Quantum simulation of extended polaron models using compound atom-ion systems

TL;DR

This paper explores the potential of using hybrid atom-ion systems for quantum simulation of condensed matter models with strong electron-phonon interactions, highlighting the system's unique phonon structure and the possibility of observing bipolaron states.

Contribution

It derives an effective Hamiltonian for atom-ion systems, relates it to extended Hubbard-Holstein models, and discusses how to enhance phonon coupling to observe novel quantum phenomena.

Findings

Phonon-induced long-range interactions can emerge in atom-ion systems.

The system can potentially host localized and extended bipolaron states.

Methods to enhance phonon coupling for experimental realization are proposed.

Abstract

We consider the prospects for quantum simulation of condensed matter models exhibiting strong electron-phonon coupling using a hybrid platform of trapped laser-cooled ions interacting with an ultracold atomic gas. This system naturally posesses a phonon structure, in contrast to the standard optical lattice scenarios usually employed with ultracold atoms in which the lattice is generated by laser light and thus it remains static. We derive the effective Hamiltonian describing the general system and discuss the arising energy scales, relating the results to commonly employed extended Hubbard-Holstein models. Although for a typical experimentally realistic system the coupling to phonons turns out to be small, we provide the means to enhance its role and reach interesting regimes with competing orders. Extended Lang-Firsov transformation reveals the emergence of phonon-induced long-range interactions between the atoms, which can give rise to both localized and extended bipolaron states with low effective mass, indicating the possibility of fermion pairing.