Physicists solve a quantum mystery that stumped scientists for decades

In quantum many-body physics, scientists have long debated how impurities behave when surrounded by large numbers of other particles. These impurities can be unusual electrons or atoms (i.e., exotic electrons or atoms). One widely used explanation is the quasiparticle model. In this picture, a single particle moves through a sea of fermions such as electrons, protons, or neutrons and constantly interacts with those around it. As it travels, it pulls nearby particles along with it, creating a combined entity called a Fermi polaron. Although it behaves like a single particle, this quasiparticle arises from the shared motion of the impurity and its surroundings. As Eugen Dizer, a doctoral candidate at Heidelberg University, notes, this idea has become central to understanding strongly interacting systems ranging from ultracold gases to solid materials and nuclear matter.

When Heavy Particles Disrupt the System

A very different scenario appears in a phenomenon known as Anderson's orthogonality catastrophe. This occurs when an impurity is so heavy that it barely moves at all. Its presence dramatically alters the surrounding system. The wave functions of the fermions change so extensively that they lose their original form, creating a complicated background where coordinated motion breaks down. Under these conditions, quasiparticles cannot form. Until now, physicists have not had a clear theory that links this extreme case with the mobile impurity picture. By applying a range of analytical tools, the Heidelberg team has managed to connect these two descriptions within a single framework.

Small Motions With Big Consequences

"The theoretical framework we developed explains how quasiparticles emerge in systems with an extremely heavy impurity, connecting two paradigms that have long been treated separately," explains Eugen Dizer, who works in the Quantum Matter Theory group led by Prof. Dr Richard Schmidt. A key insight behind the theory is that even very heavy impurities are not perfectly still. As their surroundings adjust, these particles undergo tiny movements. Those slight shifts create an energy gap that makes it possible for quasiparticles to form, even in a strongly correlated environment. The researchers also showed that this process naturally accounts for the transition from polaronic states to molecular quantum states.

Implications for Quantum Experiments

Prof. Schmidt says the new results offer a flexible way to describe impurities that can be applied across different dimensions and interaction types. "Our research not only advances the theoretical understanding of quantum impurities but is also directly relevant for ongoing experiments with ultracold atomic gases, two-dimensional materials, and novel semiconductors," he adds.

The study was conducted as part of Heidelberg University's STRUCTURES Cluster of Excellence and the ISOQUANT Collaborative Research Centre 1225. The findings were published in the journal Physical Review Letters.