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Bridging Worlds of Quantum Matter: STRUCTURES Researchers Solve Longstanding Quasiparticle Puzzle
A new theory developed in Heidelberg connects the Anderson orthogonality catastrophe for static impurities with the quasiparticle picture of mobile impurities.
When a single particle moves inside a sea of many others, their mutual interactions can give rise to new collective behaviours, such as the formation of so-called quasiparticles. These emergent forms of matter display properties of individual particles even though they arise from the coordinated motion of many particles, acting together as if they were a single one. An important example is the Fermi polaron, which forms when an impurity is introduced into a sea of fermions – particles such as electrons that obey what is known as Pauli exclusion principle. Like a pebble dropped into calm water, the impurity perturbs its surrounding, forming a particle-like pattern: the polaron. These polarons serve as a cornerstone for understanding novel quantum materials and ultracold atomic gases.
For years, however, physicists have faced a fundamental puzzle about the formation of Fermi polarons: how can their familiar quasiparticle nature coexist with a phenomenon known as the Anderson orthogonality catastrophe? The latter is a theoretical prediction stating that if the impurity is made so heavy that it becomes effectively immobile, it should instead completely disrupt its environment.
A new study by Xin Chen, Eugen Dizer, Emilio Ramos Rodríguez, and Richard Schmidt – three of whom are members of STRUCTURES – resolved this long-standing question. The researchers developed a unified theory that smoothly connects the two seemingly contradictory regimes. The key insight lies in the impurity's unavoidable response to changes in the environment, which softens the disturbance it causes. In particular, when the surrounding medium adjusts, an impurity with finite mass cannot remain at rest: even if its net momentum is zero, it must recoil as the medium reorganizes. This creates what physicists refer to as an “energy gap” – a small energy cost for disturbing the medium. As a result of this gap, the impurity and its neighbouring particles can develop a smooth, coordinated motion, forming a well-defined quasiparticle. In contrast, if the impurity becomes heavier, it can respond less to its surrounding, and the medium reacts more strongly – until, in the extreme limit of an immobile impurity, the quasiparticle nature ultimately breaks down.
This mechanism explains how quasiparticles emerge from an otherwise “gapless” medium and reveals the microscopic origin of the observed transition between polarons and molecules. The new theory provides a simple yet powerful description of interacting quantum systems, with broad implications for ultracold-atom experiments, novel atomically thin semiconductors, and future studies of strongly correlated matter.
The new study has been published in the Physical Review Letters.
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