A new theory developed by physicists at Heidelberg University brings together two long competing ideas in quantum physics, offering a unified explanation for how an unusual particle behaves inside a crowded quantum environment. The work connects two seemingly opposite descriptions of a single impurity moving through or remaining nearly motionless within a large collection of fermions, a system known as a Fermi sea.
The framework, created by researchers at Heidelberg University’s Institute for Theoretical Physics, explains how quasiparticles emerge and links two previously disconnected quantum states. The team says this advance could have important implications for experiments exploring quantum matter.
New theory unifies competing quantum models
Quantum many body physics has long relied on different models to explain how impurities, such as exotic electrons or atoms, interact with surrounding particles.
One well established picture is based on quasiparticles. In this model, a single impurity moves through a sea of fermions, including electrons, protons, or neutrons, while interacting with nearby particles. As it travels, it effectively carries those neighboring particles with it, creating a combined entity called a Fermi polaron. Although it behaves like a single particle, this quasiparticle actually arises from the collective motion of the impurity and the particles around it.
According to Eugen Dizer, a doctoral candidate at Heidelberg University’s Institute for Theoretical Physics, this quasiparticle model has become a fundamental tool for understanding strongly interacting systems, including ultracold atomic gases, solid state materials, and nuclear matter.
Solving a decades old quantum puzzle
A very different picture emerges when the impurity is extremely heavy and essentially unable to move. In this situation, a phenomenon called Anderson’s orthogonality catastrophe takes over.
Rather than producing a quasiparticle, the heavy impurity changes the quantum system so dramatically that the wave functions of the surrounding fermions lose their original form. The resulting complex background prevents the coordinated motion needed for quasiparticles to exist.
For decades, physicists lacked a theory that could explain how these two very different descriptions fit together. Using a range of analytical techniques, the Heidelberg team has now shown how the mobile and nearly immobile impurity models can be unified within a single theoretical framework.
Tiny motions reveal the missing connection
“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, a member of the Quantum Matter Theory working group led by Prof. Dr Richard Schmidt.
The researchers found that even extremely heavy impurities are not perfectly motionless. As the surrounding environment adjusts, these impurities still undergo slight movements. Those tiny motions create an energy gap that allows quasiparticles to emerge from what would otherwise remain a highly correlated quantum background.
The new framework also naturally explains how quantum systems transition between so called polaronic and molecular states.
Implications for quantum materials and future experiments
According to Prof. Schmidt, the new theory provides a versatile way to describe quantum impurities across different spatial dimensions and a wide variety of interactions.
“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,” adds the Heidelberg physicist.
The research was conducted through Heidelberg University’s STRUCTURES Cluster of Excellence and the ISOQUANT Collaborative Research Centre 1225. The findings were published in the journal Physical Review Letters.