Polaronic effects in one- and two-band quantum systems

TL;DR

This paper investigates polaron formation and dynamics in a two-band impurity system within a BEC, revealing effects like modified transport, energy shifts, and inter-band self-trapping through a variational polaron approach.

Contribution

It introduces a two-band polaron model with a variational Lang-Firsov transformation, extending understanding of impurity-boson interactions in ultracold atomic systems.

Findings

Polaron bands are renormalized with modified coherent transport.

Inter-band relaxation rates are reduced compared to Fermi's Golden Rule.

Strong coupling leads to polaron self-trapping, preventing inter-band tunneling.

Abstract

In this work we study the formation and dynamics of polarons in a system with a few impurities in a lattice immersed in a Bose-Einstein condensate (BEC). This system has been experimentally realized using ultracold atoms and optical lattices. Here we consider a two-band model for the impurity atoms, along with a Bogoliubov approximation for the BEC, with phonons coupled to impurities via both intra- and inter-band transitions. We decouple this Fr\"ohlich-like term by an extended two-band Lang-Firsov polaron transformation using a variational method. The new effective Hamiltonian with two (polaron) bands differs from the original Hamiltonian by modified coherent transport, polaron energy shifts and induced long-range interaction. A Lindblad master equation approach is used to take into account residual incoherent coupling between polaron and bath. This polaronic treatment yields a renormalized inter-band relaxation rate compared to Fermi's Golden Rule. For a strongly coupled two-band Fr\"ohlich Hamiltonian, the polaron is tightly dressed in each band and can not tunnel between them, leading to an inter-band self-trapping effect.