Polaronic slowing of fermionic impurities in lattice Bose-Fermi mixtures

TL;DR

This paper extends small polaron theory to Bose-Fermi mixtures in optical lattices, showing how fermionic impurity hopping is exponentially suppressed due to polaron formation, with potential experimental signatures.

Contribution

It introduces a polaronic framework for Bose-Fermi mixtures in optical lattices, analyzing fermionic impurity dynamics and providing quantitative predictions for hopping renormalization.

Findings

Fermionic hopping is exponentially renormalized by polaron formation.

The approach is validated against current experimental parameters.

Results include temperature, density, and interaction dependence for Rb-K mixtures.

Abstract

We generalize the application of small polaron theory to ultracold gases of Ref. [\onlinecite{jaksch_njp1}] to the case of Bose-Fermi mixtures, where both components are loaded into an optical lattice. In a suitable range of parameters, the mixture can be described within a Bogoliubov approach in the presence of fermionic (dynamic) impurities and an effective description in terms of polarons applies. In the dilute limit of the slow impurity regime, the hopping of fermionic particles is exponentially renormalized due to polaron formation, regardless of the sign of the Bose-Fermi interaction. This should lead to clear experimental signatures of polaronic effects, once the regime of interest is reached. The validity of our approach is analyzed in the light of currently available experiments. We provide results for the hopping renormalization factor for different values of temperature, density and Bose-Fermi interaction for three-dimensional $^{87}\rm{Rb}-^{40}\rm{K}$ mixtures in optical lattice.