Mass-gap description of heavy impurities in Fermi gases

Abstract:

We present a unified theory that connects the quasiparticle picture of Fermi polarons for mobile impurities to the Anderson orthogonality catastrophe for static impurities. By operator reordering of the underlying many-body Hamiltonian, we obtain a modified fermionic dispersion relation that features a recoil-induced energy gap, which we call the `mass gap’. We show that the resulting mean-field Hamiltonian exhibits an in-gap state for finite impurity mass, which takes a key role in Fermi polaron and molecule formation. We identify the mass gap as the microscopic origin of the quasiparticle weight of Fermi polarons and derive a power-law scaling of the weight with the impurity-to-fermion mass ratio. The associated in-gap state is shown to give rise to the emergence of the polaron-to-molecule transition away from the limiting case of the Anderson orthogonality catastrophe in which the transition is absent.

X. Chen, E. Dizer, E. R. Rodríguez, R. Schmidt, „Mass-gap description of heavy impurities in
Fermi gases“, 21. Juli 2025, arXiv:2507.15957 (2025).

https://arxiv.org/abs/2507.15957

Related to Project C01, C07