Quantum simulations of extended Hubbard models with dipolar crystals

Abstract

In this paper we study the realization of lattice models in mixtures of\natomic and dipolar molecular quantum gases. We consider a situation where polar\nmolecules form a self-assembled dipolar lattice, in which atoms or molecules of\na second species can move and scatter. We describe the system dynamics in a\nmaster equation approach in the Brownian motion limit of slow particles and\nfast phonons, which we find appropriate for our system. In a wide regime of\nparameters, the reduced dynamics of the particles leads to physical\nrealizations of extended Hubbard models with tuneable long-range interactions\nmediated by crystal phonons. This extends the notion of quantum simulation of\nstrongly correlated systems with cold atoms and molecules to include\nphonon-dynamics, where all coupling parameters can be controlled by external\nfields.\n