier experiments we could already measure their momenta with single-atom resolution, but when it came to position, the resolution of our imaging method was not sufficient: the initial cloud of atoms is about as large as the resolution of our optical imaging system, so without magnification all we would see is a single featureless blob."

Essentially, Brandstetter and her colleagues set out to develop a new approach that would allow them to reliably "magnify" a many-body system before it is examined with single-atom imaging. Such a strategy could enable the observation of hidden spatial structures in a system that would otherwise go unnoticed.

"The idea behind our approach is closely related to how an optical microscope works: two lenses are combined to produce a magnified image," explained Brandstetter. "In our case, instead of glass lenses, we use two carefully designed laser-formed potentials that let the atoms' wavefunction expand in a controlled way.

"By adjusting these 'lenses,' we can change the resolution or field of view, but just like in optics, even slight misalignments would distort the image. With careful tuning, we achieved a clean magnification that revealed spatial structures otherwise hidden from view."

To assess their proposed method and demonstrate its potential, Brandstetter and her colleagues used it to study quantum systems with well-established wavefunctions. This included a system comprised of two interacting atoms and another with six non-interacting fermions inside a harmonic trap.

Notably, the results of the team's experiment were closely aligned with theoretical predictions and what is known about the two systems. This suggests that their magnification scheme works, reliably expanding the atoms' wavefunctions.

"We now have a general method to reveal microscopic structures in ultracold atomic systems that were previously hidden by the limits of optical resolution," said Brandstetter. "An important strength of our approach is that it can be readily adopted by other groups, which is why we wrote the paper as a kind of instruction manual to help with implementation.

"As one example, researchers studying atoms with long-range dipolar interactions often use extremely small lattice spacings—too small to image directly. Our magnification scheme makes it possible to observe and analyze these interactions in real space, opening the door to new types of measurements and more direct comparisons with theory."

This recent study opens exciting possibilities for the future study and simulation of strongly interacting quantum systems. Brandstetter and her colleagues are currently conducting a further study, where they will use their method to study how pairs of fermionic atoms are formed.

"This is the microscopic mechanism underlying superfluidity," added Brandstetter. "With our magnification method, we can now track this process in both momentum space and real space, offering unprecedented insight into how pairing develops in finite-sized systems. This question even connects our ultracold atom experiment to nuclear physics."