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An exact many-body solution for Fermi polarons

writerHui Hu (PRL)

Vol.32 (Aug) 2022 | Article no.22 2022

Physicists at the Swinburne University of Technology in Melbourne, Australia, have proposed an exact and solvable model for Fermi polarons that is experimentally realizable in current cold-atom laboratories. The resulting exact many-body solution allowed them to rigorously prove all exact and universal quasiparticle features of Fermi polarons.

The behavior of an impurity immersed in a many-body background—i.e., polaron physics—is a long-standing problem in condensed matter physics and many-body physics. The first study involving polaron physics can be traced back to Lev Davidovich Landau in 1933, who proposed one of the most fundamentally important concepts in modern physics: “quasiparticles,” a situation where a part of the impurity may still behave like a free particle under the interaction with the many-body background, as measured by quasiparticle residue, which is positive but smaller than unity.

Over the past two decades, there have been numerous efforts from the ultracold atom community to quantitatively understand polaron physics. The unique advantage the ultracold atom community provides is the possibility for unprecedented controllability. The interaction between the impurity and the many-body background can be tuned very precisely. The mass of the impurity can be changed. One can also choose the many-body background to be either fermionic or bosonic, leading to the so-called Fermi polaron or Bose polaron problems. A few salient quasiparticle features of polarons have now been predicted by approximate diagrammatic theories, including the ground-state attractive polaron, the excited repulsive polaron with a finite lifetime, and the dark continuum and the molecule-hole continuum, which separate the attractive and repulsive polaron branches. Experimental observations of these salient quasiparticle properties are important, providing a stringent test of the many-body theories of both Fermi and Bose polarons.

In this respect, an exact solution of the polaron problem that exactly establishes these salient quasiparticle features would be of great interest. However, in quantum many-body physics, exact solutions are rare, especially in dimensions higher than one. In a recent work [1, 2] contributed by researchers at Swinburne University of Technology, Australia, an exact and solvable model of Fermi polarons is surprisingly provided in the heavy impurity limit and is solved using a novel functional determinant approach. The model, which describes an impurity immersed in a BCS Fermi superfluid, is feasible to experimentally realize, by using, for instance, heavy 133Cs atoms (as impurities) in a BCS Fermi superfluid of 6Li atoms.

The key ingredient of their exact and solvable model is the superfluid pairing gap of the many-body background, which strongly suppresses the multiple particle-hole excitations in the background BCS superfluid, as the pair-breaking costs energy. This avoids the famous “Anderson’s orthogonality catastrophe,” which would completely destroy the quasiparticle residue of a heavy impurity in a non-interacting Fermi sea due to infinitely many particle-hole excitations. As a result, all the universal salient features of a polaron are revealed via an in-principle exact calculation, as shown in Fig. 1.

Fig. 1
figure 1

The spectra of Fermi polarons (formed by immersing an impurity in a BCS Fermi superfluid) at three different temperatures: T = 0, 0.1TF, and 0.15TF, as indicated by different lines. Here, TF is the Fermi temperature of the background Fermi sea. Two interaction strengths between the impurity and the background spin-up atoms are considered: a a relatively weak interaction without a two-body bound state in a vacuum and b a relatively strong interaction in the presence of a two-body bound state. In both cases, there is no interaction between the impurity and the background spin-down atoms. Various exact quasiparticle properties are indicated. The two dashed lines show the features related to the Yu-Shiba-Rusinov bound states [credit: Physical Review Letters]

This interesting work builds on their earlier work on a novel “crossover” polaron problem [3], which addresses the behavior of an impurity immersed in a strongly interacting Fermi superfluid, connecting between a non-interacting Fermi gas (i.e., the Fermi polaron problem) and a weakly interacting molecular condensate (the Bose polaron problem).


  1. J. Wang, X.-J. Liu, H. Hu, Exact quasiparticle properties of a heavy polaron in BCS Fermi superfluids. Phys. Rev. Lett. 128, 175301 (2022). https://doi.org/10.1103/PhysRevLett.128.175301

  2. J. Wang, X.-J. Liu, H. Hu, Heavy polarons in ultracold atomic Fermi superfluids at the BEC-BCS crossover: formalism and applications. Phys. Rev. A 105, 043320 (2022). https://doi.org/10.1103/PhysRevA.105.043320

  3. H. Hu, J. Wang, J. Zhou, X.-J. Liu, Crossover polarons in a strongly interacting Fermi superfluid. Phys. Rev. A 105, 023317 (2022). https://doi.org/10.1103/PhysRevA.105.023317

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[Source: https://link.springer.com/article/10.1007/s43673-022-00052-5]