Meson theory of magnetic polarons in hole-doped anti-ferromagnets

By doping a fermionic Mott insulator at half filling, the anti-ferromagnetic (AFM) ground state is destroyed and a high-T_c superconducting phase can be reached. To unravel the physics of the hole-doped regime, an important first step is to understand the behavior of a single hole in the AFM. In analogy with the polaron problem, where a mobile impurity interacts with a surrounding bath, one can expect a so-called magnetic polaron to form when a hole is introduced into the AFM. The analogy between these two problems will be the main topic of this talk. After providing an overview of the Bose polaron problem – an impurity strongly interacting with a Bose-Einstein condensate – it will be argued that the magnetic polaron is more than just a hole dressed by magnetic excitations. Instead, the strong correlations in this system require a different physical picture, which will be provided in the strong-coupling limit where the hole-hopping is much faster than spin-exchange interactions. Very recently, the Heisenberg AFM has become accessible for quantum-gas microscopes with ultracold fermions in optical lattices. A brief overview of recent experimental progress will also be given.