EUROCORES_EuroQUAM 1. Call_Quantum-Degenerate Dipolar Gases of Bialkali Molecules (QUDIPMOL)

The Innsbruck theory group has long-standing interest and tradition in the physics of ultracold atom with special focus on the control of many-body systems and the study of its dynamical and thermodynamic properties. Starting with the first proposal for the realization of a Superfluid-Mott insulator quantum phase transition for ultracold atoms in an optical lattice, an extensive study of the Hubbard models for bosons/fermions and the tunability of its parameters via external fields has followed. Special focus was on the use of cold atoms/molecules for the implementation of atomic quantum simulators for complex many-body systems. The basic idea behind these quantum simulators is the design of a many-body system with cold gases, where the dynamical and thermodynamic properties are governed by a Hamiltonian capturing the essential features of a poorly understood phenomena in solid state physics. Thus, the study of the atomic systems allows for the simulation of the solid state system in a well-controlled environment. Recent progress in this direction are the realization of atomic quantum simulators for exotic quantum phases, and high-temperature superconductivity. The realization of quantum simulators in cold gases relies on the possibility for driving the system with strong interactions. Here, hetronuclear molecules of alkali atoms offer an method for the implementation and study of systems with strong interactions. These molecules are characterized by a permanent electric dipole which can give rise to long-range dipole-dipole interactions driven by external electric fields. In combination with reduced dimensions, it has been recently shown that such polar molecules allows for the realization of self-assembled crystalline structures, while in the presence of an optical lattice a toolbox for spin models is has been proposed. The central objective in this individual project is the complete understanding on the control and tunability of many- body systems composed of hetronuclear molecules with long-range dipole-dipole interactions. In particular, this includes the derivation of Hubbard models in the presence of an optical lattice and the understanding of dynamical and ground state properties. It has been recently shown that polar molecules offer the possibility for the realization of systems with strong three-body interactions. Such three-body interactions are known to give rise to topological phases which play an important role for topological quantum computation; the most prominent example beeing the Pfaffian state, which is the exact ground state of an electron gas with three-body interation in a magnetic field. The prospects of polar molecules for the realization of a topological phase with non-abelian anyons will be analyzed.