Many quantum many-body physics researchers are not able to reach exact conclusions or solutions, especially in more than one dimension. This holds true also for the Fermi Polaron problem. It describes instances where the many-body quantum background is not a Fermi gas.

Over the past decade, extensive research has been done on the Fermi Polaron problem. It has been very difficult to predict the quasi-particle properties Fermi Polarons with high levels confidence.

Researchers at Swinburne University of Technology recently introduced a model that could be used to predict the exact quasi-particle properties of a heavy polaron in Bardeen-Cooper-Schrieffer (BCS) Fermi superfluids. The paper was published in Physical Review Letters. It presents a theoretical and exact solution to a multibody system that could be eventually tested in experiments.

This study builds upon a previous paper published in Physical Review A. This work was primarily focused on crossover Polarons with a mobile Impurity.

Jia Wang, one the researchers behind the study, said that “our previous work and many other theoretical studies on polarons using different approximation methods give certain universal features (such as existence of attractive/repulsive polarons or a dark continuum).” We believe suppression of multiple quasiparticles in the background medium is what explains these features.

Wang and his collaborators believe that the mechanism behind the universal Fermi characteristics of Fermi Polarons could be either the recoil energy from a mobile impurety or the existence an energy gap within a superfluid. To prove their hypothesis in experimental settings, however, they had to first represent it theoretically.

Wang stated that he came across a fascinating paper which examined immobile impurities within non-interacting Fermi gas. This model can be solved using the ‘functional determinaant approach (FDA).” Due to the infamous “Anderson’s Orthogonality Catastrophe”, polarons are not possible in such systems. This is due to the fact that immobile impurity doesn’t have recoil energy and multiple particle-hole excitations can destroy the polaron resonance.

Wang and his colleagues have described a many-body system in which a superfluid gap can reduce the polarons’ multiple particle-hole excitations. They set out to apply the FDA method to their BCS superfluid system, which is usually inapplicable for Fermi Fermi Polarons.

Wang stated that experiments were also being done to investigate Fermi superfluid-excitations. This topic has been a long-standing research subject. “Several experiments recently revealed that it is possible to introduce another species of atoms into a BCS superfluid, which could play the role as impurities. These systems are accessible and one can use the spectrum of polarons of impurities to measure the background superfluid excitation spectrum features (such as superfluid gap or sub-gap Yu Shiba-Rusinov).

Wang and his colleagues assume that immobile impurities are present in a system. However, the calculations provide an approximate estimate of heavy impurities. Alternately, in experimental settings, physicists may be able to locate impurities using an optical lattice deep enough to detect them.

Wang said that our study was theoretical. “Our model considers an immobile impurity system in a Fermi superfluid with two components. We assume that the impurity has two inner states (hyperfine spinning states), and that the superfluid interacts strongly with one of them. The other state is non-interacting.

The FDA-based theoretical model enabled the researchers to reveal all universal polaron features using a simple in principle exact calculation. This is an amazing achievement considering that previous studies could not prove the universal quasi-particle properties in Fermi polaron system systems.

Wang stated, “Preparing the impurity initially in the non-interacting condition, we calculated and denoted as A(o) the probability that the impurity absorbs a photon, switching to the strongly interacted state as a function the photon frequency. “Suppose that the absorption probability shows sharp peak at some frequency o. This indicates the existence a quasiparticle with energy, which we call heavy cross-polaron.

The theoretical work of this group of researchers could be used to create cold atom laboratory experiments that test their hypothesis. In addition, physicists could also draw inspiration from their paper to conduct slightly different tests known as “Ramsey-interference-type experiments,” which involve some of the processes and technical details outlined in their paper.

Wang and his coworkers have presented a theory that is quite general. It could be applied to many different experimentally feasible systems. The team proposes an experimental implementation of the proposed system with heavy 133Cs impurities in BCS Fermi superfluids of 6Li atoms. This was previously realized in some other works.

Wang stated that “the contributions of our work were two-fold.” “First, we created a model that could be solved precisely and gave all the universal features of Fermi Polarons. Although these features were only approximately calculated in previous studies, our analysis shows that they are due to suppression of multiple particle-hole excitations within the fermionic medium. We also discover a finite temperature phenomenon in which a magnetic impurity interacts with two components of the superfluid at different strengths. This is a Fermi superfluid that has two components.

The researchers discovered that the polaron spectrum had additional enhancement peak at finite temperatures. This corresponded with the subgap YuShibaRusinov bound. These interesting theoretical predictions may soon be tested in other physics labs around the world.

Wang said that this was the first study to apply polaron-related theories to study subgap Yu-Shiba-Rusinov bound state in ultracold gasses. “We plan to study heavy polarons within other superfluid systems such as topological superfluid in our next studies.” Wang added. Our method is based on an in-principal exact calculation and we hope it will allow us to understand the topological phase transition of the background medium.

Jia Wang et al, Heavy polarons in ultracold atomic Fermi superfluids at the BEC-BCS crossover: Formalism and applications, Physical Review A (2022).DOI: 10.1103/PhysRevA.105.043320